You are offered an investment, whose payoff is linked to a stock. You are given
(i) The current stock price is 100.
(ii) The continuously compounded risk-free interest rate is 3%.
(iii) The stock pays continuous dividend at a rate of 1%.
(iv) The annual volatility of the stock is 0.3.
(v) The payoff is min{max{S(1), S(0)e0.05}, S(0)e0.20} and is made at the end of one year, where S(t) denotes the stock price at time t.
Determine the expected present value of the investment at time 0, based on
(a) the Black-Scholes framework;
(b) the binomial tree framework with every 6 months being one period.
(Hint: Express first min{max{S(1), S(0)e0.05}, S(0)e0.20} as call/put option payoffs.)