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.

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.

I was surprised that the TV series was popular itself, but after that it went on to become more popular over the years and thus it seemed eventually that they would turn it into a movie.

I prefer to remember the happy things over 10 years, the things that went well. Let me see, what did go well?

What I try to do for my readers is to pass on some of the things that I found out about being thirteen after doing it for forty years.

I think I've become a much better singer and a much better player. Years and years of playing a couple of hours every day will do that.

There is no need to do any housework at all. After the first four years the dirt doesn't get any worse.

The robe of flesh wears thin, and with the years God shines through all things.

The Republicans claim they are for strengthening Pell grants when the truth is that over the last four years, their legislation has done the exact opposite.

I want to thank all the fans for their support over the years. Keep supporting the Knicks, we're moving in the right direction here and we will be exciting to watch and competing against the best in the NBA. Come back to the Garden for those exciting games.

I am told that there have been over the years a number of experiments taking place in places like Massachusetts Institute of Technology that have been entirely based on concepts raised by Star Trek.

I couldn't sleep for two years, they tried to break my nerves. They used a lot of psychology to brainwash.

What the war did was give me the opportunity of three years of continuous reading, and it was in the course of reading that I became convinced that I should become an economist.

You look at the whole Human Rights questions, I happened to be there at just the right time when the country was awakening - this goes to the first question you asked - the whole country was awakening to a hundred years of injustice that hadn't been resolved yet.

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.

I had a wonderful time with the Stones but after 31 years, I thought it was time to move on.

The average life spans of many bands are not that long, up to five years if they are lucky.

For years the Trio did nothing but play for musicians and other hip people. We practically starved to death.

Had the Hebrews not been disturbed in their progress a thousand and more years ago, they would have solved all the great problems of civilization which are being solved now under all the difficulties imposed by the spirit of the Middle Ages.

There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. It is only myth that attempts to say how the universe came to be, either four thousand or twenty billion years ago.

Plan Colombia was supposed to reduce Colombia's cultivation and distribution of drugs by 50 percent, but 6 years and $4.7 billion later, the drug control results are meager at best.

So the guy that we're really targeting our system at this year is one of the guys who brought a 16bit system three or four years ago and has pretty much had it with that, and he's ready to buy something new.

As a scientist, my attention became totally focused on global warming some 15 years ago by the elegant and powerful measurements of carbon dioxide trapped in ice cores taken as much as 2 miles deep from the great East Antarctica ice sheet.

I have everything I had 20 years ago, only it's all a little lower.

Confidence comes from hours and days and weeks and years of constant work and dedication.

In the past 3-4 years I've developed a habit of keeping numerous small cassette recorders in my house and in a bag with me so that I'm able to commit to tape memory song ideas on a constant basis.

I've been a financial journalist for 30 years.

If Davis Cup was a little bit less or once every two years, I would be more inclined to play. But the way it is now, it is too much tennis for me.

I'd been trying for all of the eight years we'd been married to have a child, and finally I did.

I don't shop. I haven't shopped in about four years.

Yippee! I can't believe I made it. It feels like a long haul to get here. I'm so fine with it. People want you to have some sort of breakdown, but I'm relieved to be 40 years old, and I've lived a life.