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.
From 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.
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.
Our research led on to other things, such as the fact that exchange rates are not lognormally distributed.
Our starting point then was trying to find a way to incorporate mean reversion into the HoLee model.
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 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.
We started giving presentations at practitioner conferences in 1986, and since then all of our derivatives research has been stimulated by contact with practitioners.
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.
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