To: Chuzzlewit who wrote (82182 ) 11/25/1998 6:04:00 AM From: Geoff Nunn Read Replies (2) | Respond to
re: Black-Sholes model statistical model. The methodology uses basic statistical concepts such as probability distribution, expected value, variance and fair game. The concept of "fair game" is crucial to understanding B/S options valuations, and to the debate we are having. fair game for each side? Let's assume Dell May 65 calls currently have a value of $11 according to B/S. This tells us that if you were to purchase this option many times under the same circumstances that exist now, each time paying $11, then you would tend to break even(ignoring transactions costs) in the long run. The same break-even property would also apply to the writer. It is the price of $11 that makes the option not only a zero sum game but also a fair game. The $11, it should be noted, is a prediction of the average value of the option at expiry -- albeit a biased one. Actually, it is a prediction of the present value of the expected value of the option at expiry. Therefore, if the interest rate is .06 the model implies the expected future value of the May option at expiry is $11x(1+.03).The following numbers come from the CBOE. The theoretical price of a $50 call at the money, with 30% implied volatility and a 4% interest rate (no dividends): 90 days ($3.25), 60 days ($2.625), 30 days ($1.8125) and 15 days ($1.25). Now, assuming that a covered call is written, and that the position is liquidated at the strike price on the day of expirey, we have the following annualized rates of return: 30.84%, 38.21%, 55.75%, and 83.61% respectively
