Ito's Dilemma

This case introduces students to the concepts of option valuation and asks them to estimate option prices using the Black-Scholes pricing model. It illustrates the importance of volatility to option pricing and allows the introduction of the concept of implied volatility. The case is used most effectively in sequence with “Ito's Delight” (UVA-F-1333) to introduce option-pricing concepts. Different versions of this teaching plan have been successfully used for both MBA and executive-education audiences. Excerpt UVA-F-1283 ITO'S DILEMMA On February 20, 2001, Louise Ito was studying the Wall Street Journal's quotations of put and call options traded on the Chicago Board Option Exchange (CBOE). Ito had just finished a one-day seminar on options and futures at the local university, and she was eager to test her new knowledge on actual option prices. Perhaps the most puzzling concept for her was why an option increased in value as the underlying stock became more risky. The instructor repeated time and again, “Without risk, an option has no purpose and therefore no value. The more risk associated with holding a stock, the more you're willing to pay either to avoid it by hedging with an option or to take advantage of it by holding a naked option position!” Much of the seminar had been spent defining and measuring the risk of the underlying stocks. Ito was so impressed with the importance of the volatility, or σ term, in the Black-Scholes formula that she had purchased her first laptop computer. The computer came with Excel loaded on it, so she could immediately add the option-pricing model used during the seminar. All she needed to compute her own estimates of option values for her favorite stocks was the ability to compute past stock-return volatility. She had compiled and entered 30 weeks' worth of past stock prices for Duke Energy, IBM, and Microsoft in a Microsoft Excel spreadsheet (Exhibit 1). After calculating weekly returns, she computed a standard deviation of returns over the 30 weeks, which she then converted into an annualized number. She was surprised at the differences between the volatility estimates of the three stocks, but decided to enter the estimates directly into the computer model to see what came out for a few of the options that were currently being traded (Exhibit 2). As she began to compare her estimates with the actual prices, Ito was surprised to discover that the Black-Scholes estimates were not consistently lining up with the actual prices reported in the Wall Street Journal. The differences between her estimates and the actual prices caused her to think, “Either I'm doing something wrong or there are quite a few opportunities out there for me to make money buying and selling puts and calls. So, should I believe the Black-Scholes model and start trading these risky securities or should I believe that markets are efficient and leave option trading for the professionals?” Such was Louise Ito's dilemma. . . .