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Strategies & Market Trends : Roger's 1998 Short Picks -- Ignore unavailable to you. Want to Upgrade?

To: BelowTheCrowd who wrote (14545)	10/12/1998 11:08:00 AM
From: Marconi	Respond to of 18691

Hello Mr. Gat: the essential truth to Black/Scholes and Merton/Scholes is that they provide the best possible pricing mechanism for derivatives, factoring in all known data about volatility in the underlying asset. The problem is that when volatility changes rapidly, the formulas break down. Agreed for the formula. But the original partial differential equation expressed in stochastic variables should accommodate rate of change of volatility too, by defining an appropriate distribution for that variable. But I think therein lies the rub. I suspect one or more of the simplifying assumptions that allowed the reduction to a simple formula would have to be changed into a variable. I suspect the result of doing so might end up being either a higher order of complexity in the equation and possibly requiring a difficult to determine parameter (hopefully it could be related back to changes in implied volatility or something tractable like that), or possibly a simple formula coupled with tables of a numerically calculated parameter required to accommodate the variability of volatility. Maybe one of the fledglings still in the hopper like Jonathon Babb has looked at some of this math and could comment further. This old scientist is long removed from having such mathematics under my wing. I remember reviewing a paper--quite a few pages--laying out the stochastic calculus and then running the PDE with a number of assumptions to arrive at a tractable formula--I was very impressed at the time by how carefully they had threaded their way through to a neat formula. With the impression that, wow! one could sure go in a lot of directions and get lost from this generalized mathematical formulation , but these fellows put together something that actually could be related well to simple market data! At the time, it was a substantial stepping stone. I think there will be many more advances to come in that field of thought, and acknowledge much has been accomplished too in the intervening years. I also agree with your thought that although the Black-Scholes OPM is a useful guide, it remains an estimator, not the definitive quantifier of value that many in the financial services seem to have put it to use without sufficient mindfulness of the qualifying assumptions. Best regards, m