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Unformatted text preview: Options 1 OPTIONS Introduction • A derivative is a financial instrument whose value is derived from the value of some underlying asset. • A call option gives one the right to buy an asset at the exercise or strike price. • A put option gives one the right to sell the asset at the exercise price. Options 2 • An option has an exercise date , also called the strike date, maturity, or expiration date . • American options can be exercised at any time up to their exercise date. • European options can be exercised only at their exercise date. Options 3 • Complex types of derivatives cannot be priced by a simple formula such as the BlackScholes formula. • In this chapter: – heuristic derivation of BlackScholes formula Options 4 Why do companies purchase options and other derivatives? Answer: to manage risk In 2000 Annual Report, the Coca Cola Company wrote: • Our company uses derivative financial instruments primarily to reduce our exposure to adverse fluctuations in interest rates and foreign exchange rates and, to a lesser extent, adverse fluctuations in commodity prices and other market risks. Options 5 • We do not enter into derivative finanicial instruments for trading purposes. • As a matter of policy, all our derivative positions are used to reduce risk by hedging an underlying economic exposure. Options 6 • Because of the high correlation between the hedging instrument and the underlying exposure, fluctuations in the value of the instruments are generally offset by reciprocal changes in the value of the underlying exposure. • The derivatives we use are straightforward instruments with liquid markets. Derivatives can and have been used to speculate. • But that should not be their primary purpose. Options 7 Call options Suppose you purchased a European call on 100 shares of Stock A with exercise price of $70. • At expiration, suppose Stock A is selling at $73. • The option allows you to purchase the 100 shares for $70 and to immediately sell them for $73. – gain of $300. • Net profit isn’t $300 since you paid for the option. • If the option cost $2/share, then you paid $200 Options 8 • Moreover, you paid the $200 up front but only got the $300 at the expiration date. • Suppose expiration date was 3 months after purchase and r is 6% per annum or 1.5% for 3 months. • The dollar value of your net profit is exp( . 015)300 200 = 95 . 53 at t = 0 and is 300 exp( . 015)200 = 96 . 98 at t = T . Options 9 • We will use the notation ( x ) + = x if x > 0 and = 0 if x ≤ 0. • With this notation, the value of a call at exercise date is ( S T K ) + , where K is the exercise date and S T is stock’s price on the exercise date, T . Options 10 • A call is not exercised if strike price is greater than stock price....
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This note was uploaded on 04/06/2008 for the course ORIE 473 taught by Professor Anderson during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 ANDERSON

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