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

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.

We need to keep investing in economic and homeland security. We need to bank on the right kind of economic development. We need to embrace opportunities, but with the right kind of safeguards.

The other great development has been in photography, but that too was influenced by Conceptual art.

The education of my brother and myself was of paramount importance to my parents, and in addition to their strong encouragement, they were prepared to make any sacrifice to further our intellectual development.

While I recognize the great value and importance of prescription drugs and strongly support a continued U.S. focus on pharmaceutical research and development, our nation's seniors cannot be asked to subsidize the drug costs of other wealthy industrialized nations any longer.

Hence the same instant which killed the animals froze the country where they lived. This event was sudden, instantaneous, without any gradual development.

In my fifty years of experience and memory, I have seen the most amazing increase in the standard of living of a people ever achieved anywhere in the world. This is why I am so sure that our system of free competition and industrial development is sound and must be preserved.

Be unselfish. That is the first and final commandment for those who would be useful and happy in their usefulness. If you think of yourself only, you cannot develop because you are choking the source of development, which is spiritual expansion through thought for others.

I was much involved in the development of the spark chamber as a practical research tool.

As a scouting department, with the confidence we have in our player development, if a guy has the potential that we think they have and the makeup and they stay healthy, we think they will be a productive Major Leaguer. We take a lot of pride in that.

Clearly, programming courses should teach methods of design and construction, and the selected examples should be such that a gradual development can be nicely demonstrated.

One of the biggest development issues in the world is the education of girls. In the United States and Europe, it has been accepted, but not in Africa and the developing countries.

Practically the only way to dry the swamp of radical Islam is through economic development and an improved standard of living.

I tend to arrive in the rehearsal process with very strongly developed ideas about what I want to do. But I don't like those ideas to be things that are not subject to change, or subject to development, or subject to challenge.

There are not many males, black or white, who wish to get involved with a woman who's committed to her own development.

Manufacturers account for nearly 60 percent of all industrial research and development.

During my nearly five years as director-general of WHO, high-level policymakers have increasingly recognized that health is central to sustainable development.

Software development is technical activity conducted by human beings.

Those who decide to use leisure as a means of mental development, who love good music, good books, good pictures, good plays, good company, good conversation - what are they? They are the happiest people in the world.

Research and development needs permanent tax credits to build the technology that spurs our growth. But no government programs alone can get America's students to study more science and math; parents must push and help their children to meet this goal.

Why did human development proceed at such different rates on different continents for the last 13,000 years?

It's actually not unlike Google at that stage of development. They had an up-and-running site. It wasn't losing very much money, it wasn't making very much money, but it was growing.

The distinction between the old and the new formulations consisting in the incorporation of the concept of the rate of chemical reactions is so great that it immediately asserted itself in the objective development of catalysis.

Close contact between science and the practice of collective farms and State farms creates inexhaustible opportunities for the development of theoretical knowledge, enabling us to learn ever more and more about the nature of living bodies and the soil.

Of all work-schools, a good farm is probably the best for motor development.

Advocates of unrestricted abortion do not want the public to focus on these undeniable facts of fetal development, but the facts cannot be ignored.

The United Nations has a critical role to play in promoting stability, security, democracy, human rights, and economic development. The UN is as relevant today as at any time in its history, but it needs reform.

The essential job of government is to facilitate, not frustrate, job development.

By perfecting this legislative machinery and by participating in the various international agreements we intend to contribute to the wholesome development of world trade.

I'm doing comedy development at National Lampoon.