Reference no: EM133233460

A binary option (also called digital option) is an exotic option for which the payoff at maturity to the holder of the option is either some US dollar amount or nothing at all. One example of a binary option is a cash-or-nothing option written on a stock. It pays the holder of the option the fixed US dollar amount H at maturity T > 0 ("cash"), but only if the stock price at time T is above a certain threshold K. Otherwise, the payoff is zero ("nothing").

Suppose a stock price is currently at $100. Assume that over each of the next two one-month periods the stock price will either go up by 10% or go down by 10%. The risk-free interest rate is 1% p.a. with continuous compounding.

Use a two-step binomial tree model to compute today's arbitrage-free price of a cash-or-nothing option written on that stock which pays the holder $10 in two months, but only if the stock price at that time is above today's price of $100, and nothing otherwise.