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.
More Quotes from John Hull:
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.John Hull
Our starting point then was trying to find a way to incorporate mean reversion into the HoLee model.
John Hull
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.
John Hull
We concluded that you cannot rely on delta hedging alone. It sounds simplistic to say that now, but back then, this was the sort of thing people were only just beginning to realize.
John Hull
Yes, our tree has an interesting shape. The center branches reflect the shape of the zero curve. When extreme parts of the tree are reached the branching pattern changes to accommodate the mean reversion.
John Hull
I guess any simple idea that is really good will catch on quickly.
John Hull
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Based on Topics: Speaking QuotesBased on Keywords: briefly, hedging, pricing, stochastic, volatility
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