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Words 295

Pages 2

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation. The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option pricing are: The Black-Scholes model, binomial trees and Monte Carlo Simulation.

The three different methods of option…...

... 2 let u=z- , then e 1 z 2 2 dz du 1 and z = u= and z=- u=- - =- + dz Now we make the substitution u z and the integral becomes u 2 1 12 1 z 1 z 2 u z du u 1 1 2 2 dz dz e e e 2 du dz 2 2 u 2 z 12 u 2 but the function f u e is symmetric about zero, i.e. f u f u it follows that 12 12 u u 1 1 2 e du 2 e 2 du N 2 hence we obtain 1 t 2 1 1 z2 t z 2 e dz e 2 N as claimed. e 2 7 Theorem (Key Result for option pricing): Let V ~ log normal m, s 2 so that the standard deviation of the log of V is s var log e V Then the expectation E max V K ,0 is given by the formula E max V K ,0 E V N d1 K N d 2 where 1 log e E V / K s 2 2 d1 s 1 log e E V / K s 2 2 d s d2 1 s 8 proof Since V is lognormal we have E V e 1 m s 2 2 1 It follows that ln E V m s 2 2 1 and that m ln E V s 2 2 the variable z ln V m s has the standard normal distribution because ln V N m, s 2 The variable V can be written as V exp ln V exp sZ m We can express the expectation as an......

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...Individual’s Assignment Atlantic Computer: A Bundle of Pricing Options As Atlantic computer was largest manufacturer of servers and other hi-tech product, Jason Jowers has been assigned the task of developing the pricing structure for the Atlantic Bundle, a unique combination of the TRONN server along with the software tool - Performance Enhancing Server Accelerator – called PESA. The TRONN server has been specifically designed to address the current US market demand. In conjunction with the PESA, the TRONN ‘s performance capacity is four times faster than standard speed. Atlantic has continued to hold a significant portion (20% revenues) of the high-performance sector, but as the continual growth of the internet reached new heights, the demand of a basic server increasing rapidly. Hence, in order to meet the demand of market, the Atlantic company is planning to launch a basic server TRONN with a software tool PESA which will grow up the efficiency of server approximately four times. First of all, apart from choosing the suitable pricing method for Atlantic computers, the broad of this company also need to consider about the lifecycle of their product. Basing on the case of IBM HTTP Server or The server products of Microsoft, it seems that the lifecycle of high tech products is decreasing rapidly nowadays. According to some experts in this field, they believe that the average life expectancy of these products is around 3 or 4 years depending on many factors which......

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...determinants of the option price in the Black-Scholes option pricing model for European options is likely to change the price of a call option. A derivative is a financial instrument that has a value determined by the price of something else, such as options. The crucial idea behind the derivation was to hedge perfectly the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk" (Ray, 2012). The derivative asset we will be most interested in is a European call option. A call option gives the holder of the option the right to buy the underlying asset by a certain date for a certain price, but a put option gives the holder the right to sell the underlying asset by a certain date for a certain price. The date in the contract is known as the expiration date or maturity date; the price in the contract is known as the exercise price or strike price. The market price of the underlying asset on the valuation date is spot price or stock price. Intrinsic value is the difference between the current stock market price and the exercise price or simply higher of zero. American options can be exercised at any time up to the expiration date. European options can be exercised only on the expiration date itself. (Hull, 2012). For example, consider a July European call option contract on XYZ with strike price $70. When the contract expires in July, if the price of XYZ stock is $75 the owner will exercise the option and realize a......

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... Jon M. Huntsman School of Business Master of Science in Financial Economics August 2013 Pricing and Hedging Asian Options By Vineet B. Lakhlani Pricing and Hedging Asian Options Table of Contents Table of Contents 1. Introduction to Derivatives 2. Exotic Options 2.1. Introduction to Asian Options 3.1. Binomial Option Pricing Model 3.2. Black-Scholes Model 3.2.1. Black-Scholes PDE Derivation 3.2.2. Black-Scholes Formula 1 2 3 4 4 5 6 7 3 3. Option Pricing Methodologies 4. Asian Option Pricing 4.1. 4.2. 4.3. 4.4. Closed Form Solution (Black-Scholes Formula) QuantLib/Boost Monte Carlo Simulations Price Characteristics 8 8 10 11 14 5. Hedging 5.1. Option Greeks 5.2. Characteristics of Option Delta (Δ) 5.3. Delta Hedging 5.3.1. Delta-Hedging for 1 Day 5.4. Hedging Asian Option 5.5. Other Strategies 6. Conclusion 16 17 17 19 20 22 25 26 27 32 34 Appendix i. ii. iii. Tables References Code: Black-Scholes Formula For European & Asian (Geometric) Option 1 Pricing and Hedging Asian Options 1. Introduction to Derivatives: Financial derivatives have been in existence as long as the invention of writing. The first derivative contracts—forward contracts—were written in cuneiform script on clay tablets. The evidence of the first written contract was dates back to in nineteenth century BC......

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...determinants of the option price in the Black-Scholes option pricing model for European options is likely to change the price of a call option. A derivative is a financial instrument that has a value determined by the price of something else, such as options. The crucial idea behind the derivation was to hedge perfectly the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk" (Ray, 2012). The derivative asset we will be most interested in is a European call option. A call option gives the holder of the option the right to buy the underlying asset by a certain date for a certain price, but a put option gives the holder the right to sell the underlying asset by a certain date for a certain price. The date in the contract is known as the expiration date or maturity date; the price in the contract is known as the exercise price or strike price. The market price of the underlying asset on the valuation date is spot price or stock price. Intrinsic value is the difference between the current stock market price and the exercise price or simply higher of zero. American options can be exercised at any time up to the expiration date. European options can be exercised only on the expiration date itself. (Hull, 2012). For example, consider a July European call option contract on XYZ with strike price $70. When the contract expires in July, if the price of XYZ stock is $75 the owner will exercise the option and realize a......

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...Three Similar but Different Wars Justin P. Wilson Excelsior College Abstract Wars share similarities in cause, though not all are the same. The same goes for effects. The French & Indian War, Revolutionary War, and the War of 1812 all share this. Each war had its similarities but each war had its own outcomes and reasons for the start of the war. Each war was a turning point in the history of the newly independent United States. Three Similar but Different Wars The Revolutionary war, War of 1812, and the French and Indian war had similar yet different effects on the new United States. The young United States would learn new ways of fighting and dealing with conflicts. Each war had its similarities but each war had its own outcomes and reasons for the start of the war. Each war was a turning point in the history of the newly independent United States. The French and Indian war was a starting point for the American Revolutionary War. The War of 1812 was a war to expand and verify territory borders. All the wars involved the British, French, and the Americans. The War of 1812 and the French and Indian War involved the Indians. Each war had a different treaty or agreement that settled the disagreement and evolved the way the countries fought and handled disputes. The French and Indian war was composed of three different phases. The leading causes started back in Europe with the King George’s War, which took place in between the years of 1744 and 1748. The first...

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...Finite Difference Methods 1 Finite Difference Methods A finite difference method obtains a price for a derivative by solving the partial differential equation numerically Example: • An American put option on a stock that pays a continuous dividend yield q. ƒ ƒ 2ƒ 2 2 (r q) S ½ 2 S rf t S S • Finite difference methods aim to represent the differential equation in the form of a difference equation • We form a grid by considering equally spaced time values and stock price values • Define ƒi,j as the value of ƒ at time iDt when the stock price is jDS 3 Implicit Finite Difference Method In ƒ ƒ 1 2 2 2ƒ (r q) S S rƒ 2 t S 2 S we set at the node (i,j): ƒ ƒ i ,j 1 ƒ i ,j 1 S 2DS and: 2 ƒ ƒ i ,j 1 ƒ i ,j ƒ i ,j ƒ i ,j 1 DS 2 DS DS S 2 ƒ ƒ i ,j 1 ƒ i ,j 1 2ƒ i ,j 2 S D S2 or If we also set ƒ ƒ i 1,j ƒi ,j t Dt we obtain the implicit finite difference method. Re-arranging we get: a j ƒi ,j 1 b j ƒi ,j c j ƒi ,j 1 ƒi 1,j where: The Boundary Conditions • Example: American put fN,j=0 fN,j=0 N,j a j ƒi,j 1 b j ƒi,j c j ƒi ,j 1 ƒi 1,j • N-1 equations • N-1 unkowns • Exactly 1 solution fN,j=max(K-jΔS,0) f0,j=K 6 Explicit Finite Difference Method If f S and 2 f S 2 are assumed to be the same at the (i 1,j ) point as they are at the (i,j ) point we obtain the explicit finite difference method f i 1, j 1 f......

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...DIFFERENT KINDS OF METHOD Different Kinds of Method COMPUTERS AND INFORMATION PROCESSING CIS/319 Different Kinds of Method Best Method for Input: \ The best method for printed questionnaires is the optical data reader. It is easier to read, and it is more accurate reading. Just put the answer you choice to be in the bubble. When the reader is place in a machine, it reads what you put. If the answer is wrong, it will put a red mark. The best method for the telephone survey is the operator data entry. With this method, any survey will be more accurate. Because, the operate will be able to give a clear question to the caller, and the caller will be able to respond to the question with no confusion. As this is happening the operator will enter the caller answer to the system with no errors. The best method for the bank checks is the automatic teller machine. This system is more communing use around the world. It is fast and simple to use. Just swipe the card and it will automatic deduct from the checking account. Every card has a security code. Only the card holder will be able to do the transaction. The best method for the retail tags is the bar code scanner. Every items that has a tag on it, has to have bar code scanner. It is easier to tack on the system. On how many items goes out and how many are on stock. The best method for the long documents is the optical data reader. Any long documents can be converting to a small data...

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...Atlantic Computer: A Bundle of Pricing Options 1. Determine the price for two Tronn servers plus PESA according to the following pricing methods: * Status-quo pricing * Competition-based pricing * Cost-plus Pricing (Hint: footnote # 5) Note: Jowers makes a conservative estimate that two Tronn servers plus PESA equals the performance of four Ontario Zink servers. To calculate the prices you could use the spreadsheet file included in the course content (Week 3). 2. Determine the Value-based price for two Tronn servers plus PESA. Follow these steps use the spreadsheet file included in the course content (Week 3): 1. Calculate the costs of running for a year 4 Ontario Zink serves, 4 Atlantic Tronn servers, and 2 Atlantic Tronn servers with PESA 2. Calculate the annual savings of owning 2 Atlantic Tronn servers with PESA 3. Determine the Value-based price for two Tronn servers plus PESA assuming that 50% of the savings will be passed to the consumer. At the end of the session each team should raise their card with an answer. 4. How is Cadena’s sales force likely to react to your recommendation? What can Jowers recommend to get Cadena’s hardware-oriented sales force to understand and sell the value of the PESA software effectively? In conclusion, based on our analysis we recommend using Competition Based Pricing because this approach acknowledges competitor prices and gives superior services at a same rate.......

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...Option Pricing, Interest Rate Risk in U.S Diana PĂUN & Ramona GOGONCEA (2013). Interest Rate Risk Management and the Use of Derivative Securities. Economia Seria Management. Retrieved from: <http://www.management.ase.ro/reveconomia/2013-2/4.pdf> The study by these two authors aims at demonstrating how derivative financial instruments can be utilized to prudently manage interest rate risk majorly faced by numerous banks and financial institutions as well as enable the efficient application of monitoring and control tools. There are a couple of risk management methods at the disposal of banks including both balance sheet and off the balance sheet such as the gap method of managing interest rate risk for purposes of controlling short-term rates exposure, combined with derivatives such as options to manage the residual interest rate exposures. Interest rate risks emanate from interest rates sensitivity differentials of capital outflows and inflows. Due to the common view or misconception that high interest rates are the best way of fighting inflation, banks’’ engaging in monetary policy. Financial institutions play a major role in influencing interest rates since they engage in releasing capita to the public by buying assets in the primary markets and selling securities in the secondary market so as to fund purchase of assets. Furthermore, any interest-bearing asset for instance a loan or bond may face interest rate risk caused by changes in the value of assets......

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...studio is obtained from the popular movies. If Arundel had the option to choose to produce the sequel movie out of all the movies released by a studio they have a contract with, they could decide producing only the one with high return and achieve a positive NPV for this business, provided that the studio and Arundel will agree on a set and appropriate price per movie. In this scenario, it is also essential to buy the rights on the movies before they are even made in order to achieve information symmetry, where all relevant information is known to all parties involved. Otherwise Arundel would find itself in a risky situation where if negotiated per movie, the studio would have access to more information in comparison to Arundel and also negotiating on the price of a movie would be based on perceptions of each party because it would also have to depend on artistic judgements in addition to commercial considerations. Arundel doesn’t want to be in a position, where an artistic judgement was required in lieu of its investors. Valuing the PerFilm Price and Calculation Details The maximum per‐film price for the sequel rights that Arundel Partners should pay is $5.12M. We assume that Arundel Partners will purchase a portfolio of films similar to one used in the analysis. The average net inflow of hypothetical sequels ($21.57M) is used to figure out the value of the state variable for the real options model. The state variable is the average net inf......

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...Arbitrage: The Key to Pricing Options by Ed Nosal and Tan Wang A rbitrage is the act of simultaneously buying and selling assets or commodities in an attempt to exploit a profitable opportunity. Although the idea behind arbitrage is fairly simple, it is quite powerful because the ability to exploit such opportunities is needed for markets to operate efficiently. Arbitrage ensures, for example, that buyers and sellers of foreign exchange can be assured that they are getting the “correct” rates for the currencies they are buying and selling independent of the national foreign-exchange markets they happen to be using. When markets are efficient, the prices of the objects being traded reflect their true value. And having prices reflect true values is important in decentralized economies, such as the United States, since it is the relative prices of various goods, services, and assets that determines how many will be produced, how they will be allocated, and how funds will be invested. If prices did not reflect true value, then the resulting allocation of goods, services, and investment would not be, in general, economically efficient. This Commentary focuses on a particular episode in which the recognition of an arbitrage “opportunity” made financial markets more efficient. It wasn’t a chance to make a profit that got noticed, it was the way the principles of arbitrage could be applied to the problem of correctly pricing options. Once......

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...1. Introduction Transfer Pricing is becoming highly important as soon as a multicorporate enterprise or business is structured across borders. Transfer Pricing deals with structuring international transfer prices within a multicorporate enterprise or business, in particular the evaluation of tangible and intangible assets be-tween business entities within the same multicorporate organisation or, more specifically, the price one segment (subunit, department, division and so on) of one organisation charges for a product or service supplied to an-other segment of the same organisation. Every multicorporate enterprise or business aims at minimising its tax obligations in order to maximise its overall profits. In principal, multicorporate businesses have to pay tax in their respective host countries, based on the share of their profit which arises in (or is allotted to) the respective business in such host country. These host countries can be different in various respects e.g. tax systems, customs duties, currency exchange rates, legislation and so forth. As a result, Transfer Pricing also affects revenue and customs authorities, investors, creditors and alike. The obligation to comply with national and international tax regulations regularly conflicts with the goal of a tax-efficient allocation of profits within a multi-national entities on the one hand and the respective tax legislation which is primarily nationally-focused on the other hand. Thus, an anticipatory business...

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...Selecting a Pricing Method 3 major considerations in price setting : costs of production, distribution, communication set a floor to the price competitors’ prices and the price of substitutes provide an orienting point customers’ assessment of unique features establishes the price ceiling (plafond) Companies select a pricing method that includes 1 or more of these three considerations. We will examine 6 price-setting methods: Mark-up pricing, target-return pricing, perceived-value pricing, value pricing, going-rate pricing and auction-type pricing Mark-up pricing (ajout de marge sur coûts de production): Add a standard mark-up to the product’s costs. Unit cost = Variable cost + fixed cost / unit sales Mark-up price = unit cost/ (1- desired return on sales) Mark-ups are generally higher on seasonal items (to cover the risk of not selling), speciality items, slower-moving items, items with high storage (stockage) and handling (manipulation) costs, and demand-inelastic items, such as prescription drugs. This method works only if the marked-up price actually brings in the expected level of sales. Target-return pricing (objectif de rendement): The firm determines the price that would yield (rapporter) its target rate of return on investment. General Motors has priced its automobiles to achieve a 15-20% of return on investment (ROI). Public utilities need to make a fair ROI use this method. Target-return price = unit cost +......

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...Major Findings: This paper examines the problem of pricing a European call on an asset (Stock) that has a stochastic or variable volatility. Addressing this problem was done by investigating two cases: the first case is to determine the option price when the stochastic volatility is independent of stock price. The second case is to determine the option price when the stochastic volatility is correlated with the stock price. This paper provides a solution in series form for the stochastic volatility option, in addition to a discussion about the numerical methods that are used to examine pricing biases, and an investigation about the occurrence of the biases in the case of stochastic volatility. As for the results obtained, this paper presents interesting results for each of the two cases. When the stochastic volatility is independent of stock price, the results show that the price calculated using Black-Scholes equation is overestimated for at-the-money options and underestimated for deep in-and out-of-the-money options. This overpricing takes place for stock prices within about ten percent of the exercise price. Moreover, it is shown that the degree of the pricing bias can be up to five percent of the Black-Scholes price. For the second case when the stock price is positively correlated with the volatility, the results show that the Black-Scholes formula overprices in-the-money options and underprices out-of-the-money options. On the other hand, when the stock price is......

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