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To: rkral who wrote (61182)	8/30/2002 9:06:38 AM
From: GVTucker	Respond to of 77400

OT, rkral, RE: In fact, every Black-Scholes equation I've ever seen in textbooks has been for European style options. I wonder how it is modified for American style options. Actually, for a stock that doesn't pay dividends, it doesn't matter, because for call options there wouldn't be a risk of early exercise anyway. Early exercise is a risk for stocks that pay dividends and deep in the money puts. For dividend paying stocks, Richard Roll and Robert Geske developed a modified Black-Scholes that predicts the prices of those options well. (If you're really curious about the formula, their papers were published in the Journal of Financial Economics back in the early 80's.) For deep in the money puts, Cox and Rubenstein further modified Black-Scholes to develop a pretty good predictive model. Their work was published sometime in the mid-80's, although I don't recall it specifically.

To: rkral who wrote (61182)	8/30/2002 10:34:00 AM
From: Ira Player	Read Replies (2) \| Respond to of 77400

One point you are missing... Yes, the Black-Scholes model is for European options. But with European traded options, the owner can sell them after 5 years and take the current value. An employee with 7 year vesting leaving at 5 years gets nothing. Unless there is a method of modifying the formulas to take this into consideration, the model overvalues the options significantly. What would you pay for an option that, on top of the movement of the underlying stock price, was dependent on something outside of your complete control? (Hows this: The option is only valid if your 10 year old cat, which is allowed to go outside, is still around in 7 years.) I don't think so... Ira