Black and Scholes Options Evaluation Message Board

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Strategies & Market Trends : Black and Scholes Options Evaluation

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To: Uri Miller who wrote ()	11/16/1996 6:35:00 PM
From: Richard Loo	of 44

Uri, I don't know how simple my explanation can be because the concept is rather horrendous. I'll try. Black Scholes is a formula used to calculate the price of a call (or put) option given six pieces of information: 1. Current stock price (S), 2. Strike price of option (X), 3. Time of expiration of option (T) 4. Current time (t). So (T-t) is the time between now and the end of the option's life. 5. Volatility of stock price (s). This is the standard deviation (it is the "sigma" in statistics which I don't have on my keyboard) of the stock price over a period of time. 6. Interest rate (r) on a no-risk bond (like T-bill) maturing at time T. The formula for the price of a call (c) then is c = S * N(d1) - X * e^[-r(T-t)]* N(d2) where d1 = { ln(S/X) + [r + (s^2)/2] * (T-t) } / { s * (T-t)^(1/2) } ln is the natural logarithm d2 = d1 - s * (T-t)^(1/2) N(x) means the normal distribution function; like the bell-curve. (Technically called the "cumulative probability distribution function for a standardized normal variable.") What happens is that d1 and d2 will lie somewhere between 0 and 1 and you'd look up the normal distribution to figure out a standard deviation value. If you can see through all the noise, the formula boils down to c = S - X which is obvious: the price of a call is the current stock price minus the strike price. What happens is that it is adjusting the price (S) by a probability component N(d1) which depends on the stock's volatility, and the strike price (X) by another probability component N(d2) as well as a time-value-of-money componnt e^(x) because the strike price happens in future. Price of a put (p) is X * e^[-r(T-t)] * N(-d2) - S * N(-d1) d1 and d2 are same as above. This is for a European-style put option that cannot be exercised early.

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