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Options and Futures

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1. This problem requires you to use the Black-Scholes formula. A call option with X=\$50 on a stock currently priced at S=\$55 is selling for \$10. Using a volatility estimate of sigma = .30, you find that N(d1) = .6 and N(d2) = .5. The risk free rate is zero. Is the implied volatility based on the option price more or less than .30? Explain.

2. The S&P portfolio pays a dividend yield of 2% annually. Its current value is 1300. The T-bill rate is 5 percent. Suppose the S&P futures price for delivery in one year is 1350. Do these figures appear to be in equilibrium? If not, explain how to take advantage of the mispricing. Can you make an arbitrage profit? If you weren't the only one to notice the problem, what would happen to the prices of the stocks in the S&P index? What would happen to the futures price?