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Our research led on to other things, such as the fact that exchange rates are not lognormally distributed.
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.
The HoLee model was the first term structure model. I remember reading their paper soon after it was published and as it was fairly different from many of the other papers that I had read, I had to read it quite a few times. I realized that it was a really important paper.
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.
If each of your time steps is one week long, you are not modeling the stock price terribly well over a one-week time period, because you are saying that there are only two possible outcomes.
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.
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.
Our starting point then was trying to find a way to incorporate mean reversion into the HoLee model.
The problem with interest rates are that you are not modeling a single number, you are modeling a whole term structure, so it is a sort of different type of problem.
There are challenges in terms of the measurement of VAR for what are known as nonlinear derivatives, where things like gamma and vega are important dimensions of the risk.
I think VAR is a very healthy development within the industry.