Suppose the interest rate r is equal to 0. Let U be the option that pays off at time te. What is the price of U at time 0? If V is as in Exercise 28.6, then U + V is the option that pays off the...

Suppose the interest rate r is equal to 0. Let U be the option that pays off

at time t_e. What is the price of U at time 0?

If V is as in Exercise 28.6, then U + V is the option that pays off the maximum of the stock price minus the minimum of the stock price, in other words, “buy low, sell high.” Naturally such an option would be expensive. It is remarkable that there exists a trading strategy that can duplicate this payoff, even though the times when the maximum and minimum occur are not stopping times.

Chapter 29