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.

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.

Be where the acting is. I live in Houston. Dallas is 4 1/2 hours away. I let them know there's no difference.

Well concerning the world records that I did, I think it helps a lot to me, yeah. I think it's a very individual thing because I heard some people say, like, oh I don't like it at all. But I definitely, for me it really made a big difference.

There are many experiments and a great deal of research that can be performed on the station that make a difference in our lives and we are committed to supporting this important vocation.

We started filming in 1993 which was only four years after the fall of communism. The difference in Budapest over the last five years has been remarkable.

The difference between talking on your cell phone while driving and speaking with a passenger is huge. The person on the other end of the cell phone is chattering away, oblivious.

What the hell difference does it make, left or right? There were good men lost on both sides.

The difference between a bad artist and a good one is: the bad artist seems to copy a great deal; the good one really does.

I was grateful for the opportunity to make a difference. The political violence really started in 1970-1971. The political difficulties start a little bit beyond that.

I think the human body is beautiful, and I don't really have a huge problem in dealing with it, but it's the context, the environment and what I feel about it that that makes the difference for me.

From my very first day in the Mayor's office, I have worked closely with the Council members who share our vision of a city hall that really protects taxpayers and cares... yes... about the little things that make a big difference in people's lives.

I never considered a difference of opinion in politics, in religion, in philosophy, as cause for withdrawing from a friend.

All this is applicable to the intellectual faculties of man. There is a considerable difference between one person and another as regards these faculties, as is well known to philosophers.

I love those hockey moms. You know what they say the difference between a hockey mom and a pit bull is? Lipstick.

The difference between style and fashion is quality.

I used to think that it didn't make any difference how far you ran if you had a good, strong musculoskeletal system and no underlying cardiovascular problems.

The difference between relief pitching when I did it today is simple, there is too much of it. It's one of those cases where more is not necessarily better.

It makes no difference if I burn my bridges behind me - I never retreat.

It is important to nurture any new ideas and initiatives which can make a difference for Africa.

The difference between literature and journalism is that journalism is unreadable and literature is not read.

Do not confuse beauty with beautiful. Beautiful is a human judgment. Beauty is All. The difference is everything.

We must remember that one determined person can make a significant difference, and that a small group of determined people can change the course of history.

It don't make no difference where I go or what happens, so long as I can play the full nine.

We are all Adam's children - it's just the skin that makes all the difference.

I had to tell about my colonic, which expresses the fact why I'm so neat today as opposed to a few years ago. I never knew that the weight made that much difference.

I've always swung the same way. The difference is when I swing and miss, people say, 'He's swinging for the fences.' But when I swing and make contact people say, 'That's a nice swing.' But there's no difference, it's the same swing.

All of us want to have meaning in our lives and want to feel like we're doing something that makes a difference. I believe we're doing that in the Justice Department.

Once the Afghan people vote and they choose their President with direct, secret ballot from all over the country, there will be a lot of difference in this country and a lot of legitimate power to flow with implementation.

It's not what you've got, it's what you use that makes a difference.

Example moves the world more than doctrine. The great exemplars are the poets of action, and it makes little difference whether they be forces for good or forces for evil.