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.

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.

Almost every wise saying has an opposite one, no less wise, to balance it.

But this is a true saying among men: the gifts of enemies are no gifts and profitless.

I've done a lot of acting. I'm not saying I'm the greatest, but I'd love to act, I'd love to sing.

Let me start by saying, I'm utterly disgusted with the former members of the Dead Kennedys.

That other saying, I'm a part of all that I have met, I think that would have to begin with my wonderful parents back in Atlanta when I was a youngster five years old I was tongue tied.

But clearly at the same time you've got to get out there and connect with voters and actually respond to the needs, the frustrations, whatever problems their now saying are not being adequately solved.

The Kiss scene was attempted three times. The first was in a peculiar spot of the fort on the ground level. It felt forced to me, and I knew right away that, in spite of what others were saying, it was dead wrong.

I am saying pornography hurts anyone who reads it, garbage in, garbage out.

I was in the middle of a crossroads, which is a nice way of saying crisis, physically, emotionally and spiritually. You know the physical part. We just talked about it.

I am a genius. Then it amused me to keep saying so, but now it does not. I expected to be happy sometime. Now I know I shall never be.

A salute from this corner to President Bush for saying he was willing to investigate raising or eliminating the cap on salaries subject to the Social Security tax.

Love in the real world means saying you're sorry 10 times a day.

I had something I was trying to say and sometimes the message is an easy transmission and sometimes it's a difficult one but I love the power of saying it so I'm gonna do it whether it's hard or easy.

And, quite frankly, I fully expected to be charged with murder, because they weren't charging anybody. I did it in terms of, I felt like I was throwing down the gauntlet saying look, this is what happened. There's a family out there that needed to know what happened.

I know I stand visibly onstage, but my function is still unseen, because I rarely see the immediate results of what I am saying or doing or writing.

And before our current legislature adjourns, we intend to become the first state of full and true choice by saying to every low and middle-income Hoosier family, if you think a non-government school is the right one for your child, you're as entitled to that option as any wealthy family; here's a voucher, go sign up.

They give me the money, I give them the book. Having input into the adaptation would be kind of like selling a house and coming back three years later and saying, 'Paint it this color!'

You know it's hard to hear what a bearded man is saying. He can't speak above a whisker.

We had an eyeball-to-eyeball agreement at a restaurant before I came back that, if I came back, he would never talk to me that way again or I was simply saying no.

So, in a way I was hedging and saying that if the Olympic stuff doesn't work out at least I can be a lawyer.

I hadn't even watched '24' before, and the audition was kind of far away. When I got the material, there wasn't a character yet, so it almost seemed like an assistant to Jack Bauer saying, 'Yes, sir. No, sir.'

Music is more emotional than prose, more revolutionary than poetry. I'm not saying I've got the answers, just a of questions that I don't hear other artists asking.

Failure should be our teacher, not our undertaker. Failure is delay, not defeat. It is a temporary detour, not a dead end. Failure is something we can avoid only by saying nothing, doing nothing, and being nothing.

We have an open society. No one will come and take me away for saying what I am saying. But they don't have to, if they can control how many people hear it. And that's how they do it.

I didn't write any music at all, and then, I remember Jon Anderson being very insistent saying that there were two kinds of musicians: the ones who wrote music and the ones who didn't.

I'm just saying that there are high quality materials, and when we change them then there should be a way of changing them so that you can celebrate that change - rather than just 'mix it up'.

I've directed a fair amount of television series - so I'm always trying to learn new things. One episode was all hand-held and I'm trying to get better at when you should do things and when you should just shut up and watch what the people are saying.

The Vietnamese have a secret weapon. It's their willingness to die beyond our willingness to kill. In effect, they've been saying, You can kill us, but you'll have to kill a lot of us; you may have to kill all of us. And, thank heaven, we are not yet ready to do that.

I'm not saying they won't be bigger projects someday.