Monday, January 27, 2020
Character Analysis: Theory Of Personality Development
Character Analysis: Theory Of Personality Development In the analysis of the star character Rachel in the 1968 movie Rachel Rachel by Paul Newman, I have used the Theory of Personality Development by Freud Sigmund (1856-1939). Sigmund developed this theory about psychoanalysis from his works on patients with mental problems several years back. In this theory, Freud Sigmund believed that allthe spheres ofsomeonespersonality were in one way or another determined by the sex of the person and aggression.Sigmund believed that other factors that shapedsomeones character also developed during this period of personality development which in totality determined the adults personality and how well they relate with the world. According to Freud Sigmund the three elements that make the personality are the Id, the ego and the superego. The ID is the part we are born with and is the part of us that wants us to be comfortable. For instance children will cry when they are hungry until they are fed in complete disregard of whether there is food or not or even whether the person attending to them is busy or not. As we have observed around us, a child will always cry until what they want is done for them or given to them. The Ego is believed to develop in children from three years of age onwards. This part enables one to realize the realities of life. At this stage of development a child can very clearly understand the consequences of their actions. For instance they can understand that some unpleasing actions can make them to be punished or rewarded. Main Body: Analysis The Superego is the part that develops by the time a child reaches five years. Once the superego develops the cycle of personal development is completed and one attains a balanced personality. The superego is also known as the conscience because it helps us distinguish between wrong and right actions and it also defines for us the ethics and morals by which we live. The movie Rachel Rachel based on the novel Jest of God by Margaret Laurence is about a 35-year-old schoolteacher Rachel Cameron who is unmarried and is portrayed in the movie as feeling terrible that she has wasted her life. The Interprofessional education would also enable me to involve all the necessary stakeholders in cases of emergency so as to limit conflicts and ensure the delivery of quality health and social care. For instance, in case I will be faced with a similar situation as the drunken patient case, I would be able to reassure the patient and ensure that they have plenty of drip water added to their body, while ensuring that before I take any steps, I consult with other adult nurses and doctors. In addition, I would advocate for joint multi-disciplinary training so as to ensure increased harmony among the IP group members at the work place. Moreover, I would also ensure that there is a clearly distinct role defined for each IP team member so that each member contributes to the situation at hand. The role of effective communication would be key to the success of my career as an adult nurse. This is because; the service user and the nurses as well as the doctors would require knowing the progress of the patient as he is being treated. In the above case, after treating the patient, he will be moved to the recovery ward where he will be attended to by other nurses and health care givers. These health care givers will require knowing the progress report of the patient, which I would ensure that they have in good time. As an adult nurse, the value of communication is immeasurable The star character Rachel lives with her mother in an apartment that was once owned by her late father in New England. It is time for the summer holidays and Rachel is not excited like the other teachers about the vacation as she figures it will just be another holiday when she will be bored and she will have to put up with her demanding mother in the house. In the movie, another character Calla Mackie who happens to be Rachels best friend,a lesbian and a fellow teacherpersuades and invites Rachel to attend a religious meeting with her. Rachel is convinced into attending the meeting and while there she is touched by the sermon delivered by the guest preacher who is a young man. This incidence marks the beginning of a series of several other events which will convince Rachel to get out of the cocoon she was hiding in and live in the real world where she can freely express her emotions and desires. Calla also feeling touched by the sermon confesses her feelings for her best friend but she is turned down by Rachel who does not have lesbian tendencies. After the religious meeting and Rachel feeling that she can express her emotions and love to those she cares about she gets involved in a short lived sexual relationship with their old family friend Nick Kazlik who was back in town to visit his folks. Rachel then has her first sexual relationship with Nick;she falls in lovewith him and starts thinking of a future with Nickmistaking the lust they have for one another for love. Nick on the other hand on noticing that Rachel is treating their relationship more seriously than it ought to be treated ends the fling because to him it was just a casual affair. Shortly after Rachel suspects that she might have fallen pregnant and this really makes her happy as she imagines having a baby of her own.Rachel therefore plans to relocate elsewhere to a place where she can raise her child now that her relationship with Nick is short-lived. Her best friend Calla helps her get another teaching job in Oregon but Rachel soon finds out that she is not pregnant but has a benign cyst. A surgery is organized and after having the cyst removed Rachel still decides to move away with her mother to Oregon and even though she is feeling alone and empty because of the loss of the man she loved and her supposed baby, she has a strong will to continue with her life. Rachels Experience Rachel Rachel is a very moving romance, classic and drama themed movie that shows the loneliness and existence of some ladies in real life where someone does not get what they have always wanted or where life seems so unfair to someone. The problem could be in our personalities where we have internal battles within us over what we want and what society or everyone else will say about us. There were several ideologies that the students discussed in low tones relating to the behavior of these students. However, this was only qualified by the fact that the medical profession students liked discussing their peers conduct and professional ethics. In this book, I learnt that Rachel had issues with other students conduct which frequently extended to the rest of the other peers both at school and at home. I concurred with critics that she often exhibited this trend. The rest of the team members agreed that the time limit of working in groups could not be construed to mean that medical students were often too pervasive. The setting of the group work was more controlled, thus limiting the results of the findings. It was agreed within my group that the real picture could be depicted in the work place though with limited variations. This was the case with the attitude of the medical students towards other medical students as well as the other students in general. The multi-disci plinary team meeting gave me insights and adequate experience in relation to the kind of communication among different professional team members. They were constantly evaluating her work which sounded kind of uneasy for Rachel. Striking a balance In emotionally sound persons, the ego normally comes out as the strongest element of personality taking care of both the Id and the superego. When these three elements are balanced someone is able to survive and exist well without taking undue advantage of others. Unfortunately not all of us can have the ego coming out stronger than our Ids and superegos. For some the Id is stronger and such a person will be self-centered and concerned only with their wellbeing and if the superego also happens to be stronger such a person can be too hard on themselves, have judgmental tendencies and relating with others would be extremely difficult for them. Like mentioned earlier the three elements are driven by sex and aggression. Sex which Freud calls the Eros stands for our desire to reproduce and live. Aggression on the other hand represents our need to acquire more wealth and protect our lives. According to Freudstheory, our ego therefore has so many tasks. It is charged with the duty of checking that everything is balanced, it deals with lifes challenges and ensures that our actions do not hurt those we care about and all this is done by employing ego defense mechanisms like: Denial- where we pretend that a problem does not exist. Suppression- where we consciously block out some thoughts from our minds especially thoughts that can hurt our feelings. Regression- where we can go back to decisions we had made earlier on. Rationalization- where we come up with logical explanations to problems or difficult situations instead of admitting the truth. Projection- where we put behaviors that are unpleasing on other people. Consequently, after looking at the storyline of the movie briefly and having explained the theory of Personality Development of the psyche by Freud Sigmund, we can say that Rachel the lead character in the movie had a personality problem. This is evident in several ways: First at 35 years of age, Rachel was still a single woman never married before and still a virgin. This shows that Rachels ego could probably be weaker than the other two elements of her personality because in Freuds explanation there reaches a point in life when every human being of reproductive age would like to procreate and have offspring of their own. And that is why when Rachel suspects that she is pregnant and her belly starts swelling she is so excited. Even though she could have ended up being a single mother she does not seem bothered at all. All that seemed to pre occupy her mind was the fact that she would have her own baby finally. This shows that Rachels super ego couldbe much stronger than her ego and her Id and that is why she was a virgin till late into her life. Secondly, Rachel looks like she has a personality development problem because she had not known who she was or what she wanted in her life before she and her friend Calla attended the crusade. It is while at the crusade that Rachel decides to have a free spirit. Rachel looks like she was hiding in some shell and it was the young preacher who helped her get out of it after which she had a sexual relationship with Nick. In this case we conclude that it is Rachels superego which was dominant once again because her morals were probably too uptight that she could not have sex before marriage. I also learnt that adult nurses should learn to downplay their differences for the common good of their patients. I also learnt that the power and authority held by students in their past affected the IP collaboration. Critics subsequently felt beaten at it. However, this has changed owing to the modern reorganization of the healthcare delivery. I learnt that other team members have now been given a chance to take lead roles in the delivery of quality health and social care. This kind of delegation was necessary due to the busy schedule of the doctors. This had to be communicated effectively within the Interprofessional teams. Nurses have been empowered and can now play a vital role which was traditionally reserved for lead doctors in the health care centers. IP working has therefore made nurses more powerful and authoritative thus providing them with ardent experience to further their careers. Rachel also does not seem to enjoy her life. Schools have closed and people are happy to be going on vacation but Rachel on the other hand is just there not excited about the holidays like everyone else. Rachel was more of an outgoing kind of person than any other character in the movie. In fact, the movie depicts Rachel as aggressive lass who not only care about her own affairs and her state of being but also the state of others. It is indeed appalling to learn that she attempts to repair the bad relationship that others have been nurturing all this while. It should be remembered that Rachels earlier background is one to reckon. I acknowledge the fact that working together as a team is integral to the success of my career. There are many times when I will have to consult various health and social care practitioners to effectively treat or deal with complications that may arise during treatment. Likewise, such professional team members may require my help in dealing with social, phys ical and mental health problems. I also appreciate the fact that effective communication within the IP teams is key since no professional staff within the health and social care can work in isolation. Professional health and social team members should attend the same training session so as to improve their IP team collaboration. Her character is mostly confused to be that of a person who is very strict and stern with all aspects of her life. This indeed helps to illuminate on the kind of character that we expect her to have. The issue again could be that her superego dominates over the other elements of her personality so much that Rachel is uptight and her conscience cannot allow her to indulge in activities that are fun even during vacation. Rachel does not seem to make decisions or to be in total control of her life. When she gets invited by Calla to attend a revival meeting Rachel goes just to please her best friend not that she really cared what was going to happen at the meeting. Fortunately for Rachel, it is a time she gets to discover herself and start doing things that other normal adults do without feeling guilty about anything. She even gets to fall in love for someone something she had never done all her entire life. The best thing is that the movie ends when Rachel seems like she is beginning to have a grip of her life and that her own life is beginning to bring meaning to her and excite her as well. Hopefully she found the love of her life where they relocated to. In the movie Rachel Rachel, several people are struggling with personality issues. The theory by Freud has helped us to study an individuals character and to be able to draw a conclusion concerning the level of development of the Id,ego and superego. My Experience During my internship at the general ward as a practicing nurse to be, I was able to experience teamwork conflicts. This experience played well during the conference, thus enabling me to learn more from a practical approach. I was also able to share my experience with the other IP team members. I also learnt important aspects of IP communication and working that are integral to the success of IP collaboration. These include, not using jargons, listening whenever other team members are talking, questioning assumptions sensibly, promoting the rights and dignity of IP team members. There are certain terms that adult nurses will use which cause confusion and ambiguity, thus making others who assume the meaning of jargons to error. On the other hand, I would also learn to resolve ethical issues within my IP team. Certain ethical issues are bound to affect the IP collaboration within my working teams. I would therefore respect other IP team members ethical standing and approach any indifference with a voice of reason in a bid to drive sense into the team members understanding. Indeed, most of the team members agreed to the fact that discrimination was indeed a shared concern. During my internship, I watched a patient walk in with his girlfriend. It was evident that from the start, the doctor on call could not give effective direction and as if this was not enough, the doctor could not take a leadership role and advice the girlfriend to calm down. I believe as a future adult nurse, I would have tackled this situation with more wit. My first step would have been to take control of the situation and give the patient options with the benefits of each. This would have given more insight to the girlfriend and reduce the conflict. I would also initiate active communication with the rest of the adult nurses for consultation in privacy. Interprofessional education would have enabled me to effectively initiate communication with my team members, thus taking control of the situation in good time. As an adult nurse, every patients condition is important since my core value is to preserve life. I have also learnt the effectiveness of working in partnership with the patients through listening and responding to their concerns. I have also learnt that it would be important to consult with the patients regarding their treatment and care before commencing such. While reflecting this experience, I shall work closely with my team members as an adult nurse and constantly communicate with the relevant authorities and IP team members for quality health and social care delivery. I truly acknowledge that I would need a succinct understanding of teamwork and modern approaches towards health and social solutions. As a future adult nurse, I will always ensure that I initiate effective communication with the rest of my IP team members so as to work together for the common good of the patients. The experience that I learnt was indeed useful as it would enable me to effectively become a successful adult nurse who would stand out from the rest. The person-centred approach was particularly imperative in ensuring that I am able to understand the genesis of multi-disciplinary teamwork. I indeed acknowledge that issues relating to patient care should be approached with interprofessional teamwork so that each medical practitioner offers advice in his or her area of professional knowledge while ensuring that they work as a team. My experience at the multi-disciplinary conference would enable me to become a successful adult nurse who values teamwork and professional collaboration. This conference has also enabled me to have a clear picture of what medical professionals go through and what can be done to avert such challenges. I now feel adequately capable of tacking these challenges that my career as an adult nurse will provide. I have also learnt to take into account the views of other people when making important decisions. Indeed issues of race, gender, class and sexuality among others should not affect multi-disciplinary teamwork. Cultural and social differences should not be construed as effective barriers to IP teamwork. As a future adult nurse, the conference was a brainstorming session which expanded my experience. I was also able to learn that certain general terms used by patients to refer to their illness may indeed cause great confusion among professional health and social care practitioners. These are referred to as stereotypes. In such a situation, the health and social professional practitioner should consult the other members of his or her IP group or team so as to come up with the proper interpretation thus limit errors in the treatment of the patients condition. Synergy model of nursing supports this argument and calls for more consultation in the treatment of the patient. The group discussion on IP education enabled me to visualize the reality between theory and practice. The patient-centred perspective was clearly illuminated by the patients voice presentation. The exclusion of IP working has been seen in collaborative treatment. Decisions made by individual inexperienced doctors have been tragic. The case of Victoria Climbie and Baby Peter can best illuminate this when Baby Tiffany passed on due to negligence. Findings from this tragic situation enabled doctors and nurses to establish a framework that saw the prevention of such situations. It was agreed that IP teams would not be able to prevent the occurrence of every tragic incidence. Some would indeed be inevitable. Hence, I was able to learn the value of communication and collaboration in the build up to my career as an adult nurse. Calla also seems to be struggling with her sexuality. She is a lesbian but before the Christian revival she cannot confess her feelings to Rachel because of the societys views on the subject but after the meeting everyone is feeling like they can open up and that is when she openly tells Rachel of her feelings even though she is turned down. Conclusion In conclusion, we can say that the three elements that make up someones personality are very crucial in molding the character of someone and greatly influence what someone turns into when they are adults. We should therefore strive to help the Id, ego and superego to grow well and the ego especially should be nurtured to surpass the other two in dominance, because as research has shown for a sound thinking adult, the ego should dominate. As much as this may not be achieved in all people, those who hang around children should motivate them so that they do not have problems in adulthood in identity or of self-esteem like was the case of Rachel and Calla. Rachels super-ego is something to reckon with though at times she seems to be not confident enough to tackle the situation at hand. She stands out as a she-wolf, always seizing any opportunity that comes her way.
Sunday, January 19, 2020
Balance Sheet and Cookie Creations Essay
CCC1Natalie Koebel spent much of her childhood learning the art of cookie-making from her grandmother. They passed many happy hours mastering every type of cookie imaginable and later creating new recipes that were both healthy and delicious. Now at the start of her second year in college, Natalie is investigating various possibilities for starting her own business as part of the requirements of the entrepreneurship program in which she is enrolled. A long-time friend insists that Natalie has to somehow include cookies in her business plan. After a series of brainstorming sessions, Natalie settles on the idea of operating a cookie-making school. She will start on a part-time basis and offer her services in peopleââ¬â¢s homes. Now that she has started thinking about it, the possibilities seem endless. During the fall, she will concentrate on holiday cookies. She will offer individual lessons and group sessions (which will probably be more entertainment than education for the participants). Natalie also decides to include children in her target market. The first difficult decision is coming up with the perfect name for her business. In the end, she settles on ââ¬Å"Cookie Creationsâ⬠and then moves on to more important issues. Instructions (a)What form of business organizationââ¬âproprietorship, partnership, or corporationââ¬â do you recommend that Natalie use for her business? Discuss the benefits and weaknesses of each form and give the reasons for your choice. (b)Will Natalie need accounting information? If yes, what information will she need and why? How often will she need this information? (c)Identify specific asset, liability, and equity accounts that Cookie Creations will likely use to record its business transactions. (d)Should Natalie open a separate bank account for the business? Why or why not? CCC2After researching the different forms of business organization, Natalie Koebel decides to operate ââ¬Å"Cookie Creationsâ⬠as a corporation. She then starts the process of getting the business running. In November 2014, the following activities take place. Nov.8Natalie cashes her government bonds and receives $520, which she deposits in her personal bank account. 8She opens a bank account under the name ââ¬Å"Cookie Creationsâ⬠and transfers $500 from her personal account to the new account in exchange for ordinary shares. 11Natalie pays $65 to have advertising brochures and posters printed. She plans to distribute these as opportunities arise. (Hint: Use Advertising Expense.) 13She buys baking supplies, such as flour, sugar, butter, and chocolate chips, for $125 cash. 14Natalie starts to gather some baking equipment to take with her when teaching the cookie classes. She has an excellent top-of-the-line food processor and mixer that originally cost her $750. Natalie decides to start using it only in her new business. She estimates that the equipment is currently worth $300. She invests the equipment in the business in exchange for ordinary shares. 16Natalie realizes that her initial cash investment is not enough. Her grandmother lends her $2,000 cash, for which Natalie signs a note payable in the name of the business. Natalie deposits the money in the business bank account. (Hint: The note does not have to be repaid for 24 months. As a result, the notes payable should be reported in the accounts as the last liability and also on the statement of financial position as a non-current liability.) 17She buys more baking equipment for $900 cash. 20She teaches her first class and collects $125 cash. 25Natalie books a second class for December 4 for $150. She receives $30 cash in advance as a down payment. 30Natalie pays $1,320 for a one-year insurance policy that will expire on December 1, 2015. Instructions (a)Prepare journal entries to record the November transactions. (b)Post the journal entries to general ledger accounts. (c)Prepare a trial balance at November 30. CCC3It is the end of November and Natalie has been in touch with her grandmother. Her grandmother asked Natalie how well things went in her first month of business. Natalie, too, would like to know if the company has been profitable or not during November. Natalie realizes that in order to determine Cookie Creationsââ¬â¢ income, she must first make adjustments. Natalie puts together the following additional information. 1.A count reveals that $35 of baking supplies were used during November. 2.Natalie estimates that all of her baking equipment will have a useful life of 5 years or 60 months and no salvage value. (Assume Natalie decides to record a full monthââ¬â¢s worth of depreciation, regardless of when the equipment was obtained by the business.) 3.Natalieââ¬â¢s grandmother has decided to charge interest of 6% on the note payable extended on November 16. The loan plus interest is to be repaid in 24 months. (Assume that half a month of interest accrued during November.) 4.On November 30, a friend of Natalieââ¬â¢s asks her to teach a class at the neighborhood school. Natalie agrees and teaches a group of 35 first-grade students how to make Santa Claus cookies. The next day, Natalie prepares an invoice for $300 and leaves it with the school principal. The principal says that he will pass the invoice along to the head office, and it will be paid sometime in December. 5.Natalie receives a utilities bill for $45. The bill is for utilities consumed by Natalieââ¬â¢s business during November and is due December 15. Instructions Using the information that you have gathered through Chapter 2, and based on the new information above, do the following. (a)Prepare and post the adjusting journal entries. (b)Prepare an adjusted trial balance. (c)Using the adjusted trial balance, calculate Cookie Creationsââ¬â¢ net income or net loss for the month of November. Do not prepare an income statement. CCC4Natalie had a very busy December. At the end of the month, after journalizing and posting the December transactions and adjusting entries, Natalie prepared the following adjusted trial balance.
Saturday, January 11, 2020
Gay Marriage â⬠persuasive essa Essay
Everyone dreams of one day becoming married and having a family, and most of the time this dream is fulfilled, that is, if they are straight. As each year passes by, there seems to be an increasing number of gay couples that aspire to become married. Even though gay marriage is becoming an extremely popular topic, people begin to realize that it does either one of two things (unless they are apathetic on the issue); gay marriage puts a strain on the outlook of society or it opens up many opportunities for the gay couples themselves. Bishops and other religious figures of the church feel that gay marriage is appalling, and should be abolished from society. The article mentioned in the National Catholic Reporter, ââ¬Å"Bishops Warn of Dangers to Marriage,â⬠it is revealed that bishops believe same-sex marriage is ââ¬Å"one of the most troubling developments in contemporary culture. â⬠(Roberts 2). According to text, the first command given to Adam and Eve was ââ¬Å"be fertile and multiplyâ⬠(National Catholic Reporter). The culture of America is perceived to be a family consisting of one mother, one father, and however many kids are desired; however, if same-sex marriage were to be allowed, it would diminish all natural aspects of our culture. Bishops of the Church believe that it is ââ¬Å"in the offspringâ⬠where ââ¬Å"married love finds its crowning gloryâ⬠(Roberts 2). To reiterate into other words, the greatest achievement of marriage is found in the child created by that man and woman. Though one may not believe in Christ or anything to do with religion, the Church is against gay marriage because they believe that men and women were created to produce fertile offspring, a task impossible for gay couples. Most people against gay marriage agree that it can nit and should not be permitted because the female necessitates a dominant male figure to protect her. In the Weekly Standard, ââ¬Å"The Worst Thing About Gay Marriage,â⬠teaches us that ââ¬Å"marriage is a part of a kinship systemâ⬠and kinship depends on the ââ¬Å"protection, organization, and often exploitation of female sexuality vis-i -vis maleâ⬠(Schulman 3). Women and children have suffered and will continue to suffer from being over-protected and controlled, but the consequence of under-protection and indifference will be immeasurably worse (Schulman 4). It is understandable that over-protected women feel effected by the matter, but at least they are guaranteed someone to be there when in danger, while on the other hand, under-protected women are far more vulnerable. We realize that marriage is above all, ââ¬Å"concerned with female sexualityâ⬠and that kinship depends on the protection of women from ââ¬Å"rape, degradation, and concubinageâ⬠(Schulman 2). This is why marriage between and man and woman has been necessary in virtually every society ever known (Schulman 2). In other words, it is a priority to attain a male-female relationship in order to create the safest possible environment for the female. Same-sex marriage cannot offer the appropriate assurance for the femaleââ¬â¢s safety due to the lack of a male figure designed to protect. Often, marriage leads to the desire for kids, and adoption is the only way that desire can be fulfilled for homosexual couples, which can tremendously affect the childââ¬â¢s path in being raised as a normal kid. Psychological Reports, as mentioned in Paul Cameron and Ellen C. Perrinââ¬â¢s ââ¬Å"Insight on the News,â⬠tested 52 families and ninety-two percent of the children in those families ââ¬Å"mentioned one or more ââ¬Ëproblems'â⬠which included ââ¬Å"hyper sexuality, instability, molestation, and domestic violenceâ⬠(Cameron and Perrin 2). A great majority of kids growing up in a home with homosexual parents find it to do so because they are lacking either a mother or a father, who are both vital participants in childhood. On one Insight on the News interview, a nine year old girl growing up with gay parents reveals her feelings of discomfort at home and how ââ¬Å"all of a sudden [she] felt like a different person because [her] mom was a lesbianâ⬠(Cameron and Perrin 2). Every marriage between a man and a woman is capable of giving any child that they create or adopt a mother and a father, which is the opposite for gay couples (Gallagher 109). Gay adoption can be a negative part of a childââ¬â¢s life because it is usually found to be hard on the child growing up, due to the fact that they lack either a mother or father figure. While a high number of individuals are against gay marriage, there are also the ones who believe everyone should be granted equal rights. America has always been set on the idea of equality for all because ââ¬Å"our fathers brought forth this continent, a new nation, conceived in liberty and dedicated to the proposition that all mean are created equalâ⬠(Lincoln). Sadly this nation has taken a long time to live up to that promise of equality (Olson 2). Society encourages marriage because of the commitment not only to each other but also to their families which creates a union between the two; however, society doesnââ¬â¢t seem to accept this same idea for homosexuals. If same-sex marriage were to be legalized, it would beâ⬠recognition of basic American principlesâ⬠as it would ââ¬Å"represent our nationââ¬â¢s commitment to equal rightsâ⬠(Olson 2). Historical figures from Americaââ¬â¢s history to now have always promised equal rights for everyone, yet hays seem to continue to be discriminated against. The basis of America has always been freedom and equality for all, discarding all of homosexuals who are granted limited marriage rights. As mentioned earlier, marriage naturally leads to the aspiration for having children, and adoption is the only way for homosexual couples to do so, which in the end is a positive side of gay marriage because it opens up the doors for a child in need of a loving home. As stated in The First Post, there are never enough parents to adopt out all of the children in foster care homes, so ââ¬Å"whether the family is gay or straightâ⬠it is usually ââ¬Å"better than the foster-care systemâ⬠(1). Gay adoption can open up many opportunities for the children trapped in the foster-care system because they will be showed the love and other vital aspects of childhood that would never be expressed in foster-care. A new twenty five year study, as mentioned in the Atlanta Journal Constitution, shows that children of gay parents showed higher ratings than their peers in ââ¬Å"social, academic, and overall competenceâ⬠and ââ¬Å"lower in aggressive behaviorâ⬠(Manford and Chrisler 1). Children of gay parents are overall better off than children with heterosexual divorced parents because they have two full-time parental figures that are always there for them (Manford and Chrisler 1). Children of gay parents demonstrate a more confident statue mainly because they are supported by two parents, whereas an increasing majority of children have divorced parents. A positive idea of gay marriage is gay adoption because it creates a positive outlook for kids who thought they would never have a chance in the foster-care system. Many people against gay marriage believe that it ruins the prosperity of heterosexual marriage, when in reality they just search for any possible reason to make gay marriage appear as an unspeakable issue. In his editorial found on About. com, Tom Head explains that in the countries that have legalized same-sex marriage, the rate of heterosexual marriage has either ââ¬Å"gone up, remained stable, or declined consistent with other countries in the region that do not recognize same-sex marriageâ⬠(Head 1). In other words, gay marriage has absolutely no affect on heterosexual marriage as shown in the statistics of Tom Headââ¬â¢s editorial, because the rates of heterosexual marriages stay the same as they would if gay couples didnââ¬â¢t exist. Found on the Daily Paul Liberty Forum, Bruce Hausknecht admits that ââ¬Å"there is no aspect of family lifeâ⬠that is impacted by a homosexual agenda that is ââ¬Å"fundamentally at odds with the biblical view of marriage and sexualityâ⬠(Hausknecht 1). To recap, there is no family containing heterosexual parents that is impacted by the views of gay marriage; gay marriage isnââ¬â¢t harming anyone. An optimistic outlook on gay marriage is the idea of it harming nobody, especially heterosexual marriages, which is a main target in trying to destroy gay marriage. Gay marriage has always been and will continue to be a highly controversial issue among the believers and non-believers. There will always be those people who oppose gay marriage, accepting that male-female marriage was generated to produce fertile offspring. There will also be those who want equality for all. These two beliefs are the basis of the controversy of the issue, and it will continue to be until gay marriage is accepted in society.
Friday, January 3, 2020
The Application Behind Options Pricing Models - Free Essay Example
Sample details Pages: 17 Words: 5096 Downloads: 8 Date added: 2017/06/26 Category Finance Essay Type Research paper Did you like this example? Derivatives are financial products whose values are derived from one or more underlying asset or financial instrument. In todayà ¢Ã¢â ¬Ã¢â ¢s world derivative products are being used extensively as a means of managing financial risks. These products are used to transfer risk from one party who cannot take that risk to counterparty who has the appetite to assume that risk .Some types of derivatives called Exchange Traded Derivatives are traded publicly on exchanges while others called Over the Counter Derivatives are traded between private parties in private transactions. Donââ¬â¢t waste time! Our writers will create an original "The Application Behind Options Pricing Models" essay for you Create order Options are a kind of derivative product which gives the holder the right but not the obligation to buy or sell an asset at a price called Exercise price on or before a certain date called the Exercise Date. They are traded publicly over exchanges around the world. The underlying asset can range from foreign exchange, futures, commodities, etc. Apart for its use as hedging instruments it is also used by speculators and arbitrageurs in the markets. This report aims to provide a basic understanding into the various options pricing models which are used to calculate the theoretical fair value of an option. The report also aims to give technical insights on using those pricing models with reference to the option pricing model developed by the author in Microsoft Excel using Visual Basic Programming (VBA). The Excel application developed by the author can be used by traders, speculators or anyone participating in the options markets to determine the theoretical fair price of an o ption and then compare it with the actual option price to determine whether the option is overpriced or underpriced. This will enable the user take appropriate positions in the market. The author has developed the application so that one can price an option according to three popularly used models i.e. Binomial Model, Black Scholes Model and Monte Carlo Simulation Model. The Author has also provided for a functionality which automatically downloads latest stock price data of stocks in the Dow Jones Index and gives user option to select the stock to price, automatically loading the stock price in the model. Chapter 1-Introduction 1.1-Objectives In finance, the wide number of potential outcomes adds uncertainty and risk in estimating the future value of financial instruments. Monte Carlo simulation (MCS) is one technique that helps to reduce the uncertainty involved in estimating future outcomes. This simulation method can be used to evaluate the accuracy and performance of other models. Apart from MCS , Black Scholes and Binomial Model are the other commonly used options pricing models in the financial markets. Aim of the Project: 1.Ãâà Ãâà Ãâà Ãâà Ãâà To research the efficiency of the Monte Carlo Simulation models when applied to pricing derivative options. 2.Ãâà Ãâà Ãâà Ãâà Ãâà To compare the Monte Carlo Simulation technique with other options pricing derivative techniques like Binomial Pricing Model and Black Scholes Model. 3.Ãâà Ãâà Ãâà Ãâà Ãâà To Develop an Excel Based Application which prices options using Monte Carlo Simulations, Binomial Model, Black Scholes Models also providing additional information like volatility, options Greeks which are useful for options traders and structurers. 1.2-Scope There are various options pricing models that have been developed over time some of which focus on certain specific types of derivatives. This project is not intended to be a comprehensive guide to all the options pricing models. It is rather a means of understanding the options pricing models most commonly used in the market. Equipped with this knowledge one should be able to understand the other pricing models available which are not within the scope of this report. The basic scope of this report is to get a basic overview of the options terminology and basic pricing models which may serves as a base for further academic research in detail. 1.3-Report Organisation Chapter 2-Literature Review 2.1-Introduction to Derivatives In the financial markets there are various types of risk faced by market players, corporations etc. The ability of a firm to get low cost financing can be hindered because of the highly volatile interest rates. Exporters have to hedge their currency risks as their profit strongly depends on how undervalued their currency is. Companies may be needed a commodity which is a vital input in the future but uncertainty in the future price might affect its profitability. These are some of the risks that can be mitigated by use of derivatives. They have been around for a long time but its importance and use has been growing exponentially in the past few decades because of the rapid industrialisation and maturing of the world financial markets. As the name suggests Derivatives are products that derive their value from an underlying asset or commodity. The underlying assets can be real assets like commodities, metals, etc. As well as financial assets such as bonds, stocks, stock index, fut ures, etc. 2.2-Forwards and Futures An asset can be sold today as per the decided price or later in the future according to a price which is decided today. Forward contracts are used for the latter contracts. They are contracts between two parties who decide to trade an asset based on a price decided today, the transfer of which will take place sometime in the future. One of the parties is which agrees to take the delivery of the underlying asset in the future for a certain specified price is called the long. The other party which agrees to make the delivery of the asset in the future at the agreed price is called the short. Neither party pays any amount to get into the contract but the contract is binding and to cancel the contract the party has to enter into an offsetting contract with the same counterparty or it may also assume an offsetting contract with another counterparty in which case it assumes and additional counterparty risk. These forward contracts are mostly done in private transactions and hence its terms are also customised to the needs of both the counterparties. In Most of the cases the asset to be traded is actually delivered by the Short Party to the Long Party. Thus forward contracts are usually settled by delivery. image1.gif Figure : Payoffs from Forward Contracts As it can be seen in the payoff diagram about the Long will profit only if the price of underlying increases whereas if the price of the underlying decreases the long will be forced to buy at a higher rate than what is available in the market. As far as the Short is concerned it will profit from the transaction only if the price of the underlying decreases in the future as if the price increases it will be forced to sell at a lower price than it could have sold the underlying at current market price. Thus this is a zero sum game; one partyà ¢Ã¢â ¬Ã¢â ¢s gain is another partyà ¢Ã¢â ¬Ã¢â ¢s loss. Forward contracts are mostly used for mitigation of risk i.e. hedging rather than for speculati on purposes. A Common example of forward contracts is a corporation which is due to receive payments in Pounds 2 months later. It is exposed to fluctuations in the currency market and hence sells pounds 2 months in the future thereby assuming a short position and mitigating its risk by locking an exchange risk at which it can sell pounds in the future. As opposed a corporation which has to make payment in pounds in 2 months will assume a long position and enter into a forward contract to buy pounds 2 months later at a price agreed upon today there by eliminating the uncertainty factor and hedging its currency risk. Some of the problems faced in the forwards markets are that though the contracts being private with the terms customised according to the counterparties offer a lot of flexibility, but it makes them non standardised and difficult to trade. Also a large part of the transaction is risky because of counterparty risk. If one party does not honour the terms of the contract the other party goes in losses. Futures are similar to forward contracts but remove some drawbacks of forward contracts like illiquidity, counterparty risk. The only difference in futures contracts is that the terms of the contract such as the price at which the underlying asset will be delivered, how much of the asset has to be delivered, date of delivery, etc are the same for all contracts i.e. standardised. They are usually traded on public exchanges in which case the risk of the other party defaulting is highly reduced as the exchange is always the counterparty for every trade. For example if one party wants to assume a long position the short position will always be assumed by the exchange and vice versa which highly reduces the problem that the other party will not honour the terms of the contract. Futures Forwards Trade on an organised exchange OTC in Nature Standardised and hence liquid Customised hence less liquid Margin Payment Required No Initia l Margin Payment Required Daily Settlement Settlement at End of Day Table 1-Distinction between Futures and Forwards 2.3-Options Options are very much different from the other derivative products like forwards and futures. In forwards and futures once the parties enter in the agreement they are obliged to honour the terms of the contract or complete the transaction as per recorded in the contract irrespective of whether they are in profit in loss. Whereas in options contracts both the parties decide to trade a particular asset sometime in the future at a price which they decide during the initiation of the contract. The difference lies in the fact that the buyer of option i.e. Long party has to pay an initial sum of money called the premium in order to gain the privilege of having a right but no the obligation to exercise the contract. While the party selling the option i.e. Short receives this premium for the risk it takes. Thus the Long party will only exercise the option if the transaction is profitable to him according to the market rates prevalent at the time of expiration of the contract Call Option : A Call Option Gives the buyer a right but not the obligation to buy an asset at a certain price at or before sometime in the future. The seller will receive a form of payment called premium and will still have the obligation to exercise the contract if the buyer of the call option chooses to exercise it. Consider the following at the Exercise Date of the option: S= Current Stock Price X=Exercise Price If SX: Call Option Holder will exercise the option as he is entitled to buy the asset at a lower price than the current market price. The contract is said to be In the Money in this case. If SX: Call Option Holder will not exercise the option as he is able to buy the same asset at a lower price in the global markets. The contract is said to be Out of Money in this case. If S=X: He may or may not opt to exercise the option. Also an Option price is given by: Option Price Value= Time Value + Intrinsic Value Where Intrinsic Value= Max [0, (S-X)] 525px-Payoff_call_option_svg.png Figure -Call Option Payoff Diagram Put Option: A Put option gives its buyer the right but not the obligation to sell a certain asset at some date in the future known as the exercise date at a pre specified price called Exercise Price. Just like in the Call Option the buyer of the contract has the right whereas the seller of the contract has the obligation to buy the asset at the exercise price should the holder of the option decides to exercise it. Consider the following at the Exercise Date of the option: S= Current Stock Price X=Exercise Price If SX : The Put option holder will exercise his option as he is able to sell the underlying assets at a price higher than what he would have got if he would have sold at current market prices. Such an option at expiration is said to be In the Money. If SX: Put option holder will not exercise his option as he will be able to sell the same asset at a higher party if he sells them in the market. In this case put option holderà ¢Ã¢â ¬Ã¢â ¢s loss is only limited to the amount initially he paid to seller of put option as premium. Such an option at expiration is said to be Out Of Money. 525px-Payoff_put_option_svg.png Figure -Put Option Payoff Diagram 2.4: Option Greeks The Price of an option can be influenced by many factors. These factors help the options traders determine the positions they ought to take and hence their profitability. It is therefore of utmost importance to know about the à ¢Ã¢â ¬Ã
âGreeksà ¢Ã¢â ¬? which are a set of risk measures which determine to what extent is an option price dependent on changes in the underlying price, implied volatility and time value. Most commonly used by traders are four Greeks namely Delta, Theta, Vega and Gamma. CallÃâ Options Increase in Volatility Decrease in Volatility Increase in Time to Expiration Decrease in Time to Expiration Increase in the Underlying Decrease in the Underlying Long + + + Short + + + Figure : Factors Affecting Long and Short Call Options Price PutÃâ Options Increase in Volatility Decrease in Volatility Increase in Time to Expiration Decrease in Time to Expiration Increase in the Underlying Decrease in the Underlying Long + + + Short + + + Figure : Factors Affecting Long and Short Put Options Price As it can be seen from figure 4 an increase in volatility, increase in time to expiration and increase in price of the underlying will increase the value of the long call option. Whereas a decreased in volatility, decrease in time to expiration and decrease in price of the underlying will increase the value of short call option. Vega Theta Delta Gamma Measures Impact of a Change in Volatility Measures Impact of a Change in Time Remaining Measures Impact of a Change in the Price of Underlying Measures the Rate of Change of Delta Figure : The Major à ¢Ã¢â ¬Ã
âGreeksà ¢Ã¢â ¬? Delta: It can be considered as a value which measures the change in the price of an option i.e. premium paid buy option buyer, which results from the change in the price of the underlying asset (commodity, futures, etc.). For put options the value of delta ranges from -100 to 0 while for call options the value of the delta ranges from 0 -100. Since put premiums fall with an increase in the price of the underlying i.e. puts have a negative relationship to the underlying, puts have negative delta. The calls have a direct relationship with the price of the underlying and hence have a positive delta. Consider an example where the delta of an sugar call option is 0.5 and if the price of sugar increases by 10 cents then the premium for the all option will also increase by 5 cents (0.5 x 10). Gamma: The Greek called Gamma is dependent on the value of the earlier Greek discussed i.e. Delta. It is the rate of change of delta and also called the à ¢Ã¢â ¬Ã
âfirst derivative à ¢Ã¢â ¬Ã
âof delta. The value of gamma for a long call as well as a long put is always positive. This means that the value of delta will increase with the increase in the price of the underlying and value of delta will decrease with the decrease in the price of the underlying. The Value of Gamma for at the money options is highest and its values decrease as it goes out of money or in the money which can be seen by the figure below. Greeks_OTM-ATM-ITM.png Figure -Effect of Moneyness on the value of Greeks Theta: The third commonly used Greek theta is not much used but is an important theoretical concept. Theta measures the rate of decline of time-premium resulting from the passage of time. In simple terms, an option premium that is not intrinsic value will decline at an increasing rate as expiration nears. The Value of Theta like the other Greeks for at the money options is highest and its values decrease as it goes out of money or in the money which can be seen by the figure below. Vega: Vega, our fourth and final risk measure, quantifies risk exposure to implied volatility changes. Vega tells us approximately how much an option price will increase or decrease given an increase or decrease in the level of implied volatility. Option sellerà ¢Ã¢â ¬Ã¢â ¢s benefit from a fall in implied volatility, and its just the reverse for option buyers. The further an option goes in the money or out of money the smaller will be the value of Vega. Chapter 3- Option Pricing Models 3.1-Introduction In the financial world among all the products available derivatives are considered the most complex ones and hence the most difficult to price as well. Of course, some derivatives are far more difficult to price than others. Over the past decades researchers have come up with many numbers of options pricing models and they can be broadly categorised into three categories: Analytical Models Numeric Models Simulation Models The Simulation models refer to the mathematical method called Monte Carlo Simulation which has been named after a famous casino in Monaco on the French Rivera. The Motel Carlo Simulation was initially used to find a reasonable estimate of the probability of winning a game of pure chance. The method works by simulating the outcomes of a process by generating random numbers. In this process the accuracy of the approximation of the results is directly proportional to the number of replications and gives results that are more closer to analytically correct solution. Since the Monte Carlo simulation method requires the process to be run over and over again for sometimes thousands of times this process is quite heavy on the CPU and would require a faster computer for it to run effectively. Monte Carlo simulation can be used in all sorts of business applications whenever there is a source of uncertainty (such as future stock prices, interest rates, exchange rates, commodity prices, etc.). To illustrate the basic concepts, I will be focusing on pricing options, which are generally the most difficult types of Derivatives to value. Analytical Models: A Classic example of these kinds of models is the Black Scholes model which is one of the most widely and commonly used option pricing models used in the financial industry. They are the most elegant of the pricing methodologies. In the analytical approach one begins with assumptions about how the input variables of the model will behave and these assumptions are then converted into direct mathematical questions which give the desired result. These mathematical relationships are used as a means to establish a connection between the input variables (eg, Current Stock price, Exercise price etc.) and the output variable ( in this case the theoretical fair value of the option). The model that is developed as the end product using the analytical method takes the form of a formula or equation which connects the input to the output .This formula is often referred to as the à ¢Ã¢â ¬Ã
âsolution.à ¢Ã¢â ¬? The main advantage of using analytical models is the ease with which one can use them to produce a precise valuation. It has some disadvantages as well. First, it is difficult to derive the analytical models if one does not have the knowledge of advance calculus. Second, in certain cases it may not be feasible to use the analytical method of problem solving. Third, the models or equations derives using the analytical models and very much in flexible. That is they can be only applied to calculate the desired assumptions under the set of assumptions that were used initially to design the model. Figure :Categories of Option Pricing Models Option Pricing Models Simulation Models E.g. Monte Carlo Simulation Models Numeric Models E.g. Binomial Pricing Models Analytical Models E.g. Black Scholes Model Numeric Models: The second type of model is Numeric Models which are considered to be much more flexible than the earlier discussed analytical models. In these kind of models we again start with a set of assumptions on how the input variable behave but we employ an algorithmic way using a finite series of steps to arrive at the desired value rather than using an equation which relates the input to the output. Thus an approximate value of the desired output is derived rather than a precise value as in the case of analytical models. The advantages of numeric models are they are not so complex to build as compared to the analytical models and also do not require advanced knowledge of the stochastic calculus to build, understand and critically appreciate them. The second advantage lies in the dat they are much more flexible than the previously discussed analytical models. The assumptions made to build the model can be easily changed later to adapt to the new problem situations. The disadvantage tho ugh however lies in the fact that the degree of accuracy of the desired output value is directly proportional to the number of times one runs the models. This means to get a very hig degree of accuracy we would have to run the models and may have to make thousands of calculations. But this disadvantage is no longer valid in current world as rapid technological advances has increased the speed of the microprocessors rapidly and also reduced the cost which has made them more accessible. Simulation Models: The third category of options pricing models is the Simulation models. These models are less elegant than the analytical models and also not as fast as the earlier tow models we discussed. But their main advantage lies in the incredible flexibility which can be used to price very complex derivatives that depend on facts which cannot be modelled using either the analytical or the numerical valuation technique. Indeed, the future price of any financial asset can be simulated when it is expressed in the form of an expected value. In the simulation approach, we program a computer to à ¢Ã¢â ¬Ã
âsimulateà ¢Ã¢â ¬? observations on the random variable of interest. But also Care must be taken to ensure that the values that we simulate must be according to a type of distribution (Binomial, Exponential) and the other statistical parameters as each individual problem may demand. 3.2- Binomial Options Pricing Model In this section we will have a deeper understanding of the binomial option pricing model and also its application using VBA in the option pricing application that the author has developed. One Period Binomial Model: In a Binomial Model the stock price is allowed to either go up or down possibly at different rates. A Binomial Probability distribution is one in which there are two outcomes and states. This probability distribution governs the probability of the up and down movement of stock prices. Consider a stock with current stock price S on which options are available. The beginning of the period is today and referred to as time 0 and end of the period is 1. At time 1 the stock can take one of the two values. It can go up by a factor of u or go down by a factor of d. If the stock price goes up the stock price at time 1 will be uS and if stock price goes down stock price at time 1 will be dS. Therefore the intrinsic value of call option at expiration is : Cu= Max [0, uS-X] Cu= Max [0, dS-X] binomial model diagram.jpg Figure :One Period Binomial Model Let r be the risk free rate and we assume that investors can borrow and lend at the risk free rate. The aim of this model is to determine the fare theoretical value of an option which is them compared with its actual price in the market and which tells us whether the option is underpriced or overpriced. We develop the formula for option price C by constructing a risk free portfolio consisting of a mix of stocks and options. Consider a portfolio of h shares of stocks and a single written call. Let V denote the current value of the portfolio .V is given by V=hS-C. We can think of V as the amount of money we require to construct this portfolio. At Expiration the value of the portfolio can be given by Vu if the stock price goes up or Vd if the stock price goes down. Thus Vu = huS Cu Vd = hdS Cd We can think of Vu and Vd as the money that we will get back at expiration when we sell the portfolio. According to our earlier assumption we defined this portfolio as risk free which means regardless of the stock price going up or down the portfolio should give the same riskless return i.e. Vu= Vd huS c = hdS Cd Solving for h gives us h If the portfolios initial value is growing at the risk free rate its vale after one period at expiration will be V (1+r) = (hS à ¢Ã¢â ¬Ã¢â¬Å" C) (1+ r) = Vu = huS Cu On substituting the value of h and solving for the option value C we get: C = Where p is given by p= This is a very basic formula derivation for options price on which the other multi period models are based on which we will go through in the next section. Two Period Binomial Models: In the 2 period binomial models there are three time points as compared to two in the one period model. The option prices at expiration are given by: Cu2 = Max [0, u2S à ¢Ã¢â ¬Ã¢â¬Å" X] Cud = Max [0, udS X] Cd2=Max [0, d2S à ¢Ã¢â ¬Ã¢â¬Å" X] binomial model diagram.jpg binomial model diagram.jpg Figure : Two Period Binomial Model Using the same method as in the one period model we can obtain the following formulas: Cu = Cd = [ pCud + (1-p) Cd2 ] / [(1+r)] Therefore the call price at time zero can be found by calculating the weighted average of the two possible call prices in the next period i.e. C = The probability value of the stock price moving either way is determined using the volatility value of the stock where: U = e ^. v=volatility D= e ^. The value of p can also be derived by the assumption that over a period of time dT the underlying asset will yield the same profit as an riskless investment , so that if it is worth at S at time t, it will be S.e^(r.dT) at the time t+dT . Thus S.e^(r.dT) = (p.u.S + (1-p).d.S) and solving for p we get P= Thus we can say that the binomial pricing model is an iterative model that models the evolution of options price over a number of periods of time. Extending the Binomial Model to n Periods: We can extend the binomial option pricing model to any number of periods. As the number of time periods increase the option value also gets more closer to the actual precise value. We do assume that there are n periods remaining until expiry of the options and also that the option pays no dividends. clip_image012.jpg Figure Multi period Binomial Model Implementation in VBA: The author has implemented the multi period binomial model using Visual Basic for applications (VBA) in the excel pricing model he has developed. The functionality provides for pricing both American and Europeans types of calls and put. The user can also specify the number of steps or periods and the model will give the value of the Call and put along with the commonly used option Greeks like Delta, Gamma and Theta. Below is a snapshot of the application developed by the author: Figure : Binomial Application Snapshot Public Function CRRBinomial(OutPutFlag As String, AmeEurFlag As.jpg As you can see above in the code a Function named CRRBinomial has been defined to price option using the Binomial Model. OutPutFlag : used to determine what kind of information the function returns when it is called. Eg if OutPutFlag =à ¢Ã¢â ¬?pà ¢Ã¢â ¬? function will return the option value and so on. AmeEurFlag: determines whether the option to be priced is an American or a Europ ean option. CallPutFlag: determines whether the option to be priced is Call or Put option. OptionValue: defined as an array which runs till n+1 where n is the number of periods? This variable is used to calculate the Call option price at various points in time which are then discounted back at the risk free rate of return to give the option price at current time period. U,d : probability of stock price going up or down dT: time in each period calculated as (time to expiration)/(number of period) Df : Discounting factor using riskless rate of return calculated as Exp(-r * dt) For j = n 1 To.jpg The Code above calculates the option price value using the formula for the multi period binomial model. The If condition is to check whether the type of option to be priced is American or European type and accordingly applies the formula to calculate the option value. The variables ReturnValue(1) , ReturnValue(2) , ReturnValue(3) calculate the option Greeks Delta, Gamma a nd Theta respectively. 3.3- Black Scholes Options Pricing Model. Assumptions of Black Scholes Model: As Mentioned earlier all models are based on a certain specific set of assumptions. The following assumptions are made in the Black Scholes model. Stock Prices evolve according to Lognormal Distribution and behave randomly: We here assume that the behaviour of the stock prices is random which is also a common assumption in pricing most derivatives. Although some fund managers claim that they can predict stock prices uses past trends and other methods. Studies have shown that there may be only small room for predictability and that stock returns are largely unpredictable. We also mentioned that stock returns are log normally distributed. The logarithm of a number is the power to which a base must be raised in order to equal that number. The base of natural logarithms is e which is equal to 2.718. In finance mostly natural logarithms are used. A lognormal distribution is one in which the log of a variable is normally distributed. This distribution of stock returns has positive skewness i.e. most of the variables lie to the right side of the mean in the distribution. This assumption of lognormal distribution is quite a good approximation of the real prices and also prevents the stock price from being negative.
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