Explain Why It Is Impossible To Derive An Analytical Formula For Valu :: essays research papers

Explain Why It Is Impossible to Derive An Analytical Formula For Valuing American Puts. Explain why it has proved impossible to derive an analytical formula for valuing American Puts, and outline the main techniques that are used to produce approximate valuations for such securities Investing in stock options is a way used by investors to hedge against risk. It is simply because all the investors could lose if the option is not exercised before the expiration rate is just the option price (that is the premium) that he or she has paid earlier. Call options give the investor the right to buy the underlying stock at the exercise price, X; while the put options give the investor the right to sell the underlying security at X. However only America options can be exercised at any time during the life of the option if the holder sees fit while European options can only be exercised at the expiration rate, and this is the reason why American put options are normally valued higher than European options. Nonetheless it has been proved by academics that it is impossible to derive an analytical formula for valuing American put options and the reason why will be discussed in this paper as well as some main suggested techniques that are used to value them. According to Hull, exercising an American put option on a non-dividend-paying stock early if it is sufficiently deeply in the money can be an optimal practice. For example, suppose that the strike price of an American option is $20 and the stock price is virtually zero. By exercising early at this point of time, an investor makes an immediate gain of $20. On the contrary, if the investor waits, he might not be able to get as much as $20 gain since negative stock prices are impossible. Therefore it implies that if the share price was zero, the put would have reached its highest possible value so the investor should exercise the option early at this point of time. Additionally, in general, the early exerices of a put option becomes more attractive as S, the stock price, decreases; as r, the risk-free interest rate, increases; and as , the volatility, decreases. Since the value of a put is always positive as the worst can happen to it is that it expires worthless so this can be expressed as where X is the strike price Therefore for an American put with price P, , must always hold since the investor can execute immediate exercise any time prior to the expiry date. As shown in Figure 1,

Piaget Stages of Development Essay

Child development undergoes various stages from infancy to adulthood. This process of development is called by various psychologists as â€Å"progression through development† to which, age is often attached on each developmental stage. The first stage is called the infancy stage which is from birth to one year during which the physical and psychological occur most rapidly. In Piaget’s developmental theory, the child’s development during this stage is called â€Å"sensorimotor† because the child’s behavior at this stage is mostly simple motor responses to sensory stimuli† (Kalat 170). The stage of toddlerhood which is from one year to three years old is partly connected with infancy stage because as Olga Drebben asserts, â€Å"in these early childhood stages, the infants and toddler’s growth and development include very multifaceted processes of physical, cognitive, and psychosocial transformations. Drebben affirms that the primary modes of infant and toddler are sonsorimotor. The childhood stage or as Piaget calls it, the â€Å"preoperational stage of development† is the stage in which children are subject to externally imposed rules and adhere unquestioningly to rules and the directives of powerful adults. In this stage, peer relationship is an important factor towards constructing a self separate from others and towards developing the capacity to think in terms of other peoples’ attitude one self. Deutsch, Coleman and Marcus stated, â€Å"Equal peer relationships give children a chance to experience reciprocity which greatly assists them in perspective taking and problem solving† (Deutsch, Coleman, and Marcus 359). Adolescence stage on the one hand, is seen to takes place at the beginning of puberty or from 10 to 12 year for girls and 12 to 14 years for boys and end and at the age of 18 for girls and 21 for boys. While psychologist admits the lack of precision as to age limit, this stage â€Å"assume more responsibility for personal attainment and well being† (Arnett 168). It is also the stage to earn a living and a time when interest in fun increased. The stage of adulthood on the other hand are divided into three; early, middle and senior adults. The early adulthood which starts at age 21 up to 34 years, is concern on being able to engage in intimate relationships and in finding more satisfying work. This stage is also period of focusing on long term goals, nurturing other physically, finding a meaning in life, and developing a tolerance for delayed gratification to meet long-range goals (Corey and Corey 88). The middle adulthood ages 34 to 49 is regarded as the period of reassessment of one’s work satisfactions, of involvement in the community and of accepting choice made in life. According to Gerald and Marianne Corey, this period of life is a time for â€Å"solidifying one’s philosophy of life. The senior adults 50 to 64 are regarded as the beginning of the wisdom years. This period is characterized as the time for serving the community and planning for work transitions and retirement. Finally, the elderly, 65 years onward is the time â€Å"to find new levels of meaning in life and to appreciate what one has accomplished† (Corey and Corey, 89). This stage is a period of physical weakness because it is a time of diminished strength and increased dependence on others. Of all these stages, the development stage that is more susceptible to schizophrenia are the early adulthood ages 21 to 24 for men, while 40 and above for women. This is because the vast majority of the onset of this disease â€Å"falls within the interval of 15-54 years of age (Hirsch and Weinberger, 215). Steven Hirsch and Daniel Roy Weinberger noted that onsets of schizophrenia in men â€Å"peak steeply in the age group 20-24† (215), and it slowed down at lower level thereafter. This onset for men is the reverse for women above forties. The stages that are more prone to Alzheimer are definitely middle adults, senior adults and the elderly because this disease takes place during these stages of life. Question 2. Two of Piaget’s universal developments are the sensorimotor stage and the preoperational stage. The sensorimotor development stages starts from birth up to the end of the second year. Also called the neonatal stage, it is the period of development when the infant where simply a passive being that acts with out any systematic goal. Sensorimotor stage is the development of the child that includes intelligence based on perceptual experiences such as reflexes from 0-1month, primary circular reactions from 1to 4 months which is a repetition of certain pleasurable behaviors and formation of habits, secondary circular reactions 4 to 8 months, the coordination of secondary schemata and so forth. An example to this is the hand exercises. The child can follow simple instruction to close or open his or her hands as this is pleasurable exercise, during the infancy stage. But when the child is over one year old he can already follow basic instruction with basic understanding. Preoperational stage on the other hand begins at 2 up to 6 years of age. Salkind implies that Piaget’s preoperational stage of universal development is the progression of the infant from a reflexive organism to towards understanding of the symbolic world (248). Michie Swartwood and Kathy Trotter pointed out that in Piaget’s preoperational stage, the key feature of children’s thinking â€Å"is symbolic representation† (69). Swartwood and Trotter cited that during this stage, the child is able to use symbol, an object, or a word to stand for something else (69). Thus, though preoperational stage occurs right after the sensorimotor stage terminates, the child experiences tremendous progress during this stage. An example to this is the ability to follow simple instruction not to touch this or that, or that, on the ground that it will harm him or her, or that it will hurt him. In comparing both stages of development the child acquires certain degree of progression before each stage terminates. Both stages also display some degree of intelligence as the child now learns a lot of things through his or her experiences. But these stages also differ on some grounds. First, children in the sensorimotor stage do not think symbolically, while in preoperational stage they do think symbolically. Second, in the sensorimotor stage, the â€Å"child is limited to direct interaction with the environment, while in the second stage, the children learns to â€Å"manipulate symbols that represent the environment (Salkind, 248). In general however, both these stages show the child’s remarkable and development. Question 3. Some of the major stress that I am dealing with in my everyday life are first and foremost are the pressures from deadlines that must be met. This creates tension in me especially when I am running short of time. Biased treatment and sexism are also a great source of stress because it angers me. I really hate these things and I felt stress every time I encounter it. Some minor stressors however that I encounter everyday are the peer pressures. Peers insistences of something I do not like create pressures on me. Stern and unsmiling faces also s a source of stress especially those I meet daily. Some of the coping skills that I learned over time to keep the minor stressors from becoming major issues are; first, to ease my self of being too competitive. I learned this skill after I realized that I do not actually need to compete with my self. I simply need to make a list of priorities and take things at a time based on the priority list. Second, is to be friendly. I just realized that there is nothing wrong to great people with a smile regardless of how they would respond at me. I realized that by doing this, I could prevent the minor stress from becoming a major stress as I actually overcome it. Question 4. Schizophrenia is a disease. It is a chronic disease and severe mental disorder with a typical onset in adolescence and early adulthood and a lifetime prevalence of 1%. Dwight Evans cited that on average â€Å"male have their illness onset 3 to 4 years earlier than female† (78). Schizophrenia is not a developmental disorder but a chronic mental disease. The four type of schizophrenia are the following, paranoid, disorganized, catatonic, and undifferentiated. The characteristic and symptoms of paranoid are hallucinations and delusions. In the disorganized type, it symptoms and characteristic are reflected by disorganized speech, disorganized behavior, and inappropriate affect. The catatonic type manifest clinical syndrome such as excessive purposeless motor activity, extreme negativism, peculiar voluntary movements and so on. The undifferentiated sub type is diagnosed when the patient â€Å"does not meet criteria for the previous type yet does meet the criteria for schizophrenia† (Maddux & Winstead, 182). It is more likely that schizophrenia has a genetic cause than environmental. It is quite common that when there is schizophrenia in the family, it is passed down to another member. Thus this disease is called â€Å"psychobiological† illness amenable to chemical intervention and modification of the environment. An example to this is when a person is exposed to violence and all other abuses since birth, he has the tendency to have psychological trauma which causes schizophrenia. Question 5. One incident that happened in my lifetime was when I read the story about a plane crash killing all the more than two hundred passengers. After I read the story, I was shocked and I developed psychological fear regarding boarding an aircraft. Psychology fit in this scenario because I knew pretty well that it was simply an accident. In this experience, I developed some fear as it would always come to my mind that this plane might crash too. But as I came to realize, accident happens anywhere to anybody, at any given time and cause. Since I cannot prevent it nor predict it, the best thing to do is to just be very careful and avoid those that I can, but those that I cannot; I just leave my fate in the hands of God. The connection here between psychology and life is that, life is real; we should rather be practical and realistic than be overcome by fear and anxiety about our bad experiences. Question 6. I have incorporated in my work of art elements of psychology through my use of colors and designs. In using bright colors, I usually expressed strong emotion such as anger, or fear, or other emotions. I also incorporated psychology in my designs such as shapes that expresses meanings like lovely ideas or joyful situations. I will incorporate them in the future in the same way I incorporated it the last time with perhaps some improvement or modification. I could connect the process that I go through as an artist with psychology through putting meaning on my experiences in the light of what I have learned about psychology. That is, I must seek the context of what I am trying to portray to which I labor so much. It means that my work of art should be reflective of what life is, of the emotions, such love, fear, and other strong feelings that we often encounter or should I say, that always experience on a daily basis. Finally, one influence that will mesh with my future work of art is those that wear green colors, or things that are green. I am fascinated by this color and this influence in me can help meshed up with my future work of art. Work Cited Arnett, Jeffrey Jensen. International Encyclopedia of Adolescence, Volume 1 USA: CRC Press, 2007. Corey, Gerald & Corey Marianne Schneider. I Never Knew I Had a Choice: Explorations in Personal Growth USA: Cengage Learning, 2006 Deutsch, Morton; Coleman, Peter T. ; & Marcus, Eric Colton. The Handbook of Conflict Resolution: Theory and Practice USA: John Wiley and Sons, 2006 Drebben, Olga. Patient Education in Rehabilitation USA: Jones and Bartlett, 2010 Evans, Dwight Treating and Preventing Adolescent Mental Health Disorders: What We Know and What We don’t Know New York: Oxford University Press Hirsch, Steven & Weinberger Daniel Roy. Schizophrenia Great Britain: Wiley-Blackwell, 1995 Kalat, James W. Introduction to Psychology USA: Cengage Learning, 2008. Maddux, James & Winstead, Barbara. Psychopathology: Foundations for a Contemporary Understanding USA: Routledge, 2005. Salkind, Neil J. An Introduction to Theories of Human Development USA: Sage Publications, 2004 Swartwood, Michie & Trotter, Kathy. Observing Children and Adolescents: Student Workbook USA: Cengage Learning, 2004

Discuss the importance of LOYALTY in Millers Essay

Loyalty is one of the big themes in this play and most people are loyal to each other in the neighborhood, because there are quite a few illegal immigrants living there and working at the piers, so everyone trusts everyone else. This shows loyalty between this neighborhood because no one would snitch on anybody else. Because people understand that life is hard back home and they need the money to help their families, because perhaps there isn’t any work to earn the money they need, so they come to a better country hoping they have a better life there. Eddie and Beatrice are happily married, and live together in an apartment with Beatrice’s niece, Catherine. Beatrice as Eddie’s wife is very loyal and loves Eddie, he also loves Beatrice very much, but he is not as loyal to her as she is to him. I can see this on page 24, when Beatrice says to Eddie, â€Å"When am I gonna be a wife again, Eddie? † I think that Beatrice is insecure about how Eddie feels about her and their marriage. It seems that Eddie is paying more attention to Catherine then Beatrice, because he is worried that Rodolfo is taking Catherine for a ride, but he isn’t, Eddie is just getting worried over nothing, but Beatrice thinks that Eddie may think that she is just jealous, but she is just insecure about the way Eddie really feels about Catherine. Beatrice respects Eddie so much, I can see this because when Eddie is telling Beatrice that nobody will go to that wedding until Marco apologizes to him, on page 61 and Beatrice’s response to this was, â€Å"I cant Katie, I cant†¦ She says this because Eddie had already told her before that if she goes to that wedding then she as well not come back. So Beatrice obviously chose her husband and his wishes, rather than go to her nieces wedding. This proves that Beatrice is loyal and would do anything for Eddie. However, Eddie is not so faithful to Beatrice. Evidence of this is on page 47 when Eddie kisses Catherine on the mouth; I can see that she didn’t want Eddie to do that because the text says, ‘he reaches out suddenly, draws her to him, and as she strives to free herself, he kisses her on the mouth! Then suddenly Rodolfo pulls on Eddies arm and says, â€Å"Don’t! Stop that. Have respect for her. † Rodolfo obviously thinks that what Eddie is doing is wrong and he is trying to stop him. Like I mentioned before, Catherine lives in the same apartment as Eddie, and they get along really well, in fact a little to well. Catherine is a 17 year old young woman, she wants to prove to people that she isn’t a little girl anymore, but Eddie is having some trouble believing that. For example on page 5, Catherine comes in wearing her new skirt and shows it of to Eddie. He likes it but he doesn’t want other boys to see her wearing that and so he says to her, â€Å"you’re a baby, you don’t understand these things. † Eddie is saying that she can’t be going out wearing short skirts, high heels and ‘walking wavy’. He is only looking out for Catherine. Beatrice has also realized that Catherine is still acting like a little girl in front Eddie. Beatrice says to Catherine on page 30, â€Å"†¦ like you sit on the bathtub talkin’ to him when he’s shaving, in his underwear. † Beatrice is trying to explain to Catherine that she can’t still be doing that, because Beatrice knows that Catherine is trying to show everyone that she is independent, but Catherine doesn’t seem to understand because Beatrice says to her again on page 30, â€Å"but if you act like a baby, then he be treain’ you like a baby. Like when he comes home sometimes you throw yourself at him like when you was 12 years old! † This shows that Beatrice is really trying to tell Catherine that she has to stop acting like that in front of Eddie, because she isn’t 12 years old anymore, she is nearly 18 years old. This links in quite well with the meaning of this play because; Catherine wants Eddie to have enough faith in her, to let her go to do whatever she wants. Another character who is part of this is, Rodolfo. He and his brother, Marco, are illegal immigrants from Italy. They are Beatrice’s cousins and who have come over to America to work and earn some money to send back home, for their poor families. From the first time Rodolfo met Catherine he really liked her, and as Catherine got to know Rodolfo, she began to like him, a lot. Eddie soon realizes that there is something going on between Catherine and Rodolfo, because they are going out a lot together and coming home late. Eddie feels jealousy towards Rodolfo because he feels like Catherine is never at home anymore and she is always out with Rodolfo. Eddie is obviously jealous of Rodolfo, and he doesn’t really like him as much as he did, this is because Eddie thinks that all Rodolfo wants is his papers so he could stay in America and become an American citizen. This is not true at all, Rodolfo and Catherine are in love and that is why they want to get married. When Eddie found this out he really didn’t know what to do, but he did know that he wasn’t going to attend their wedding! This made Catherine really upset and she felt as thought she had lost her faith in Eddie, because he can’t be happy for her; whoever she would be with. This brings me to a different character in the play, someone who is very trustworthy and loyal. Alfieri is a lawyer and so he knows everyone in the neighborhood and their problems. Everyone always comes to Alfieri because he is a very honest and fair man, who people respect. From the first moment Eddie started to feel ‘bad’ about the whole Catherine and Rodolfo situation, he straight away turned to Alfieri, because Eddie knew he could tell Alfieri anything; even if it’s nothing to do with the law. When Eddie is talking to Alfieri on page 31, Eddie had explained the whole situation to Alfieri asked Eddie if there is a question of law somewhere and he also added, â€Å"Because there is nothing illegal about a girl falling in love with an immigrant. † But Eddie is convinced that all Rodolfo wants is his papers, Alfieri said to Eddie that he doesn’t know that but Eddie is determined for Catherine not to be with Rodolfo. As the conversation draws to an end, Alfieri says to Eddie on page 34, â€Å"†¦ let her go. That’s my advice. You did your job, now it’s her life. † Alfieri is trying to help Eddie saying that there is nothing he can do just wish her luck and let her go. Eddie thanks Alfieri; this shows trust between Eddie and Alfieri because even though Eddie doesn’t like Alfieri’s advice, he still tells him he won’t do anything, because there is nothing he can do. But later on Eddie betrays Alfieri’s trust and he calls the immigration bureau. On page 50 he says, â€Å"I want to report something. Illegal immigrants. Two of them. That’s right. † He also tells them the address and that he is just around the neighborhood. But when they start to question him further, he hangs up. There is also a lot of trust between the neighborhood and people seem to get along quite well. But when Eddie found out that there are two more illegal immigrants living upstairs with Marco and Rodolfo, who are Lipari the butchers nephews, he realizes that he just snitched on them as well as Marco and Rodolfo. Now he is scared because Lipari the butcher’s families are very hot headed and he will be in trouble when Lipari finds out Eddie snitched on them. So when the immigration officers show up on Eddie’s door Beatrice is shocked because she realizes what Eddie had done and she is ashamed with Eddie, because she never thought he would actually do that. The immigration officers start to search the apartment, they found no one, and so they run upstairs. Soon they come back down with Marco, Rodolfo and the two strange immigrants; Catherine follows down, suddenly Marco breaks from the group and dashes into the room and faces Eddie, Marco spits in Eddies face and shouts, â€Å"that one! I accuse that one! † Marco wants the whole neighborhood to know that Eddie was the man who snitched them up and Eddie was the man who snitched them up and Eddie tries to explain himself on page 58 but Lipari turns away with his arm around his wife, and they walk away, Eddie shouts â€Å"for Christ’s sake! I kept them, I gave them the blankets off my bed! † by saying this he is still trying to explain himself to everyone, but they just turn away and walk off, even his close friends, Louis and Mike. Eddie now learns how important trust is and he also realizes that the neighborhood has lost their trust and loyalty in him. In conclusion I have found out that in this play there is a lot of trust and loyalty between; Catherine and Eddie and Rodolfo, Beatrice and Eddie, and Alfieri and Eddie, but in the end there is not so much trust between Eddie and the neighborhood, more like betrayal. In that neighborhood there are quite a few immigrants working on the piers, but people keep it to themselves, because no one wants to snitch. This proves there is trust between everyone in the neighborhood. I think that Miller’s point of this play was to, actually make people realize that life isn’t just all happy endings but there are some issues which need to be talked about, like trust and loyalty in a illegal immigrant environment. I think this quote I got from the back of the book explains my point, â€Å"all the plays that I was trying to write were plays that would grab the audience by the throat and not release them, rather than presenting an emotion which you could observe and walk away. † – Arthur Miler.