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Unformatted text preview: 1 UNIVERSITY OF TORONTO AT SCARBOROUGH DEPARTMENT OF MANAGEMENT MGTC71: Introduction to Derivatives Markets Problem Set – 4 _______________________________________________________________________________ 1. a) In the risk-neutral method, we price options by discounting their risk-neutral expected future payoffs with the risk-free interest rate. We can do this because the major players in the options market have risk-neutral preference and they do not demand a risk premium in returns for holding options. Agree/Disagree b) Recently the VIX index measuring the market volatility has increased substantially. This implies that the market degree of risk aversion has also increased. The option premiums, however, should not be impacted, as options are priced using risk neutral valuation. True/false/uncertain. Explain. 2. XYZ is currently trading at $50. Over each of the next two months, XYZ will either move up by 25%, or down by 20%. Each month, the probability that XYZ will move up is 60%. The annual (c.c) risk-free rate is 11.94%. Furthermore, assume that in exactly one month, XYZ will pay a dividend which will be equal to one-tenth (or 10%) of the price of XYZ stock at that time. (If the price is $40 in one month, the dividend will be $4.00.) a) Write out a two-month, two-period binomial tree for the stock price of XYZ. Solve for the binomial model parameters u; d; r; p. b) Use the binomial method to find the price of a two-month American call option on XYZ with K = 50. c) Use the binomial method to find the price of a two-month American put option on XYZ with K = 50. Find the delta of the put at each node. d) Use the binomial method to find and the price of a European (binary) option which pays off $100 if the price of XYZ is greater than or equal to K = $50 in two months and zero otherwise....
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- Spring '11
- Management, Rational pricing