National Transportation Safety Board Aircraft Accident Brief

National Transportation Safety Board Aircraft Accident Brief Accident Summary The Hendricks Motorsport plane crash occurred on 24 October 2001.   The airplane crashed in the mountainous regions in Stuart Virginia killing the crew and passengers aboard. The plane crash occurred after a missed landing on the runway 30 of the Martinsville Blue Ridge Airport (NTSB, 2006).   The plane contained two crewmembers and eight passengers who were part of the Hendricks Motorsport Racing team.   All the people on the aircraft died in the accident.   The plane crashed and exploded into flames after impact.   The team was traveling from Concord airport in North Carolina for a racing event. Information from the FAA records of communications and operations of the flight shows that the plane followed all the right procedures including altitude and headings.   However, the problem arose while approaching the Martinsville airport runway (NTSB, 2006).   The plane scheduled a landing on runway thirty but failed to do so under the advisement of the controller tower.   The controller informed the crew that they were second in line for the runway and initiated a holding pattern that extended to 28 minutes.   The flight crew received the message and started 5-mile legs to wait. The team undertook a five-mile holding pattern by making a right turn and ascent to 4000 ft.   The team went on with the holding pattern until the controller cleared them for landing and instructed them to announce their approach to the runway (NTSB, 2006).   The crew followed instructions, informed the controller of the inbound approach, and began their descent to the runway.   The controller confirmed the approached through the radio frequency and the crew proceeded with the approach by descending from 3900ft to 1400ft.   The plane maintained this attitude for approximately over one minute.   It was then that the team announced a missed approach was prompting the controller to ask for confirmation.   The crewmembers ceased all communications after confirming the missed approach.   The Controller further advised the flight crew to ascend to 4400ft but received no response and lost the radar. The Bull Mountains of Stuart Virginia were the scene of the crash about 2400ft away from the landing site.   Eyewitness reports indicated that the aircraft was operating efficiently before the accident.   The engine produced a smooth continuous sound that may have meant idling (NTSB, 2006).   Further reports showed that the plane was flying extremely low at a slow velocity.   There did not seem to be any challenges to the aircrafts performance at the time. However, it is important to note that there was fog in the atmosphere at the date of the crash.   The fog was a factor limiting visibility as it covered the Bull Mountains.   Reports indicate the visibility was up to a quarter mile. A review of the pilots credentials presented him as qualified. He had an estimated 10,733 hours of flight with almost 2000 in the Beech aircraft.   He was 51 years of age and had a significant amount of experience as a pilot.   He had also undergone rigorous training and passed his previous reviews.   The first officer had less experience totaling to 2090 hours of flight (NTSB, 2006).   However, she was qualified evidenced by her qualifications and past performance.   The multiengine plane had passed inspection a few months later with an accumulated flight time of 8079 hours.   The plane had a GPS system with an old database.   It also lacked ground proximity detectors that would have warned the pilot when flying at low altitudes.   The plane was scheduled for a systems upgrade later in the year.   The weather report during the accident indicated cloudy atmosphere with high humidity and patchy fog.   A pilot for the plane ahead of the Hendrickss Motorsports plane claimed that the climate under the clouds had relatively high visibility up to 2 miles.   However, the weather kept on shifting during the flight. Reference NTSB, (2006). Accident Investigations NTSB National Transportation Safety Board. App.ntsb.gov. Retrieved 15 February 2017, from https://app.ntsb.gov/investigations/fulltext/AAB0601.html

The Taino and the Spanish Essay -- History Spanish Historical Papers

The Taino and the Spanish Cristà ³bal Colà ³n landed on an unknown island in the Caribbean on October 10, 1492. He planted banners in the beach claiming the land for the Spanish throne. Colà ³n’s perceptions and interactions with the indigenous people, the Taino, sparked the events that lead to the colonization of the Americas. Colà ³n’s perceptions of the Taino were misinterpreted by him. His misconceptions about the Taino were built from a compilation of his own expectations, readings of other explorers, and strong religious influence in Western Europe. The Taino also misunderstood the Spanish as well. Their false beliefs about the Spanish were driven by their religious beliefs as well as their mythology. Through misunderstandings backed by the religions, physical appearances, and the histories of both the Taino and the Spanish, the Taino believed that the Spanish were god-like figures that fell from the sky, while the Taino were perceived by the Spanish as simplistic, uncultured natives, that would be easily converted to Christianity and used as servants (Wilson, Hispanola p. 48-49).1 To better comprehend these events one must look at the preceeding events in both the lives of the Taino and The Spanish. Before the time of Cristà ³bal Colà ³n, Spain had recently had several encounters with colonization. They had taken over the kingdom of Granada and the Canary Islands. These colonizations gave Spain their model for subsequent colonizations. The dominance of Christianity in the colonizations was quite evident. Religious unity was believed to be required for social order and was a premise for the exercise of power (Quesada, Implicit Understanding p. 97-107).2 This relates to the Taino in that the Spanish believed the Taino would be c... ... encountered the Taino is dependent upon the understanding the religious and historical backgrounds of both. One must understand that the mythology of the Taino, the expectations of the Spanish, and the appearances of both played a major role in the reactions of these two cultures when they collided. Works Cited Colà ³n, Cristobal. The Diario of Cristà ³bal Colà ³n’s Voyage to America, Transcription and Translation Oliver Dunn and James E. Kelley Jr. de Las Casas, Bartolomà ©. The Devastation of the Indies: A Brief Account. Translation, Briffault, Herma, Johns Hopkins University Press, Baltimore and London  © 1992. Quesada, Miguel. Miguel Quesada, â€Å"Spain 1492: Social values and structures,† Stuart Schwartz, ed. Implicit Understandings, Cambridge University Press. The Mission. Directed by Joffà ©, Roland. Written Credits, Bolt, Robert. Genre, Drama.  ©1986.

U.S. Economy in the 19th Century

Peter Hart History 1:00-1:50 U. S. Economy in the 19th Century The Industrial Revolution first took place in Britain where it spread like wild fire. Eventually it made its way to America in the late 1800’s to the 19th century where it would eventually change America in every aspect. The American Revolution began because of a single British man named Samuel Slater who brought over manufacturing technologies. The creation of the cotton gin by Slater would soon be the beginning of the Industrial Revolution.The Industrial Revolution brought many new ideas and inventions that made the economy boom. The North would be the first to start the Industrial Revolution while the South stayed true to their old ways; agriculture. The effects of the Industrial Revolution put a strain on both the South and the North. On top of all of this, many changes were being made in this time period such as transportation, manufacturing, and communications. All of these changes transformed the daily lives of Americans as much as it did as any other historical event that has happened in history.Because of this major event, many effects were being taken place; Unions, working conditions and labor itself were accounted for the changes in the 19th century. The North started out as a commercial industry where trading and selling was a big part of American life. Before the Industrial Revolution hit America, people made all of their goods/products in their homes. Factories weren’t that prominent in the North until the Industrial Revolution came by. Technological advancements were nowhere to be found because they were used to making everything at home by hand.The South was farther behind in innovations than the North itself. They were strictly agricultural and farming. In due time though, a man named Samuel Slater brought over new manufacturing technologies from Britain to the United States where it would start the Industrial Revolution. From there, many more inventions were created such as the steamboat by Robert Fulton which marked the beginning in technological innovations. This invention would make transportation of goods and services quicker and more effectively. Another invention during this time period was the telegraph. The telegraph was reated by Samuel Morse. This invention was created in 1837 which allowed America to send messages to international countries all around the world. The new inventions being created in America would lead America in a direction of prosperity and a dominant force in production and at the same time agricultural ways. America would eventually emerge as the center of industry and agricultural in the late 19th century. As an effect of the Industrial revolution, population tripled, farming doubled in the amount of work due to technological inventions such as the steel plow by John Deere.This invention allowed farmers to plow fields faster and plow more fields without having to change the iron plow every time they uproot the grou nd. Due to this invention, more workers were needed to harvest the crops when the time came. Fortunately, a certain invention was made that helped the harvesting process go quicker and more efficiently. This invention was known as the reaper which was made in 1831 by Cyrus McCormick. Certain inventions helped working production go a lot faster than it was before the Industrial Revolution started. The U. S.Patent Office had a record of 276 inventions during the 1790’s, during the 1890’s a record of 235,000 inventions were registered. At first, the South was resistant against this new generation of inventions and industrialized cities. Ultimately, the South would fall under the new ways of the North. From 1880 to 1900, the amount of cotton mills increased dramatically; 161 to 400 in less than decade. As the need for workers rose, so did the amount of cotton. The amount of cotton increased by eightfold while the amount of workers increased by fivefold.All of these increas es resulted in the creations of new inventions. As production increased, so did the need for labor. But as labor increased, so did changes in working conditions, labor itself, and Unions were created on behalf of all of the workers. Even though all of these inventions prospered America, working conditions in the factories that were producing goods such as steel, cotton fabric, and other goods were bad and harmful for the workers. The life of a 19th-century American industrial worker was far from easy. Even in decent times, wages were low, hours were long, and working conditions hazardous.Little of the wealth which the growth of the nation had produced went to its workers. The situation was worse for women and children, who made up a high percentage of the work force in some industries and often received but a fraction of the wages a man could earn. Periodic economic crises swept the nation, further eroding industrial wages and producing high levels of unemployment. At the same time, the technological improvements, which added so much to the nation's productivity, continually reduced the demand for skilled labor.Yet the unskilled labor pool was constantly growing, as record numbers of immigrants, 18 million between 1880 and 1910, entered the country, looking for work. Before 1874, when Massachusetts passed the nation's first legislation limiting the number of hours women and children factory workers could perform to 10 hours a day, there was literally no labor legislation that existed in the country. It was not until the 1930s that the federal government would become actively involved. Until then, it was left to the state and local authorities, few of whom were as responsive to the workers as they were to wealthy industrialists.The laissez-faire capitalism, which dominated the second half of the 19th century and fostered huge concentrations of wealth and power, was backed by a judiciary which time and again ruled against those who challenged the system. For mil lions, living and working conditions were poor, and the hope of escaping from a lifetime of poverty was slight to none. As late as 1900, the United States had the highest job-related death rate of any industrialized nation in the world. Most industrial workers still worked a 10-hour day (12 hours in the steel industry), yet earned from 20 to 40 percent less than the minimum deemed necessary for a decent life.The situation was only worse for children, whose numbers in the work force doubled between 1870 and 1900. On top of working in harsh conditions, workers had to face low wages and long hours that consisted of a 60 hour week load. These conditions were outrageous and then eventually led to the forming of unions. The first major effort to organize workers' groups on a nationwide basis appeared with The Noble Order of the Knights of Labor in 1869. Originally a secret, ritualistic society organized by Philadelphia garment workers, it was open to all workers, including blacks, women a nd farmers.The Knights grew slowly until they succeeded in facing down the great railroad baron, Jay Gould, in an 1885 strike. Within a year they added 500,000 workers to their rolls. The Knights of Labor soon fell into decline, and their place in the labor movement was steadily taken by the American Federation of Labor (AFL). Rather than open its membership to all, the AFL, under former cigar union official Samuel Gompers, focused on skilled workers. His objectives were straight-forward and simple: increase wages, reduce hours and improve working conditions.Per se, Gompers helped turn the labor movement away from the socialist views earlier labor leaders had supported. Due to the capital not granting their goals, riots started to break out. A certain riot known as the Great Rail Strike of 1877 was taken place because of 10 percent cut in wages. This started a line of riots that spurted throughout the country. Finally, after many riots and negotiating with the bosses at the factorie s, conditions in factories were better and hours were decreased and wages were increased.Child labor laws were forced upon everyone, while women were given the chance to have equal opportunities and equal wages as men. All of these effects of the Industrial Revolution played a vital role in forming what is now known as America today. The Industrial Revolution led America in a way that forever changed it. It was one of the most historic events to ever happen in American history. Due to new inventions and ideas, America was led into an Industrial Revolution. With the Industrial Revolution came more jobs and Unions to protect the people in the factories from harsh working conditions, long hours, and small wages. .

Pricing Options Using Binomial And Trinomial Methods - Free Essay Example

Sample details Pages: 10 Words: 3083 Downloads: 10 Date added: 2017/06/26 Category Finance Essay Type Compare and contrast essay Did you like this example? Published in the 1970s, the Black-Scholes-Merton model provided an entirely new definition for the financial option market, half a century later the Binomial tree option pricing model was published, and that is the true key that allows the option market to be generalized to the world. Based upon the Binomial model, the Trinomial option pricing model was built to reduce possible errors and persons thus expected it to be a better approach. Still how much better is the Trinomial model, and is it worth spending the time on calculations? These will be the key comparisons provided in this dissertation. Don’t waste time! Our writers will create an original "Pricing Options Using Binomial And Trinomial Methods" essay for you Create order The comparisons are based upon computer calculating time used, and approximation error. An illustrative example is used to build the data base for further comparison of the convergence speed of these two models. All the values are calculated using the Matlab program and Casio calculators in order to provide examples of the assumption that the Trinomial option pricing model is a better model in reducing the approximation error, but takes much longer than the Binomial tree model to get the results. Chapter 1 introduction The emergence of financial derivatives in the 1970s marked a highly significant and exciting event in the history of finance. Options trading began in the United States and European markets in the late eighteenth century, and over the last 20 years, options played a key role in all financial derivatives. The option price was an old question for the financial world. Back in the 1900s Louis Bachelier published his academic dissertation à ¢Ã¢â€š ¬Ã…“ThÃÆ' ©orie de la speculationà ¢Ã¢â€š ¬? (Theory of Speculation), which became known by the public as the milestone of modern finance. The à ¢Ã¢â€š ¬Ã…“random walk theoryà ¢Ã¢â€š ¬?, which built a random model of the stock priceà ¢Ã¢â€š ¬Ã¢â€ž ¢s changing pattern and how it follows in the stock market, was first applied in his paper. In 1964, Paul Samuelson (Nobel Prize in Economic Science winner) revised L.Bachelierà ¢Ã¢â€š ¬Ã¢â€ž ¢s model, and instead of the stock price he used stock returns to eliminate the negative figu res which might occur in L.Bachelierà ¢Ã¢â€š ¬Ã¢â€ž ¢s model. Based upon this new model P.Samuelson also studied the Call Option pricing problem, and built a pricing equation for it. Although the equation was quite a beauty to watch, it could not be used in real world dealings since two of the main factors depended upon the investorà ¢Ã¢â€š ¬Ã¢â€ž ¢s personal predilection. Futures and options are traded actively on many exchanges throughout the world. Before any certain systematization models of the option had been created it was impossible for people to evaluate any kind of option price in a common way. Any approximations of the price based traderà ¢Ã¢â€š ¬Ã¢â€ž ¢s personal experience would well likely result in mistakes. The only method to maximize the good of the option price would be to build a standard and systematization model and find the quantification of the option trading. This was an important event in the financial world at that time. Since the emergent of optio n trading, and especially of securities options trade, researchers have been busy in the studies of options pricing. In 1973, Fischer Black and Myron Scholes published à ¢Ã¢â€š ¬Ã…“The Pricing of Options and Corporate Liabilitiesà ¢Ã¢â€š ¬? at the University of Chicago, where they presented the famous Black-Scholes model for options pricing (B-S model for short). They derived a partial differential equation, which governs the price of the option over time. Once it has been published, the B-S model received strong responses and gained a breakthrough in this field. While some researchers conducted thorough tests on the modelà ¢Ã¢â€š ¬Ã¢â€ž ¢s accuracy, many others presented various opinions on the problems in the model and expanded on them for the purposes of improvement and extension. Because of this glary partial differential equation and all of the contribution that it had created, M.Scholes and R.Merton (F.Black was deceased) both won the Nobel Prize for Economics. In 1 979, Cox, Ross and Rubinstein published a paper called Option Pricing: à ¢Ã¢â€š ¬Ã…“A Simplified Approachà ¢Ã¢â€š ¬?, and in a simple manner obtained the pricing formula using the Binomial model, which was applied widely. This is the event that really changed the option trading market because it made option trading more transparent to most traders, and advanced the improvement of the market. During the option, the trading market developed more and more different sorts of option models, with the most famous and widely used models being the European option and American option. As these two options were named, they were mainly applied in Europe and America and the main difference between the two options is when the option will be fulfilled (I will fully explain this at a later stage). The Binomial option pricing model is essentially a Binomial Tree which shows possible values that an underlying asset or stock initial stock price can take, and the resulting value of the option pr ice at each individual stage of the asset. The main idea of the tree is constructed by assuming that the stock can only go up or down by a factor related to the length of time period, and volatility of the stock. Trinomial model was developed by Prelim Boyle in 1986; it is an adjusted and improved version of the Binomial Tree. Instead of assuming the stock can only go up or down, the Trinomial Tree allows a third choiceà ¢Ã¢â€š ¬Ã¢â‚¬ the stock remains constant. Compared to the Binomial and Trinomial tree model, the Black-Scholes model is a more mathematical and theoretical model: V = SN (d1) à ¢Ã¢â€š ¬Ã¢â‚¬Å" N (d2) (Will be explained at later stage) Although the binomial option pricing model and trinomial tree values converge on the Black-Scholes formula value as the number of time steps increases. With these two simplified methods the option pricing theory and option market became more generalized and easier for the public. With the time flows, the option market began to prevail all over the world, and therefore more and more specific different types of options were created to adapt to the disparate country. In this dissertation I will mainly study and present the relation and difference between the Black-Scholes model, the Binomial Option Pricing model and the Trinomial Tree model, in both a mathematical and financial way. Chapter 1: This chapter is mainly about the Black-Scholes modelà ¢Ã¢â€š ¬Ã¢â€ž ¢s differential equation, including every valuable deduction I provide a few interesting examples to give a straight forward view of this method. Chapter 2: In this chapter I will explore the Binomial pricing model with European and American options. By presenting the formulas and equations I will study how to calculate the option price and explain some basic financial terms. At the main time I will also compare the results of the Binomial Tree model to the Black-Scholes model. Chapter 3: In this chapter I will demonstrate the Trinomia l model with examples and large amount of figures by using the Matlab software. The European and American options will be compared with the Trinomial model. Chapter 4: In the last chapter in my dissertation I will look at how effectively the Trinomial tree model is improved based on the Binomial model. The Matlab code I wrote will help me process this comparison up to a million steps. This will be my thesis of this dissertation and this project. 1.1 Risk Many of the valuation and risk management principles apply across all financial options. In this section, I will first briefly introduce some basic concepts and features of risk management and financial derivatives, especially the option pricing problems. RiskUncertainty of the result The risks obtained and a personà ¢Ã¢â€š ¬Ã¢â€ž ¢s unexpected profit is the same as bringing loss or even damage to a person. In the financial market, risk is ubiquitous with: asset risk (stock), currency risk (exchange rate): credit risk, and so on. There are two ways of facing the risks. Risk Avoidance Risk-taking The process of selecting investments with higher risk in order to profit from an anticipated price movement, is called speculation. Financial derivatives are types of risk management instruments whose payoff depends upon the behaviour of the underlying assets. The most common derivatives are forward contracts, futures and options. Forward contract: A cash market transaction in which delivery of the commodity is deferred until after the contract has been made. Although the delivery is made in the future, the price is determined  on the initial trade date. The party agreeing to buy the underlying asset in the future is called a long position, and the party agreeing to sell the asset in the future is called a short position. The value of a forward position at maturity depends upon the relationship between the delivery price (K) and the underlying price (ST) at that time. For a long position this payoff is: fT = ST à ¢Ã‹â€  K For a short position, it is: fT = K à ¢Ã‹â€  ST Forward contract is normally traded over-the counter, OTC. Futures contracts are very similar to forward contracts, except they are not exchange-traded or the contract is standardized, and thus does not have the interim partial payments due to marking to market. Before studying the Binomial Tree method, I will look at what options are. 1.2Options An option is a derivative financial instrument that gives the buyer or holder the right, but not the obligation, to buy or sell an underlying financial asset or commodity. The buyer of the option gains the right, but not the obligation, to engage in some specific transaction on the asset. An option which conveys the right to buy something is called a call option, and an option which has the right to sell is called a put option. The reference price at which the underlying may be traded is called the exercise price or strike price. Most options have an expiration date. The process of activating an option is called exercise. If the option is not exercised by the expiration date, it becomes void and worthless. The options and related concepts can be classified into the following types: 1. Exchange-traded options Exchange-traded options (also called listed options) are a class of exchange-traded derivatives. Exchange traded options have standardized contracts, and are set tled through a clearing house with fulfillment guaranteed by the credit of the exchange. Since the contracts are standardized, accurate pricing models are often available. Exchange-traded options include:[4][5] stock options, commodity options, bond options and other interest rate options stock market index options or, simply, index options and options on futures contracts callable bull/bear contract 2. Over-the-counter Over-the-counter options (OTC options, also called dealer options) are traded between two private parties, and are not listed on an exchange. The terms of an OTC option are unrestricted and may be individually tailored to meet any business need. In general, at least one of the counterparties to an OTC option is a well-capitalized institution. Option types commonly traded over the counter include: Interest rate options Currency cross rate options, and Option on swaps or swaptions. 3. Option styles Some options with complex financ ial structures are called exotic options, and these include: Barrier option any option with the general characteristic that the underlying securitys price must pass a certain level or barrier before it can be exercised. Double barrier option-A double barrier option involves a mechanism where if either of two limit prices is crossed by the underlying, the option either can be exercised or can no longer be exercised. Cumulative Parisian barrier option à ¢Ã¢â€š ¬Ã¢â‚¬Å"A cumulative Parisian barrier option involves a mechanism where if the total amount of time the underlying asset value has spent above or below a limit price, the option can be exercised or can no longer be exercised. Standard Parisian barrier option-A standard Parisian barrier option involves a mechanism where if the maximum amount of time the underlying asset value has spent consecutively above or below a limit price, the option can be exercised or can no longer be exercised. Binary option-A binary opt ion pays a fixed amount or nothing at all, depending on the price of the underlying instrument at maturity. An Asian option is an option where the payoff is not determined by the underlying price at maturity but by the average underlying price over some pre-set period of time. Bermudan option an option that may be exercised only on specified dates on or before expiration. For a cleaner view, I summarized various types of options in to a table below: standard of classification Types of options Option buyerà ¢Ã¢â€š ¬Ã¢â€ž ¢s right Call option and put option Excises time of option buyers. European option and American option intrinsic value In the money options, out of the money options and at the Money options Trading place Exchange-traded options and OTC options(Over-the-counter) Structures of options exotic options and vanilla options Margin of option. Unsecured and secured options There are two main reasons why investors would use options: to reduce risk and to gain more profit such as to speculate and to hedge. These will be discussed later. There are two main types of options, one is the European option the other is American option. The European option can only be exercised on the expiry date, while the American options may be exercised at any time before or on the expiry date. Assume k is the strike price; T is the expiry date, and the payoffs Vt: Vt = (St-K) + (call option) Vt= (K-St) + (put option) In this case, S is the spot price of the underlying asset. (t=T) Next, I will discuss the option pricing problems. Options are a type of bond derivative; its price depends upon the movement of underlying assets. The change of price of underlying assets is random because it is a kind of risk asset. Once the price of underlying assets is confirmed, then the option price can be confirmed too. This is saying that at the time the price of the underlying asset is St, the option price w ill be Vt and there exists function V(S, t) so that Vt= (St, t). At the expiry date, the value of option VT is the payoffs. VT = (ST-K) + (call option) VT= (K-ST) + (put option) The option pricing problem is to calculate V=V(S, t), (0, V(S, T) = Especially when t=0, and let the stock price is S0, what is the premium? p=V (S0, 0) =? Therefore, the option pricing problem is a working backward problem. 1.3 Types of investors. Now, I will look at three types of people in the stock market Hedger: An individual who enters into hedging trades. Hedging is a way of reducing risk. Hedgers want to avoid exposure to adverse movements in the price of an asset. For example: A Chinese company needs to pay a British supplier one million pounds after 90days.The company is facing the risk of fluctuation of exchange rate. If there is a big exchange-rate rise, this will affect its anticipated profit because of the extra cost. If the exchange rate is 12.5 Yuan / pound. The company considers two Hedging plans in view of the probability that the exchange rate may rise. Plan 1. Buy a forward contract stated to use 12625000 Yuan to purchase one million pounds after 90days. Plan 2. Buy a call option contract stated to use 12500000 Yuan to purchase one million pounds after 90days and pay a 250000 Yuan premium (as 2%). I now list the two hedging strategies in the table below: Spot exchange rate (Yu an/pound) 90dayslater exchange rate(Yuan/pound) Without hedging Forward contract Purchase call option contract 12.5 Increase to13 13million Yuan 12,625,000 Yuan 12,750,000 Yuan Decrease to12 12million Yuan 12,625,000 Yuan 12,250,000yuan According to the statistics provided, it can be seen that there will be extra costs when the exchange rate rises if the company does not use any hedging strategies. The costs are fixed after90days if they choose the forward contract but they may miss the chance that if the exchange rate goes down, they will gain from unforeseen profit .Meanwhile the company will prevent extra costs (rise in exchange rate) and gain profits (decrease in exchange) if they choose to purchase the call options contract, but they have to pay the premium. Speculator: An individual who is taking a position in the market. Usually the individual is betting that the price of an asset will go up or that the price of an asset will go down. Options like futures provide a form of leverage. For a given investment, the use of options magnifies the financial consequences. Good outcomes become very good, while bad outcomes may cause the whole initial investment being lost. For example, assume the stock price of X at 30th of April is à ¯Ã‚ ¿Ã‚ ¡666. The stock price may go up in August, and there are two investment strategies that investors may take. Investors spend à ¯Ã‚ ¿Ã‚ ¡666000 cash on 1000 shares of stocksà ¯Ã‚ ¼Ã¢â‚¬ º Investors purchase a call option contract which ends on 22nd of August: strike price is à ¯Ã‚ ¿Ã‚ ¡680, 1000shares, assume investors paid à ¯Ã‚ ¿Ã‚ ¡39000 premium for that. We now analyze the investorà ¢Ã¢â€š ¬Ã¢â€ž ¢s investment return in two different situations. (Ignore the interest rate) Case 1.If the stock price rises up to à ¯Ã‚ ¿Ã‚ ¡730 on 22nd August. For strategy A: The investor sells stocks on 22nd August to get à ¯Ã‚ ¿Ã‚ ¡730000 in cash. Return = (730000 -666000)/666000=9.6% For strategy B: The investor exercises his option and gets profit: Profit=730000-680000=à ¯Ã‚ ¿Ã‚ ¡50000 Return = (50000-39000)/39000 Case 2.If the stock price drop to à ¯Ã‚ ¿Ã‚ ¡660 instead of rise on 22nd August. Strategy A: Loss =666000-660000=à ¯Ã‚ ¿Ã‚ ¡6000 Return= (660000-666000)/666000 Strategy B: The investorà ¢Ã¢â€š ¬Ã¢â€ž ¢s profit is=0 He will lose à ¯Ã‚ ¿Ã‚ ¡39000, and the percentage loss is 100%. Arbitrageur à ¢Ã¢â€š ¬Ã¢â‚¬Å" An individual engaging in arbitrage. Arbitrage à ¢Ã¢â€š ¬Ã¢â‚¬Å" A trading strategy that takes advantage of two or more securities being mispriced relative to each other. Arbitrage opportunities cannot last for long. As arbitrageurs interfere in the market, the forces of supply and demand will bring the market back to equilibrium. Therefore, in my project most of the arguments concern financial derivatives such as option prices, and, forward contracts will be based on the assumption th at no arbitrage opportunities exist. 1.4 The Black Scholes Merton model There are seven important assumptions we use to derive the Black Scholes Model: It assumes that percentage changes in the stock price in a short period of time are normally distributed. It is defined as expected return on stock per year and as volatility of the stock price per year. This assumption suggests returns on the underlying stock are normally distributed, which is reasonable for most assets that offer options. It is possible to buy and sell any amount of stock, this includes short selling. There are no transactions costs , taxes or other fees. The stock pays no dividends during the options life. There are no arbitrage opportunities. Markets are efficient and Security trading is continuous. The risk free interest rate is constant and known.(