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Strategies & Market Trends : The Covered Calls for Dummies Thread -- Ignore unavailable to you. Want to Upgrade?

To: Uncle Frank who wrote (233)	4/25/2001 3:14:30 PM
From: Tom Chwojko-Frank	Read Replies (2) \| Respond to of 5205

Thanks for the Black Scholes Equation reference. That's the kind of answer I was looking for. (The Harrison Roth quote just points it out the term, doesn't explain it.) The differential equation almost answers why. If I were to model options from scratch, I would take for granted the exponential decay in time. The tricky parts are N(d1) and N(d2), which are of order sqrt(t). C = S N(d1) - X exp(-rt) N(d2) Ok, so now d1 is or order sqrt(t), and d2 is of order t. The link defines N(x) as the cumulative normal probability. I like diff. eq., I hate statistics, but I thought that normal distributions were something like exp(-k^2), which again makes it exponential. As I'm writing this, and reading the analysis below I realize my confusion. The Black Scholes equation is almost an exponential decay, but the derivative (rate of change) when all said and done has O(sqrt(t)) which comes from N(d2). Here's a nice derivation of Black-Scholes (very detailed math): physics.uci.edu All of this is really academic (in the true sense of the word), since in practice, Black Scholes is an approximate model, and ln is qualitatively similar to sqrt. Tom CF P.S. Differentiation is usually easy. Apply a bunch of fixed algorithms to manipulate the symbols correctly, and crank it out. Integration is usually hard. Guess at an answer and then prove you're right by taking the derivative. Statistics are neither easy nor hard, just crazy.