What factors contribute to the difficulty of making a delta hedge be truly risk-free? A stock is priced at $50 with a volatility of 35 percent. A call option with an exercise price of $50 has an expiration in one year. The risk-free rate is 5 percent. Construct a table for stock prices of $5, 10, 15, ... , 100. Compute the BlackScholes-Merton price of the call and the European lower bound and verify that the former is at least as large as the latter.
The following option prices were observed for calls and puts on a stock for the trading day of July 6 of a particular year. Use this information in problems 12 through 20. The stock was priced at 165.13. The expirations were July 17, August 21, and October 16. The continuously compounded risk-free rates associated with the three expirations were 0.0503, 0.0535, and 0.0571, respectively. Unless otherwise indicated, assume the options are European.
