- Mathematician | -
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.
John Hull
ProblemYouModelingStructureWhole
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.
ChallengeValueYouRealSomething
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.
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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.
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We started giving presentations at practitioner conferences in 1986, and since then all of our derivatives research has been stimulated by contact with practitioners.
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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.
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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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