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.

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.

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.

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.

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.

I didn't become interested in derivatives until 1982, 1983.

I think VAR is a very healthy development within the industry.

Alan White and I spent the next two or three years working together on this. We developed what is known a stochastic volatility model. This is a model where the volatility as well as the underlying asset price moves around in an unpredictable way.

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.

Our research led on to other things, such as the fact that exchange rates are not lognormally distributed.

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.

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.

I guess any simple idea that is really good will catch on quickly.

We started giving presentations at practitioner conferences in 1986, and since then all of our derivatives research has been stimulated by contact with practitioners.

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.

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.

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.

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.

Roosevelt's magic lay in one facet of his personality: He knew how to take the risk. No other man in public life I knew could so readily take the challenge of the new.

I do think that our freedoms are at risk.

Many a man is praised for his reserve and so-called shyness when he is simply too proud to risk making a fool of himself.

Living at risk is jumping off the cliff and building your wings on the way down.

But on the other hand, in the midst of the chaos, you find normal people. You find people who are willing to risk their lives to tell you what they saw, even though they have no dog in the fight.

I don't see the risk, I enjoy performing stunts, and I don't get scared.

Every time in this century we've lowered the tax rates across the board, on employment, on saving, investment and risk-taking in this economy, revenues went up, not down.

What you risk reveals what you value.

For me, the risks in terms of opening that brewpub were fairly high. I put my house up as collateral, I invested the liquid money I had and two years of my time to get it over, but that's really not much of a risk for what the potential reward was if it worked.

The refusal to rest content, the willingness to risk excess on behalf of one's obsessions, is what distinguishes artists from entertainers, and what makes some artists adventurers on behalf of us all.

Film is the most expensive, highest risk industry in the world.

You can't get there by bus, only by hard work and risk and by not quite knowing what you're doing. What you'll discover will be wonderful. What you'll discover will be yourself.

You don't concentrate on risks. You concentrate on results. No risk is too great to prevent the necessary job from getting done.

Every day, hundreds of thousands of men and women protect and serve, often putting their own lives at risk.

When you remove the risk, you remove the challenge. When you remove the challenge, you wither on the vine.

I'm fighting for small businesses. I'm not fighting for big oil. Don't be confused. And there are thousands of businesses in this state that are at great risk. Meanwhile, the country keeps guzzling the oil, but we're out of work down here. We need to get back to work to build this region, and we intend to do so.

Nothing in life and nothing that we do is risk-free.

I feel that David took a risk with me. I have a sense that by starting off in the theatre and going off to do films you are seen to sell out in some way. I don't hold truck with that, but you can't stop people from feeling it.

You must accept that you might fail; then, if you do your best and still don't win, at least you can be satisfied that you've tried. If you don't accept failure as a possibility, you don't set high goals, you don't branch out, you don't try - you don't take the risk.

Kennedy did not have to run the risk of having his ideas and his words shortened and adulterated by a correspondent. This was the television era, not only in campaigning, but in holding the presidency.

The risk of a terrorist victory is greater when in fighting terror, democracy betrays its own essence.

Facts are, insurance ratings are really dependent on the notion that some people are higher risk than others.

If you have something at risk, you think differently.

I'm of the mind that life is a risk, every time you leave your house it's a risk, and I see no reason to go through life with my hands tied behind my back for any reason. I'd be foolish to let something stop me from doing what I love to do.

It seems to be a law of nature, inflexible and inexorable, that those who will not risk cannot win.

Having come to live in this age is as though one were to have entered another country. Learn its language or risk being left out.

To me, life, for all its privations, is a luminous thing. You have to risk it.

Everything is sweetened by risk.

I'm not cynical about marriage or romance. I enjoyed being married. And although being single was fun for a while, there was always the risk of dating someone who'd owned a lunch box with my picture on it.