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. ↗
Within minutes of the attack, your Department of Public Safety mobilized its Operations Center, headed by a national expert on weapons of mass destruction. ↗
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. ↗
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. ↗
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. ↗
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. ↗
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. ↗
