Consider a one-period binomial model as in Problem 1 with So = 4, u = 2,...
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Consider a one-period binomial model as in Problem 1 with So = 4, u = 2, d = 1, and =. Consider a European call option with strike price K = 5 and maturity at time 1. (a) Show that the time zero arbitrage-free price of this European call option is 1.20. (b) Consider an agent who begins with wealth Xo = 0 and at time zero buys Ao shares of stock and I' options. The numbers Ao and I can be either positive or negative or zero. This leaves the agent with a cash position -4A0 - 1.200. If this is positive, it is invested in the money market; if it is negative, it represents money borrowed from the money market. At time one, the value of the agent's portfolio of stock, option, and money market assets is X₁ = AøS₁ + Io(S₁ − 5)+ − ¾ (4A, +1.200). Assume that both S and S have positive probability of occurring. Show that if there is a positive probability that X₁ is positive, then there is a positive probability that X₁ is negative. In other words, one cannot find an arbitrage when the time-zero price of the option is 1.20. Consider a one-period binomial model as in Problem 1 with So = 4, u = 2, d = 1, and =. Consider a European call option with strike price K = 5 and maturity at time 1. (a) Show that the time zero arbitrage-free price of this European call option is 1.20. (b) Consider an agent who begins with wealth Xo = 0 and at time zero buys Ao shares of stock and I' options. The numbers Ao and I can be either positive or negative or zero. This leaves the agent with a cash position -4A0 - 1.200. If this is positive, it is invested in the money market; if it is negative, it represents money borrowed from the money market. At time one, the value of the agent's portfolio of stock, option, and money market assets is X₁ = AøS₁ + Io(S₁ − 5)+ − ¾ (4A, +1.200). Assume that both S and S have positive probability of occurring. Show that if there is a positive probability that X₁ is positive, then there is a positive probability that X₁ is negative. In other words, one cannot find an arbitrage when the time-zero price of the option is 1.20.
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a The time 0 arbitrage free price of the European call option is given by C0 max0 S0 K max0 4 5 0 Th... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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