4 Binomial trees 1. Suppose that Umbrella Corporation stock currently trades at $2.25. The interest rate is 0.5% (with continuous compounding), and Umbrella Corporation shares have a volatility of 24%. Set up a two step binomial tree for the stock, with each step representing three months. Umbrella Corporation does not pay dividends. (a) What is the value of a European call option with strike price 82.20, maturing in six months time? (b) What is the value of a European put option with strike price $2.20 maturing in six months time? (c) Verify that the put-call parity relationship holds, 2. A stock price is currently $25. The interest rate is 6% (with continuous compounding). Volatil- ity is 12% per annum. In 12 months time, an exotic derivative pays off $1 if the stock price never rises above 826 over the course of the year. Otherwise the derivative pays $0. What is the derivative worth? 4 Binomial trees 1. Suppose that Umbrella Corporation stock currently trades at $2.25. The interest rate is 0.5% (with continuous compounding), and Umbrella Corporation shares have a volatility of 24%. Set up a two step binomial tree for the stock, with each step representing three months. Umbrella Corporation does not pay dividends. (a) What is the value of a European call option with strike price 82.20, maturing in six months time? (b) What is the value of a European put option with strike price $2.20 maturing in six months time? (c) Verify that the put-call parity relationship holds, 2. A stock price is currently $25. The interest rate is 6% (with continuous compounding). Volatil- ity is 12% per annum. In 12 months time, an exotic derivative pays off $1 if the stock price never rises above 826 over the course of the year. Otherwise the derivative pays $0. What is the derivative worth