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exercise_topic_06

exercise_topic_06 - mium(see Economics of Financial Markets...

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U NIVERSITY OF E SSEX D EPARTMENT OF E CONOMICS Session 2011–12 R. E. Bailey EC372 Economics of Bond and Derivatives Markets Exercise 6: Options Markets: II Price determination 1. Suppose that the current price of a stock is 120 pence per share and that the one-period interest rate is 10% with no compounding. In one period the price of the stock will become either 180 or 84. Use an arbitrage argument to calculate the price of a European call option which expires in one period with an exercise price of 158. [Hint: do not work out the decimal value of fractions until the final step (when they will all cancel out to give a simple result).] 2. Use an arbitrage argument to derive from first principles the expression for a call option pre-
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Unformatted text preview: mium (see Economics of Financial Markets , chapter 19 (section 19.2): c = πc u + (1-π ) c d R where c u and c d are defined by: c u = max [0 , uS-X ] in State 1 and c d = max [0 , dS-X ] in State 2 and π ≡ R-d u-d and 1-π ≡ u-R u-d . 3. Derive, using an arbitrage argument, the price of a European put option in the simple two-state model (see Economics of Financial Markets , chapter 19 (section 19.2): p = πp u + (1-π ) p d R where: p u = max [0 , X-uS ] in State 1 and p d = max [0 , X-dS ] in State 2. 4. Discuss the problems in applying the Black-Scholes model to predict traded options prices (for example, on LIFFE) in (a) the shares of companies, and (b) stock price indexes. *****...
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