Option Pricing Quotes

Briefly speaking, our conclusion is that stochastic volatility does not make a huge difference as far as the pricing is concerned if you get the average volatility right. It makes a big difference as far as hedging is concerned.

My principal contribution to the Black-Scholes option-pricing theory was to show that the dynamic trading strategy prescribed by Black and Scholes to offset the risk exposure of an option would provide a perfect hedge in the limit of continuous trading.

Black-Scholes works for short-term options, but if it's a long-term option and you think you know something [about the underlying asset], it's insane to use Black-Scholes.

I have a quantitative background, but really, derivatives appealed to me because they require so much creativity.

Black-Scholes is a know-nothing system. If you know nothing about value - only price - then Black-Scholes is a pretty good guess at what a 90-day option might be worth. But the minute you get into longer periods of time, it's crazy to get into Black-Scholes. For example, at Costco we issued stock options with strike prices of $30 and $60, and Black-Scholes valued the $60 ones higher. This is insane.

The longer-term the option, the sillier the results generated by the Black-Scholes option pricing model, and the greater the opportunity for people who didn't use it.

Alan White and I spent the next two or three years working together on this. We developed what is known a stochastic volatility model. This is a model where the volatility as well as the underlying asset price moves around in an unpredictable way.

In the interest rate area, traders have for a long time used a version of what is known as Black's model for European bond options; another version of the same model for caps and floors; and yet another version of the same model for European swap options.

Looking into it a bit, Jamie found that the model used by Wall Street to price LEAPs, the Black-Scholes option pricing model, made some strange assumptions.