- Nov 07, 2020
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- Last Updated on May 30, 2021
- Big Difference
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- Nov 07, 2020
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.
- Modeling
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- Nov 07, 2020
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.
- Bond
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- Nov 07, 2020
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.
- Important
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- Nov 07, 2020
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
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- Nov 07, 2020
Our research led on to other things, such as the fact that exchange rates are not lognormally distributed.
- Mean
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- Nov 07, 2020
Our starting point then was trying to find a way to incorporate mean reversion into the HoLee model.
- High
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- Nov 07, 2020
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.
- First Term
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- Nov 07, 2020
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.
- Modeling
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- Nov 07, 2020
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.
- Gamma
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- Nov 07, 2020
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.
- Beginning
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- Nov 07, 2020
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.
- Giving
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- Nov 07, 2020