...Question: Discuss how an increase in the value of each of the 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...
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...Question: Discuss how an increase in the value of each of the 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...
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...with stochastic volatility (the Heston Model) Aarhus School of Business and Social Science 2011 2 Acknowledgements My gratitude and appreciation goes to my supervisor Peter Lø chte Jø rgensen, for his kind and insightful discussion and guide through my process of writing. I was always impressed by his wisdom, openness and patience whenever I wrote an email or came by to his office with some confusion and difficulty. Especially on access to the information on certain Danish structured products, I have gained great help and support from him. 3 Abstract My interest came after the reading of the thesis proposal on strucured products written by Henrik, as is pointed out and suggested at the last part of this proposal, one of the main limitations of this thesis may be the choice of model. This intrigues my curiosity on pricing Asian options under assumption of stochstic volatility. At first, after the general introduction of strucutred products, the Black Scholes Model and risk neutral pricing has been explained. The following comes the disadvanges of BS model and then moves to the stochastic volatility model, among which the Heston model is highlighted and elaborated. The next part of this thesis is an emricical studying of two structured products embbeded with Asian options in Danish market and follows with a conclusion. Key words: structured products, Asian options, Black-Scholes model, stochastic volatilty, Heston model, calibration 4 Table of Contents ...
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...buy or sell underlying assets with certain price within a certain/specific period of time (Hull, 2012). The option can be either call (right to buy) or put (right to sell) in the form of American options (exercised any time until expiry date) or European options (exercised on expiry date) as either traded options (standard option contracts) or overt-the-counter options (tailor made options). Due to various choices of options, different option pricing models such as Put-Call Parity, Black-Scholes, Cox-Rubenstein Binominal, Risk-Neutral valuation, the Greeks and others has been developed and applied in current financial market. Black-Scholes Option Pricing Model (BS) BS is designed and introduced by Fisher Black and Myron Scholes in 1973 with the assumptions of the market is efficient, returns are lognormal distributed, no commission or transaction cost is charged, no dividend is paid, no penalties to short selling, terms of European option is used, interest rate is remained constant and known rate (Black & Scholes, 1973). Thereafter, the assumption of no dividends has been relaxed by Robert Merton in the same year....
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...Arundel Partners – The Sequels Project After evaluation of the proposed acquisition of the movie sequel rights, we recommend to offer movie studios as a per-movie price to purchase the sequel rights for their entire portfolio of movies the studios are going to produce over the next year. Arundel should make an offer to buy sequel rights as the average NPV (on a per film basis ) is $5.51 mn (this is the value calculated using real options method). Hence, we should pay a price below $5.51mn. As per informal inquiries made by us, the studios would be tempted to accept the price of $2mn or more and would not even consider a price below $1mn. We propose that we should negotiate for the price of $2mn. This would give us a profit of $3.51 mn per film. The movie studio might (or might not) be willing to sell these rights at this price because it helps the studios mitigate the risk associated with producing the sequel. Also, the fact that there is no liquid market for rights to produce sequels will also drive the price lower on account of lack of demand. Average value of Sequel rights per film using DCF Analysis Average value of sequel rights per film across all studios 1. There are 99 films in the portfolio. Arundel Partners will only produce films for which hypothetical NPV is greater than zero. Hence, we calculate NPV of each film at Year 0. Since the exhibits state that the values are already preset values, we have not rediscounted them. NPV (At year 0)...
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...The Black–Scholes /ˌblæk ˈʃoʊlz/[1] or Black–Scholes–Merton model is a mathematical model of a financial market containing certain derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options. The formula led to a boom in options trading and legitimised scientifically the activities of the Chicago Board Options Exchange and other options markets around the world.[2] lt is widely used, although often with adjustments and corrections, by options market participants.[3]:751 Many empirical tests have shown that the Black–Scholes price is "fairly close" to the observed prices, although there are well-known discrepancies such as the "option smile".[3]:770–771 The Black–Scholes was first published by Fischer Black and Myron Scholes in their 1973 paper, "The Pricing of Options and Corporate Liabilities", published in the Journal of Political Economy. They derived a stochastic partial differential equation, now called the Black–Scholes equation, which estimates the price of the option over time. The key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way, and consequently "eliminate risk". This hedge is called delta hedging and is the basis of more complicated hedging strategies such as those engaged in by investment banks and hedge funds. The hedge implies that there is a unique price for the option and this is given by the...
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... is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’ Signed …………………………………………….............. Date …………………………………………….............. ii 1. ABSTRACT Real options analysis can be used by investors to determine the value of potential investments that offer an owner the right but not the obligation to exercise a strategic decision at a predetermined time and price. Tools which are popular for valuing financial options, such as Black Scholes analysis, can be used to determine the value of real options. However, Black Scholes analysis has been criticized for its unintuitive approach to real options and also for its difficulty in determining the volatility of an investment. The purpose of this thesis is to investigate whether or not a second order moment approach can...
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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 in Mesopotamia...
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...Should Merck license the compound? Merck would be responsible for 1) the approval of Davanrik 2) the manufacture of Danavrik 3) marketing of Danavrik Merck would pay LAB for 1) initial fee 2) royalty on all sales 3) make additional pymts as Danavrik completed each stage of approval process (3 Phases) Additional facts: approval process should take 7 years patent will cover 17 years (7 of approval process nad 10 yr period of exclusivity beginning in yr 7) 1 Assumptions: All Cash flows are expressed as after tax present values discounted to time zero, including capital expenditures At any point "failure," investment decision is to stop funding Assuming Standard deviation of 0.5 Using T= 7 years in Black-Scholes Valuation 2 Decision Tree See worksheet "Decision Tree" 3 Detailed description of Real Option Technique "First, using a decision tree, I came up with a simple expected value of $13,980,000 based on the costs to complete each phase, the probabilities of completing each phase, and the costs and probabilities associated with failure at each step in the approval process. The expected value of successful completion with Depression only was $36,390,000, for weight only $1,200,000 and for both $26,880,000. The expected value of failure (including failure at any phase) was ($59,490,000). Next, I calculated the Valuations of each successful outcome using the decision tree analysis and the spectrum of outcomes with an asymetric distribution of rewards....
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...WHEN TO ISSUE THE NONVOTING CLASS A STOCK MLCM believed that market condition would deteriorate further during the week of October 5, and strongly recommended that Spiegel price the Class A shares in the next 48 hours or postpone the offering indefinitely. Now whether MLCM was right or not it will be judged by real option valuation. We showed the decision analysis by using both the FCF and the net cash flow. We have used three options such as a. Timing option, b. Decision Tree Analysis, and c. Option to Wait (Black Scholes Model). |1. Timing Option | We have used Timing Option to calculate the NPV if the stocks were issued immediately. Here we consider FCF in the three methods. Here, we assume 30% probability for high demand, 40% for average and 30% for low demand. We calculated the net annual cash flow for each scenario and then calculated the expected NPV for the issuance. |Demand |Probability |Annual FCF |E(NPV) | |High |30% |142400.97 |686590.51 | |Average |40% |109539.20 |526734.24 | |Low |30% |76677.44 |366877.96 | If Spiegel issued the stocks immediately the Expected net present value gained by the company would be...
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...Case Synopsis: Baffinland Iron Mines Corporation Set in 2010 against the backdrop of the global iron ore industry, the case is about Baffinland Iron Mines Corporation, which is caught in a tug of war between Nunavut Iron Ore Acquisition Inc. and Arcelor-Mittal. Both Nunavut and Arcelor-Mittal have their eyes set on Baffinland's Mary River project, which consists of seven deposits and reserves of 865 million tonnes of high grade, direct shipping iron ore in deposits 1-3 alone. The Mary River project has been hailed as one of the best undeveloped iron ore deposits in the world. However, with the onset of the global financial crisis, the project fell on hard times and owing to a lack of financing partners, Baffinland found itself unable to move forward with the project's development. Between October 2007 and September 2010, Baffinland's share price plummeted almost 90% from $4.68 to $0.56 and seeing this as an opportunity to secure ownership of a lucrative asset that was currently trading at a discount, Nunavut made a bid to acquire all shares of Baffinland at $0.8 per share, valuing the company at $274 million. The offer was met with much consternation from Baffinland's board, which set out to look for alternative bidders. High on its list was Arcelor-Mittal and what ensued was a series of competitive bids. As of December 2010, Nunavut had raised its bid price to $1.35 per share for a 50.1% stake in Baffinland and was offering shareholders 2% royalty on the potential sale of iron...
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...Portfolio Insurance, edited by Don Luskin (John Wiley and Sons 1988)] [reprinted in The Handbook of Financial Engineering, edited by Cliff Smith and Charles Smithson (Harper and Row 1990)] [reprinted in Readings in Futures Markets published by the Chicago Board of Trade, Vol. VI (1991)] [reprinted in Vasicek and Beyond: Approaches to Building and Applying Interest Rate Models, edited by Risk Publications, Alan Brace (1996)] [reprinted in The Debt Market, edited by Stephen Ross and Franco Modigliani (Edward Lear Publishing 2000)] [reprinted in The International Library of Critical Writings in Financial Economics: Options Markets edited by G.M. Constantinides and A..G. Malliaris (Edward Lear Publishing 2000)] Abstract This paper presents a simple discrete-time model for valuing options. The fundamental economic principles of option pricing by arbitrage methods are particularly clear in this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Black-Scholes model, which has previously been derived only by much more difficult methods. The basic model readily lends itself to generalization in many ways. Moreover, by its very construction, it gives rise to a simple and efficient numerical procedure for valuing options for which premature exercise may be optimal. ____________________ † Our best thanks go to William Sharpe, who first suggested to us the advantages of the discrete-time...
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...Discussion Issues and Derivations What is the cost of using excess capacity? Firms often use the excess capacity that they have on an existing plant, storage facility or computer resource for a new project. When they do so, they make one of two assumptions: 1. They assume that excess capacity is free, since it is not being used currently and cannot be sold off or rented, in most cases. 2. They allocate a portion of the book value of the plant or resource to the project. Thus, if the plant has a book value of $ 100 million and the new project uses 40% of it, $ 40 million will be allocated to the project. We will argue that neither of these approaches considers the opportunity cost of using excess capacity, since the opportunity cost comes usually comes from costs that the firm will face in the future as a consequence of using up excess capacity today. By using up excess capacity on a new project, the firm will run out of capacity sooner than it would if it did not take the project. When it does run out of capacity, it has to take one of two paths: &Mac183; New capacity will have to be bought or built when capacity runs out, in which case the opportunity cost will be the higher cost in present value terms of doing this earlier rather than later. &Mac183; Production will have to be cut back on one of the product lines, leading to a loss in cash flows that would have been generated by the lost sales. Again, this choice is not random, since the logical action to take is the one that...
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...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...
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...Flaws with Black Scholes & Exotic Greeks Treasury Perspectives Flaws with Black Scholes & Exotic Greeks 1 Flaws with Black Scholes & Exotic Greeks 2 Flaws with Black Scholes & Exotic Greeks Dear Readers:It’s been a difficult and volatile year for companies across the Globe. We have seen numerous risk management policies failures. To name a few... UBS, JPM Morgan, Libor manipulations by European, US and Japanese banks and prominent accounting scandals like Lehman… As rightly said by Albert Einstein “We can't solve problems by using the same kind of thinking we used when we created them.” and when you can't solve the problem, then manage it and don’t be dependent upon science as Science is always wrong, it never solves a problem without creating ten more. The same is the case with Foreign Exchange Risk Management Policies (FXRM) which if can’t be managed properly then would lead to either systematic shocks or negative implications at the bottom line of the corporate, banks, FI and trading houses P&L A/cs. That is something risk management struggles with, say the experts. In Richard Meyers’ estimation, risk managers or traders do not socialize enough. “It’s all about visibility,” he said. Meyers, chairman and CEO of Richard Meyers & Associates, a talent acquisition and management firm in New Jersey, relates the story of a firm that decided to adopt an Enterprise Risk Management (ERM) strategy. Instead of appointing its risk manager to head...
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