I didn't become interested in derivatives until 1982, 1983.
From John Hull
The real challenge was to model all the interest rates simultaneously, so you could value something that depended not only on the three-month interest rate, but on other interest rates as well.
When interest rates are high you want the average direction in which interest rates are moving to be downward; when interest rates are low you want the average direction to be upward.
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.
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.
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.
I guess any simple idea that is really good will catch on quickly.
I think VAR is a very healthy development within the industry.
One important measurement issue concerns the fat tails problem that I mentioned earlier. VAR is concerned with extreme outcomes. If the tails of the probability distributions we are using are too thin, our VAR measures are likely to be too low.
Our tree is actually a tree of the short-term interest rate. The average direction in which the short-term interest rate moves depends on the level of the rate. When the rate is very high, that direction is downward; when the rate is very low, it is upward.
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