Emerging Economies (RUSSIA) Research Paper Example | Topics and Well Written Essays - 4750 words

Emerging Economies (RUSSIA) - Research Paper Example According to the research findings the Soviet Union was considered as one of the most powerful and stable country in the world in 1980’s. The Soviet Union was getting stronger and stronger with the passage of time. The country was also stable economically. However, the policies devised and adopted by the country weakened the economic and political situation which eventually resulted in disintegration of Soviet Union. However, the analysts are of the view that the basic reason of political and economic collapse of the Soviet Union was the culture of War which caused severe impacts on the economic and political situations of the country. This increased war culture also affected the budget of the country and a greater portion of the budget was reserved only for the military. This increase in the military budget was made at the expense of the investment in the economy. By the mid of decade of 1980, half of the total output of the country was consumed by the Soviet military only. T his caused the shortages of the industrial commodities for the country and general public as a whole. Moreover, the commodities available in the market of Soviet Union were also not considered fit for use as all the commodities and goods which were in good condition were taken up by the military. Consequently, the consumers of the Soviet Union started importing the industrial goods to satisfy their desires. The economic factors that resulted in collapse of Soviet Union were also closely linked to the psychological factors affecting the people of the country. As the market was glooming day by day due to availability of few products and commodities in the market, the people were getting more and more depressed. Those who could import the goods from other countries satisfied their needs, but the other portion of the public suffered a lot. This had severe impacts on the psychological situations of the people and also on their working patterns and habits. The level of distrust in the gov ernment was so high that the workers often said that the government pretended that they were paying them for their work and they pretended that they were working for the government. The analysts are of the view that the incentives for the production were very low. In some cases, the workers were not given any incentives for the efforts they put in. This deterred the workers from working. Grigory Yavlinsky, a Russian economist, was of the view that the system of the system was not functioning properly because the workers were not working (Thayer, W. Silicon, V) At the time when the Soviet Union was facing great depression and economical instability, the Reagan administration in US decided to increase the military budget. They also proposed to implement an antiballistic missile system. This caused the Soviet Union to increase its military budget to maintain parity with United States. But at this stage, it was impossible for the Soviet Union to increase the share of its budget share fo r the military. The authorities of the Soviet Union decided to end the cold war and also the arms race which resulted in the allocation of a greater portion of budget to fulfill the military purposes only. However, this also removed the possibility of an invasion by external forces. Thus, the people of the Soviet Union also refused to accept the totalitarian system of government. As a result, the whole political system of the country was disintegrated and the Soviet Union collapsed. The post-Soviet period was a tough time for Russia. Especially, the transition period brought great challenges for the Russian government and public. The ways and methods that were adopted by the Russian administration to deal with these challenges are of significant importance. Moreover, the revolutionary changes that were brought by the Russian government in the field of education, industry and resource sectors are worth-mentioning. The economic policies adopted by the government in immediate post-Sovi et period are also of great importance. POST-SOVIET PERIOD: The Russian economy became one of the

Research paper Example | Topics and Well Written Essays - 2250 words

Research Paper Example William Faulkner wrote during the twentieth century and mostly chronicled the mentalities of the American South and the ways in which they had changed following the abolition of slavery as a social institution. The collective mentality of the South forms the story of much of Faulkner’s works. There is thus, a dark tone that he employs throughout his work. There is also an examination of the individual psyche being a symbol of the collective in Faulkner’s works. Faulkner also looks at the absurd elements of daily life and how they may after a point of time, due to habit, not appear absurd to a society anymore. This dark tone arises from the analyses of the human psyche that Poe attempts to effect in his work. In Poe’s world, it is the absurd that appears normal, thus destabilizing the world of the reader and presenting him with no clues as to what to expect after a certain point of time. Through an analysis of different aspects of the story, this paper shall argue that the society and its larger forces form the party of the victimizers rather than the characters Montresor and Emily. â€Å"The Cask of Amontillado† presents the story of two men, Montresor and Fortunato, who are interlocked in a struggle of petty power, even though Fortunato is unaware of the same. Having been insulted at a certain point of time by Fortunato, Montresor seeks to take revenge upon him through murdering him. With this in mind, he leads him through an underground hallway at the end of which he promises a rare cask of Amontillado. When they reach the end, Montresor chains Fortunato, leaving him to die there and the reader is made aware of the world’s ignorance at the end of the story. â€Å"A Rose for Emily† talks of a family of the American South which has died leaving just one member alive- Emily. She is very introverted and prefers to stay alone in the house without even paying her taxes and as a result of this, the town is surprised when she starts an affair with a man named Homer Barron. He is thought to leave her and life continues for Emily with the support of nobody but an African American servant. Her death however, reveals the decomposed body of Homer and makes the town aware of the entire history of the woman that they thought of as a symbol of stability amidst the great changes that were happening in their society. The narrative styles of the two stories are not completely similar and this has a lot to do with the fact that the change in the person of the narrative. The figure of the narrator in â€Å"A Rose for Emily† has been a subject of great critical debate since the publication of this story (Nebeker 3). The narrator changes roles quite frequently throughout the story. He or she masquerades as an all-knowing omniscient third-person figure for a large part of the story. Later, however, the readers are made to know that the narrator does not possess the knowledge that conventional third person narrat ors possess. This can be seen from the end of the narrative where the existence of the decomposed body of Homer is a new knowledge for the narrator as well. Thus, the narrator too morphs into a native of the town that the story is set in. this has implications for the kind of writing styles that are adopted by the two writers. While Faulkner writes stories that have long sentences, Poe writes using both long and short sentences. The long sentences are used while describing Fortunato

Legal Analysis Memo Case Study Example | Topics and Well Written Essays - 750 words

Legal Analysis Memo - Case Study Example Did police officers uphold the 4th amendment of the United States constitution, when they entered Mr. Smith’s home without a warrant, simply after investigating an noise complaint and observing what were thought to be illegal activities through the window, then seizing Marijuana, Cocaine and unregistered firearms? Do police have enough evidence to convict him of distribution? The state should be allowed to use the evidence gained, because Mr. Blake does not have a reasonable expectation for privacy within Mr. Smith’s home. They do not have enough evidence to convict Mr. Blake with possession of firearms because the firearms could have belonged to anyone. They also do not have enough evidence to convict him with distribution of cocaine, because the act of him transferring a white bag to someone else is ambiguous, and there is not enough evidence to corroborate the crime. Rule: The 4th amendment of the United States Constitution provides: The right of the people to be sec ure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and Warrants shall not be issued, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized (US Constitution). However, the owner of the property may consent to the search. Also the person must have a reasonable expectation of privacy. In Minnesota Vs. Carter, the courts ruled that a guest at another person’s residence does not have a reasonable expectation of privacy (unless they are spending the night), and thus are not protected under the forth amendment (Minnesota vs. Carter). Also, officers are allowed to seize anything in plain view during lawful observation. Analysis: On the grounds that police officers made observations through the window before Mr. Smith authorized a search of his property, Mr. Blake could file a motion to have all evidence stemming from thos e observations to be discarded under the 4th amendment. However, if the court grants that motion the evidence will stand, because as seen in Minnesota Vs. Carter, if you are a guest in another person’s home, you do not have a reasonable expectation of privacy and you are not protected under the fourth amendment (Minnesota vs. Carter). Even though Mr. Blake runs a business with Mr. Smith in the basement of the home, it still is not technically his home, and according to Minnesota vs. Carter, you are given a significantly less expectation of privacy in the commercial arena anyhow (Minnesota vs. Carter). Thus the evidence observed from the window as well as the evidence found after Mr. Smith consented for the officers to enter the home can be used in court. The firearms were in plain view when the police entered the home, so those can be used as well. Even though the evidence must stand, there is not enough evidence to convict Mr. Blake of all of the crimes he is being charged w ith. The police report states they â€Å"observed Mr. Blake hand a baggie of white powder to someone standing near the couch.† They then found a large amount of cocaine in Blake’s possession, cash, and a small amount of cocaine in a stranger’s possessions. While the law states that the government need not prove he received anything of value in return, the fact that they didn’t see him receive anything makes it tough to prove he was actually distributing the cocaine. While not the most intuitive explanation, it’

Santanville and its Five Issues Case Study Example | Topics and Well Written Essays - 500 words - 94

Santanville and its Five Issues - Case Study Example On the other hand, the employees do not trust their supervisor with the evaluation process since they feel that he favors some individuals. The employees also believe that their jobs have evolved thus they are advocating the organization to upgrade their jobs. Another issue from the case study is how the supervisor treats the Union Workers. He grants permission to other employees to attend some chores, but denies an employee who wanted to attend to a family issue; to attend the daughter’s play. The action has prompted the Union steward to request a meeting with Santa. There is also a problem with the toy designer who is threatening resignation if the company does not offer him pay increment. The Sales Manager is pointing at the abandonment of the company's base salary with minimum discretionary bonus and focus on incentive-based payment approach to the sales staff. The Manager is having difficulties in retaining or recruiting candidates with the inadequate payment plan. Lack of payment incentive is, therefore, the reason as to why many employees are leaving after a short period (Sathyanarayana, & Maran, 2011). There is also a problem with underpayment of workers. For instance, the North Pole and South Pole salary ranges are different. The employees suspect that company is not adhering to the National Labor Salary Range Act Book. Before deciding on the compensation plan, the company should consider the implication of poor remuneration to the company’s performance (Sathyanarayana, & Maran, 2011). Better still, Santa can avoid the secretary's demands by implementing a new compensation policy that will ensure that employees receive more insurance benefits. However, before arriving at the decision, it is imperative to consider implications on the company's competitive advantage. If an increment on employee overtime can convince them to stay, then it will be best to implement it since replacing talents is always difficult. About job evaluation, the supervisor should use  performance-based evaluation strategy rather than depend on the ranks of employees (Sathyanarayana, & Maran, 2011).

Air Pollution Essay Example | Topics and Well Written Essays - 1000 words

Air Pollution - Essay Example This research paper explores that different places in the world have different air quality, depending on the magnitude of air pollution. The air that people inhale is neither clean nor is it healthy. In fact, the air that people breathe contains harmful gases like ground level ozone gas, carbon monoxide, sulfur dioxide, nitrogen oxide, air particles and lead. Of the five gases, ground level ozone and air borne articles have been identified as the greatest risk to human health in the world major cities. There is a great difference in air qualities in the world and this is manifested in different statistical informations in the major cities of the world. The major cities of the globe are impacted by air pollution, which affects air quality. The Air Quality in the world is assessed through Air Quality Index (AQI). AQI is used for reporting air quality on a daily basis. AQI provides information about how clean or polluted the air is in the places that a person resides and what health haz ards a person should be concerned of. Environmental Protection Agency usually calculates the AQI of five major air pollutants, which are controlled by the Clean Air Act. These pollutants include ground level ozone gas, carbon monoxide, sulfur dioxide, nitrogen oxide and air particles. Of the five gases, ground level ozone and air borne articles have been identified as the greatest risk to human health in the world major cities. Most of the sources of air pollution arise from technological and industrial advancement made by humans.

Belonging Essay Essay Example for Free

Belonging Essay Essay Concept, perceptions and ideas to belong or not to belong differ from person to person. This is due to experiences that shape ones personality that come through personal, cultural, social and historical context. The idea of belonging allows one to have some sort of connection and communal with people, places, groups, communities and the wider world. In contrast not belonging causes one to suffer from alienation, exclusion and marginalisation. As a result these factors can cause an individual to be at different states of depression depending on one’s personality and situation. However in society, belonging has become and essential to life. Many texts have explored the notion of belonging and not belonging; the play Rainbows End by Jane Harrison and the short film Between the Flags Produced by Jayce White explore the concept of belonging and not belonging to place and people through several forms. Rainbows End by Jane Harrison is a play that explores the concept of belonging and not belonging thorough Harrison’s choice of cultural and historical context at the time. The play is set in the 1950’s during the time Queen Elizabeth II was visiting Australia and whilst many racist policies where practiced such as the Assimilation, Paternalistic and the White Australia policy which all discriminated and alienated the Aboriginal people from the wider community. Throughout the play, it is manifest the Aboriginal people belong and do not belong to certain placed and people. This is shown through a conversation that Nan Dear his with Dolly about her birthplace, â€Å"Well, of course I’m not gunna die. Not here anyway. Gotta go back to my old place to do that. Nan Dear Act One Scene One. This quote conveys Nan Dear’s idea of belonging to place, she assertively expresses to dolly that this is not her place and she will eventually return to where she fits most, through this may not be physically but rather spiritually, which is also part of the aboriginal culture and traditions. The understanding to belong, not belong and the longing to belong alters from one individual to another, this is extensively due to one’s overall background experiences which have ultimately shaped ones thoughts and ideas on the various notions of belonging. This is very evident throughout the play, Rainbows End as different perceptions of belonging are conveyed through conversations and incidents that occurs from characters of different social and historical background. An example of such is the conversation that Errol and Dolly have about the differences in their families. Errol attempts to convince Dolly that he is willing to give her a better life, if she agrees to marry him but away from her family. Dolly does not agree with Errol Fisher’s views on a better life and continues to question his thoughts through the repetition of his words. DOLLY: You want me to leave here for ever? ERROL: I’m offering you a better life. DOLLY: A better life? ERROL: In the city there’s department stores so big that you can spend all day in them. Why in the city there’s even little restaurants you can eat spaghetti, just like Italy. DOLLY: Spaghetti? This conversation portrayed Errol and Dolly’s different perceptions of belonging. The use of the repetition is ironic as Dolly has her family and place does not understand the meaning of â€Å"better life†. The connection that dolly has with her family and place has created her to feel comfortable there regardless of all the discriminatory acts of the time. Errol and Dollydiffering opinions come through their social and cultural context which causes them to continuously clash between each other. â€Å"Your world. And you’re just assuming that your world is better. But actually, when I think about it- when I think about nasty Nancy – she has everything that opens and shuts. I’m not sure it isbetter. I wouldn’t trade placer with her for anything. And as far as you’re offering †¦ no thank you. This is my place. I’m staying right here with my Mum and Nan† despite Dolly not being a young adult who has subjected to racial incidents, that could be prevented in the future if she accepts to marryErrol The short film Between the Flags is a Tropfest film that references and represents the incident that had occurred in the year of 2005, Cronulla riots, concerning two racial groups; the Australian and the Lebanese, which caused violence and division amongst the two races. If mixing of the two diverse racial groups had occurred at the time it often resulted in a brawl and further conflict; however the filmBetween the Flags argues this conviction through a humorous way. Several forms such as: humour, irony, popular culture and themes such as the beach and â€Å"typical Australian bloke† support the idea that two or more people can intertwine together regardless of any dispute one being removed from the external society. The use of irony is used throughout the complete film, it creates humour in-between the two characters which generates harmony amongst them, this is apparent in the film. An example of this is when the Lebanese character (character are not given names instead each represents an ethnicity which is shown through their choice of costume) approaches the Australian bloke: â€Å"What’s goin on† – Lebanese boy â€Å"G’day mate† – Australian bloke â€Å"Here for the riots† – Lebanese boy â€Å"Yeah, looks like we’re the first ones here† – Australian bloke â€Å"Maybe we should wait for a more people† – Lebanese boy  The conversation between them continues the irony of the situation is the conversation that occurs, and also the use of such words such as â€Å"mate†, as both of them are at the beach to riot against each other; instead they involve themselves together in a communal conversation. Throughout give-and-take of words between the two characters they both felt a sense belonging and ease towards each other even through the beach was supposed to be a place of non-belonging and dispute. This was majorly due to them being part of the popular culture and sharing the same interest. Their reactions were shown through the use of close up camera shots, as they enable the viewer to understand the characters emotions and have a sense of empathy towards them. The short film Between the Flags uses the beach as the setting to the film, as this is also references to the Cronulla riots as they had occurred at the beach. The attitudes that the characters have towards the beach affirm that it is a place of regular social call, also part of each ones character regardless of their ethnic background. Two characters connection with the beach enables the viewers to have an immediate understanding that it is a place of belonging to one another. This is manifest in the film through the connection that the characters grow due to playing a game of cricket, nevertheless in the film the beginning of the game the Lebanese character says â€Å"umm I don’t usually do this but†¦Ã¢â‚¬  this had displayed to the audience that he is not too liking of cricket but he starts to play as it is most appropriate to do so. This was shown through a continuous full camera shot to show the characters interaction with each ther and to also display the setting of the film. Throughout exploring and analysing texts it has become most evident that people views of belonging is constructed through their perception on the place. This concept was explored in the two texts Rainbows End by Jane Harrison and the short film Between the Flags produced by Jayce White as both texts had explored belonging, not belonging or the longing to belong to a place through the perceptions and the social, historical, cultural and personal context of an individual determined their sense of belonging and not belonging.

Comparing Binomial Tree, Monte Carlo Simulation And Finite

Comparing Binomial Tree, Monte Carlo Simulation And Finite In recent years, numerical methods for valuing options such as binomial tree models, Monte Carlo simulation and finite difference methods are use for a wide range of financial purposes. This paper illustrates and compares the three numerical methods. On one hand, it provided general description of the three methods separately involved their definitions, merits and drawbacks and determinants of each method. On the other hand, this paper makes a concrete comparison in valuing options between the three numerical methods. Overall, the three numerical methods have proven to be valuable and efficient methods to value options. Introduction In recent years, option valuation methods are very important in the theory of finance and increased wildly in the practice field. The various approaches on option prices valuation included binomial tree models, Monte Carlo simulation and finite difference methods. Binomial models are suggested by Cox, Ross and Rubinstein (1979). Boyle (1977) firstly discussed Monte Carlo simulation and then it has been used by both Johnson and Shanno(1985) and Hull and White(1987) to value options when it is a stochastic process. Finite difference methods are discussed by Schwartz (1977), Brennan and Schwartz (1979), and Courtadon (1982) (Hull and White, 1988). This essay aims to provide a comparison and contrast among the three numerical methods mentioned above. All these numerical methods focus on the objectives of both calculation accuracy and speed. The only way for any given method to achieve better accuracy and speed is to calculate with many times (Hull and White, 1988). For one thing, this es say provides general description about binomial trees, Monte Carlo simulation and finite difference methods and defines benefits and drawbacks of each method. For another thing, it makes contrast on the valuation option prices involved American and European options. Binomial tree models Hull and White (1988) provide a general description about binomial trees. They concluded that Binomial model is a particular case of a more general set of multivariate multinomial models. All multivariate multinomial models are characteristics as lattice approaches such as binomial and trinomial lattice models(Hull and White, 1988).And the binomial trees, a valuation option approach, which involved separating option into a large number of small time intervals of length Άt. The assumption of this method is that the asset price changed from its initial value to two new values, both upward and downward movement, Su and Sd separately. The probability of an upward movement was indicated as p, while the probability of a downward movement is 1-p and the parameter u, d, p are used to value option prices. (Hull, 2008) The binomial model focused on option replication. For the binomial trees, the only way to reproduce the payoff of an option is to trade a portfolio involved the stock and the risk-free asset. Within other lattice approaches, involved the trinomial tree model, do not admit option replication(FiglewskiGao, 1999).However, the fair value of option can be valued under the basic assumptions of option pricing which is the world is risk-neutral. (Hull, 2008) In this case, the fair value can be valued simply by computing the expected values within the risk neutral distribution and discounting at the risk-free interest rate (Hull, 2008).When the world is risk-neutral, any approximation procedure which is based on a probability distribution and rough risk neutral distribution and make convergence to its limit, can be used to value options prices properly. Therefore, it is necessary to use trinomial tree model even a more complex structure without lack of the ability to calculating unique option payoffs (FiglewskiGao, 1999). What is also worth mentioning about the application of binomial tree is that there exists known payouts involved dividends (Hull and White, 1988). Dividend policy was based on the principle that the stock maintains a constant yield on each ex-dividend date which was denoted by ÃŽÂ ´ (Cox et.al, 1979) Essentially, binomial and trinomial models are powerful, intuitive methods to value both American and European option. Moreover, it also provides asymptotically exact approximation based on Black-Scholes assumptions (FiglewskiGao, 1999). Consider the efficiency and accuracy of this method, the binomial method is more efficient and accurate when there are a small number of options values without dividends. However it lacks of efficient in a situation where effects of cash dividends should be analysed. Actually, the fixed dividend yield generated an improper hedge ratio despite that the assumption of fixed dividend yield is an efficient and accurate approximation. Furthermore, the binomial tree models are inefficient in valuing American options compared with European option. And it is less efficient and accurate than finite difference methods for multiple options valuation. This is because it has a conditional starting point (GeskeShastri, 1985). Monte Carlo simulation Monte Carlo simulation is a useful numerical method to implement for various kinds of purposes of finance such as securities valuation. For the valuation of option, Monte Carlo simulation use risk-neutral measure (Hull, 2008). For example, a call option is a security whose expected payoffs depend on not only one basic security. The value of a derivative security can be obtained by discounted the expected payoff in the risk-neutral world at the riskless rate (Boyle, et.al, 1997). Boyle et.al (1997) stated that this approach comprises several steps in the following. Firstly, Simulate sample paths of the underlying state variables (e.g., underlying asset prices and interest rates) over the relevant time horizon. Stimulate these according to the risk-neutral measure. Secondly, evaluate the discounted cash flows of a security on each sample path, as determined by the structure of the security in question. Thirdly, average the discounted cash flows over sample paths There is a tendency that high-dimensional integral is becoming more and more necessary to evaluate in the derivative security. Monte Carlo simulation is widely used in the option valuation due to the increases of high dimension (Ibanez Zapatero, 2004). Regarding the integral of the function f(x) over the d-dimensional unit hypercube, the simple Monte Carlo estimate of the integral is equivalent to the average value of the function f over n random points from the unit hypercube. When n tends to be infinite, this estimate converges to the true value of the integral. Furthermore, the distinct advantage of this method compared with other numerical approaches is that the error convergence rate is independent dimension. In addition, the function f should be square integrable and this is the only restriction which is relative and slight ((Boyle, et.al, 1997). Monte Carlo simulation is simple, flexible. It can be easily modified to adapt different processes which involved governing stock returns. Moreover, compared other methods, it has distinct merit in some specific circumstances. Essentially Monte Carlo simulation can be used when the process of generating future stock value movement determined the final stock value. This process mentioned above is created on a computer and aims to generate a series of stock price trajectories which is used to obtain the evaluation of option. In addition, the standard deviation also can be used simultaneously in order to make sure the accuracy of the results (Boyle, 1977). However, there are some disadvantages of this method. In recent years, some new techniques were developed so as to overcome the disadvantages. One key drawback is that it is wasteful to calculate many times and difficult to control situations when there are early exercise opportunities (Hull, 2008). Different variances reduction techniques involved control variate approach and antithetic variate method are used to solve these problems. Furthermore, deterministic sequences also known as low-discrepancy sequences or quasi-random sequences are used to accelerate the valuation of multi-dimensional integrals, (Boyle, et.al, 1997). Quasi-Monte Carlo methods are suggested as a new approach to supplement Monte Carlo simulation. It uses deterministic sequences rather than random sequences. These sequences are used to obtain convergence with known error bounds ¼Ã‹â€ Joy ¼Ã…’et.al. 1996 ¼Ã¢â‚¬ ° Until recently, Monte Carlo simulation has not been used in American options. The key problem is that payoff depends on some sources of uncertainty. The optimal exercise frontier of American options is uncertain (Barraquand Martineau, 1995). Finite difference methods Hull (2008) provides a general description of finite difference methods. He concluded that finite difference methods value a derivative by solving the differential equation that the derivative satisfies. Finite difference methods are classified into two ways those are implicit and explicit finite difference method. The former approach is related the value of option at time t+Άt to three alternative values at time t, while the latter one is related the value of option at time t to three alternative values at time t+Άt (Hull White, 1990). The explicit finite difference method is equivalent to a trinomial lattice approach. Compared with the two finite difference methods, the distinct advantage of explicit finite difference method is that it has fewer boundary conditions than the implicit way. For instance, to implement implicit method, considering the price of a derivative security S, it is vital to specify boundary conditions for the derivative security whether minimising or maximising price. By contrast, the explicit method, regarded as a trinomial lattice approach, does not need specific boundary conditions (Hull White, 1990). There are two alternative problems of partial differential equations. The first, known as boundary value problems where a wide range of boundary conditions must be specified, the second, known as initial value problems where only a fraction of valuation required to be specified. There is a fact that most option valuation problems are initial value problems. The explicit finite difference method is the most appropriate method to solve initial value problems because implicit finite method used extra boundary condition which was produced errors (Hull White, 1990). Furthermore, consider the efficiency and accuracy of valuing option, the explicit finite difference method, with logarithmical transformation, is more efficient than the implicit method. This is because it does not need the solution solved a series of simultaneous equations (GeskeShastri, 1985). In addition, for the finite difference method and jump process, the simple explicit difference approximation is harmonized with a three-point jump process, while the more complex implicit difference approximation corresponds a generalized jump process which is based on that the value of derivative security will jump to infinite future values, not just three points(BrennanSchwartz, 1978) Finite difference approach can be used in the same situation as binomial tree approach. They can control American and European option and cannot easily used when the payoff of an option depends on the past history of the state variable. Furthermore, finite difference methods can be used in the situation where there are some state variable ¼Ã‹â€ Hull 2008). However, the binomial tree method is more intuitive and easily implemented than the finite difference methods. Therefore, financial economists tend to use binomial tree methods when there are a small number of option values. In contrast, finite difference methods are frequently used and more efficient in a situation where there are a large number of option values (GeskeShastri, 1985). The comparison between the three methods Overall, compared with the three numerical methods of valuing option, Monte Carlo simulation should be seen as a supplement methods for the binomial tree models and finite difference methods. This is because the increase of a variety of complexity in financial instruments (Boyle, 1977). Furthermore, binomial and finite difference methods are implemented with low dimension of problems and standard dynamics, while Monte Carlo simulation is the proper methods to solve high dimension problems and stochastic parameters (Ibanez Zapatero, 2004) The binomial tree models and finite difference methods are classified as backward methods and can easily handle early exercise opportunities. On the contrary, Monte Carlo simulation is a looking forward method and may be opposed with backward induction (Ibanez Zapatero, 2004) For the two similar methods, finite difference approach is equivalent to a trinomial lattice method. They are both useful for American and European options and tend not to be used in a situation where the options payoff depends on the past history of state variables. However, there also are some differences between them. Binomial tree methods can be used to calculate a small number of values of options, while finite difference methods can be used and more efficient and accurate when there exit a large number of option values. In addition, binomial tree models are more intuitive and readily completed than the finite difference methods Monte Carlo simulation is a powerful and flexible method to value various options. In principle, Monte Carlo simulation is calculated a multi-dimension integral and this is becoming an attractiveness compared other numerical methods. It can be used to solve the problem of high dimension. The drawbacks should not be neglected. The computation with many times and cannot easily handle the situation where there are early exercise opportunities. Based the traditional Monte Carlo simulation, a new approach was developed, known as Quasi-Monte Carlo methods to improve the efficiency of Monte Carlo method. The basic theorem is to use deterministic number rather than random. However, it has not been used in valuing American options due to the optimal exercise frontier is uncertain. One way to value American option is to achieve combination of Monte Carlo simulation and dynamic programming (Ibanez Zapatero, 2004) Conclusion To sum up, with the complexity of numerical computation, numerical methods are wildly used to value derivative security. This paper provided general description and specific comparison between the three numerical methods mentioned above. Binomial tree models, known as lattice approach, are a powerful and intuitive tool to value both American and European option with and without dividend. When there are a small number of option values, binomial method is more efficient and accurate. On the contrary, it is inefficient in a situation where effects of cash dividend should be analysed. Finite difference method can be seen as the trinomial lattice approach. They are used with the problems of low dimension and have been regarded as efficient and accurate methods to value American and European options. Compared with binomial tree models, finite difference methods is more efficient and accurate when practicers computing a large number of values of options. Monte Carlo simulation can be seen as a supplement tool for the two methods mentioned above to value options. It can be used with high dimensional problems whereas other two methods are used with low dimensional problems. The flows of Monte Carlo simulation are that it consumes time for calculating and cannot readily handle the situation where there are early exercise opportunities. In this case, Quasi-Monte Carlo methods based on traditional Monte Carlo simulation utilise deterministic sequences known as quasi-random sequences. These sequences provide an opportunity to acquire convergence with known error bounds. Referenc: Barraquand ¼Ã…’J. Martineau, D. (1995)Numerical Valuation of High Dimensional Multivariate American Securities The Journal of Financial and Quantitative Analysis, Vol. 30, No. 3 pp. 383 -405 Boyle, P.P., Option: A Monte Carlo Approach, Journal of Financial Economics, Volume:4, pp: 323-338 Boyle, P. Broadie, M. and Glasserman,P.(1997) Monte Carlo methods for security pricing, Journal of Economic Dynamics and Control, Volume 21, Issues 8-9,29,pp:1267-1321 Brennan, M.J. Schwartz, E.S., (1978)Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis, The Journal of Financial and Quantitative Analysis, Vol. 13, No. 3 pp. 461 -474 Cox, J.C., Ross, S.A. and Rubinstein. M.(1979) Option pricing: A simplified approach, Journal of Financial Economics, Volume 7, Issue 3, pp: 229-263 Figlewski,S.Gao,B.(1999)The adaptive mesh model: a new approach to efficient option pricing, Journal of Financial Economics, Volume 53, Issue 3, pp: 313-351 Geske,R. 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