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

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.

The essential elements of giving are power and love - activity and affection - and the consciousness of the race testifies that in the high and appropriate exercise of these is a blessedness greater than any other.

Two days after moving we recommended ourselves to God, Our Lord, and fled, hoping that, although it was late in the season and the fruits of the tunas were giving out, by remaining in the field we might still get over a good portion of the land.

I didn't know at the time that the energy that I was giving off was like a battle Emcee.

For it is in giving that we receive.

All my pictures are built around the idea of getting in trouble and so giving me the chance to be desperately serious in my attempt to appear as a normal little gentleman.

This bored fantastic woman, with her animal nature, giving herself the pleasure of seeing her enemy struck down, not a particularly keen one for her because she is so weary of having all her desires satisfied.

While Kuwait is not a democracy, giving only half the population a voice in their government is not a policy this Congress should support and one that I am glad that Kuwait's leaders are changing.

When you take a look at the problems our country is facing, debt is No. 1. The math is downright scary and the credit markets aren't going to keep on giving us cheap rates.

Parents were invented to make children happy by giving them something to ignore.

The second is the structure and source of cults. They have always haunted me, and I wanted to explore the fundamental notion of giving up responsibility to an outside power.

New technologies such as solar systems or hybrid cars aren't created overnight. By extending these tax credits we are giving this industry time to grow, branch out and succeed.

My idea of managing is giving the ball to Tom Seaver and sitting down and watching him work.

I don't think anyone wants a reader to be completely lost - certainly not to the point of giving up - but there's something to be said for a book that isn't instantly disposable, that rewards a second reading.

I believe that the average guy in the street will give up a great deal, if he really understands the cost of not giving it up. In fact, we may find that, while we're drastically cutting our energy consumption, we're actually raising our standard of living.

We had avoided discovery by the Sioux scouts, and we were confident of giving them a complete surprise.

It is giving me a great satisfaction, because I had the notion that we could make great wines equal to the greatest wines in the world, and everybody said it was impossible.

Let us not be satisfied with just giving money. Money is not enough, money can be got, but they need your hearts to love them. So, spread your love everywhere you go.

Instead of giving a politician the keys to the city, it might be better to change the locks.

All of us are mad. If it weren't for the fact every one of us is slightly abnormal, there wouldn't be any point in giving each person a separate name.

The mark of a true professional is giving more than you get.

Sharing is sometimes more demanding than giving.

I want the privilege of guiding the arrows of my children and giving them the exhortations that can shoot them into the high place.

Black Power is giving power to people who have not had power to determine their destiny.

Somewhere on this globe, every ten seconds, there is a woman giving birth to a child. She must be found and stopped.

I think most Americans believe that although it's better not to use military force if you can avoid it, that the world simply doesn't provide us the luxury of giving away military force as an important tool of foreign policy.

I don't think people were betting on me, but they were giving me a chance. I think I rode a wave there, by being different in appearance than the girls who preceded me.

I don't want to spend the rest of my life giving speeches.

Being an artist is dragging your innermost feelings out, giving a piece of yourself, no matter in which art form, in which medium.

To give and then not feel that one has given is the very best of all ways of giving.