ÖAsk Dr. Risk! ^TM Columns from 1996
Other columns: current 1999 1998 1997 1996

Alternative Pricing Models (11/14/96)

Question: Dear Dr. Risk – Sometimes, I know that all I have to do to price a particular derivative product is numerically solve the corresponding boundary value problem. For any given payoff function, depending on the boundary conditions, I might be able to do that with any of a half a dozen methods, such as Monte Carlo, numerical quadrature, binomial, trinomial, explicit finite difference, implicit finite difference, explicit-implicit finite difference, or finite element model. Given enough time, maybe I could find a relatively simple expression for value, similar to the Black-Scholes formula. After I find one solution, should I spend the time looking for another? – Fast Eddie

Answer: Dear Mr. Eddie – Dr. Risk had to overcome the temptation to assure you that one solution is all you could ever possibly need, ask you which method you favor, short your company's stock, and open up a trading line with you. But that would be a breach of the Risk Doctor's Oath.

Dr. Risk thinks that relying on one method of pricing a brand new, exotic derivative is about as wise and safe as firing a single bullet to stop a charging lion, when you could easily squeeze off a few more rounds. Although all the methods you mentioned can give the same prices and Greeks under ideal conditions, it's not always obvious what ideal conditions are. If you choose bad values for key parameters of each model - such as upper and lower bounds of integration for numerical quadrature, number of periods for binomial, trinomial, or finite difference, or number of Monte Carlo paths – these various methods might produce wildly different values and Greeks. And then there's the issue of which method you use to compute each Greek. Slow down and check your results. Sometimes speed kills! – Dr. Risk

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ÖAsk Dr. Risk! TM Columns from 1996 Other columns: current 1999 1998 1997 1996

Alternative Pricing Models (11/14/96)

ÖAsk Dr. Risk! ^TM Columns from 1996
Other columns: current 1999 1998 1997 1996