# Assignment

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FinalProject: This project is intended to further your understanding of the basic concepts and applications, and to enhance your analytical skills and creativity. The requirement is that you will use what you have learned to value and apply real-world financial derivatives (options and/or futures).

As an example, you can choose to examine publicly traded options on a stock or an ETF (see below for a sample project outline). If stock options are your choice, in your report, you should discuss the stock and compare the market prices of stock options with their theoretical values provided by option pricing models. You should discuss discrepancies between the market price and the theoretical value and provide possible explanations. You should also check if option prices satisfy various no arbitrage conditions (boundary conditions, Put-Call Parity, etc.). If arbitrage opportunities appear to exist, you should discuss how you would form certain trading strategies to profit from such opportunities. You should also examine the profitability and hedging property of some commonly used trading strategies involving options (e.g., covered calls, protective puts, spreads, etc.).

***** I chose Adidas AG as my stock for this Project. Stock symbol ADR.*****

Using computer software for option analysis is an integral part of the course. Designed for this purpose is the DerivaGemsoftware, which is downloadable with your textbook purchase. You may use alternative software for your project but do discuss the alternative with me before using it.

Outline of a Sample Project: Merck & Co.

This is the outline of a project submitted by a group in a previous class. The project was on Merck stock options. The group did a good deal of work. While you may use this outline as a reference for your project, you must choose a different stock. If you do much of what is outlined below, you would have done a very nice job. However, you can choose to emphasize some aspects but not others. You can also choose to do a very different project that deals with other forms of options, real options, or futures/forward contracts.

*Introduction*

• Merck & Co.: A brief history

• Recent stock prices and activities of note

*Trading Strategies*

• Pick a date (“today”), and record the closing prices of the stock, and the calls and puts that are of interest to your group (choose several options with different strike prices and/or different maturities)

• Use the price data to describe profit functions/diagrams for writing covered calls

• Describe profit functions/diagrams for longing protective puts

• Describe bull and bear spreads of interest to you

• Describe other strategies, e.g., straddle (because of unknown outcome of many lawsuits)

• Discuss which ones of such strategies, if any, your group thinks are most appropriate at this time

*Arbitrage Opportunities**?*

• Describe if the options’ lower and upper bounds are violated

• Describe if the options’ put-call parity conditions are violated (be sure to note that all stock options are American options which have more elaborate put-call parity conditions)

• Describe if there are any other arbitrage opportunities

*Theoretical Option Prices vs. Market Prices*

• Collect closing stock prices for at least 21 trading days immediately prior to the date you have picked (more data is better but means more work)

• Use the historical stock prices to estimates the stock’s historical volatility (the procedures to do this estimate are described on pages 299-302, particularly Table 13.1 on page 302

• Use the DerivaGem software to compute Black-Scholes-Merton theoretical option prices for European options (your access code to the DerivaGem software is provided in the textbook)

• Use the DerivaGem software to compute theoretical option prices based on the binomial model for American options

• Describe differences between theoretical and market prices of the calls and puts (you will observe many differences)

• These differences may exhibit certain patterns, and if so, provide possible explanations

• Use the DerivaGem software to compute the options’ implied volatility and compare it with the historical volatility you calculated earlier

• Describe differences between implied volatility and historical volatility, and offer explanations

• Describe and explain any volatility smile and any term structure of volatility

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