6. (10 points) A binary option (also called digital option) is a financial exotic option in which the payoff at maturity is either some fixed US dollar amount or nothing at all. An example of a binary option is a cash-or-nothing option written on a stock. It pays the holder the fixed amount H at maturity T > 0, but only if the stock price at time T is above a certain threshold K. 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. 6. (10 points) A binary option (also called digital option) is a financial exotic option in which the payoff at maturity is either some fixed US dollar amount or nothing at all. An example of a binary option is a cash-or-nothing option written on a stock. It pays the holder the fixed amount H at maturity T > 0, but only if the stock price at time T is above a certain threshold K. 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