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John Hull
1
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.
moving
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want
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interest
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high
John Hull
1
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.
depended
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challenge
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three
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rate
John Hull
1
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.
sort
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structure
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whole
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term
John Hull
1
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.
first
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published
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realized
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papers
John Hull
1
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.
modeling
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period
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stock
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terribly
John Hull
1
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.
reflect
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mean
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branching
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parts
John Hull
1
We started giving presentations at practitioner conferences in 1986, and since then all of our derivatives research has been stimulated by contact with practitioners.
research
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contact
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stimulated
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started
John Hull
1
Our starting point then was trying to find a way to incorporate mean reversion into the HoLee model.
mean
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holee
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model
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trying
John Hull
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Our research led on to other things, such as the fact that exchange rates are not lognormally distributed.
rates
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distributed
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fact
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research
John Hull
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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.
delta
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simplistic
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sounds
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alone
John Hull
1
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.
challenges
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risk
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vega
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dimensions
John Hull
1
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.
average
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right
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conclusion
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concerned
John Hull
1
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.
average
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short
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rate
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term
John Hull
1
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.
mentioned
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concerns
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earlier
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measures
John Hull
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I think VAR is a very healthy development within the industry.
very
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development
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healthy
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within
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