Mathematical Statistics and Data Analysis
Mathematical Statistics and Data Analysis
3rd Edition
ISBN: 9781111793715
Author: John A. Rice
Publisher: Cengage Learning
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Chapter 1.8, Problem 68P
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select bmw stock. you can assume the price of the stock
This problem is based on the fundamental option pricing formula for the continuous-time model developed in class, namely the value at time 0 of an option with maturity T and payoff F is given by: We consider the two options below: Fo= -rT = e Eq[F]. 1 A. An option with which you must buy a share of stock at expiration T = 1 for strike price K = So. B. An option with which you must buy a share of stock at expiration T = 1 for strike price K given by T K = T St dt. (Note that both options can have negative payoffs.) We use the continuous-time Black- Scholes model to price these options. Assume that the interest rate on the money market is r. (a) Using the fundamental option pricing formula, find the price of option A. (Hint: use the martingale properties developed in the lectures for the stock price process in order to calculate the expectations.) (b) Using the fundamental option pricing formula, find the price of option B. (c) Assuming the interest rate is very small (r ~0), use Taylor…
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