Open Ended Questions (show calculations to get credit) Q1. Suppose an American put is trading for...

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Open Ended Questions (show calculations to get credit) Q1. Suppose an American put is trading for $9 and an American Call is trading for $12.00, where both options have identical trading terms. The underlying stock price is $100 and exercise price is $102. The annual risk-free rate is 5 percent and time to expiration for both options is six months. Assuming that the stock pays no dividend, Identify if you can develop an arbitrage strategy. If there is an arbitrage using put-call parity, how will you generate arbitrage profits? Show the exact amount. (16 points). Problem 3.2 (2 points) Let K > AK and c(t,T,K) be the price of a European call option with strike K and maturity T. Show that c(t,T,K-AK)- 2 c(t, T, K) + c(t, T, K+AK) 0. Financial derivatives: derivatives specification and cash flows, static no-arbitrage relationships, futures contract. Binomial option pricing models: risk-neutral pricing, replicating portfolio. Black-Scholes option pricing model: lognormal model, Black-Scholes formula, historical volatility. Derivatives risk management: Greeks, hedging. Mean-variance portfolio theory: mean-variance setting, efficient frontier, capital market line. Asset pricing models: CAPM, factor models. Investment Risks: risk measures. Behavioral Finance: efficient market hypothesis (EMH), anomalies, behavioral biases. Question 4. [30 marks] Suppose that in a particular discrete-time stock market, the stock prices follow a binomial tree model with the time step taken to be 1 year. Let u= 0.15 and d = -0.05 be the one-step rates of return of stock prices, corresponding to the price going up and down respectively. The current stock price S(0) = 50 and the risk-free rate of return for one year is r = 5%. (i) Find the risk-neutral probability of the binomial tree model. (ii) Find the risk-neutral expectation of the stock price EQ [S(2)] after two time steps. (iii) Suppose that the stock price goes up to 55 after one year. What is the risk-neutral conditional expectation of the stock price EQ [S(2)|S(1)]? Open Ended Questions (show calculations to get credit) Q1. Suppose an American put is trading for $9 and an American Call is trading for $12.00, where both options have identical trading terms. The underlying stock price is $100 and exercise price is $102. The annual risk-free rate is 5 percent and time to expiration for both options is six months. Assuming that the stock pays no dividend, Identify if you can develop an arbitrage strategy. If there is an arbitrage using put-call parity, how will you generate arbitrage profits? Show the exact amount. (16 points). Problem 3.2 (2 points) Let K > AK and c(t,T,K) be the price of a European call option with strike K and maturity T. Show that c(t,T,K-AK)- 2 c(t, T, K) + c(t, T, K+AK) 0. Financial derivatives: derivatives specification and cash flows, static no-arbitrage relationships, futures contract. Binomial option pricing models: risk-neutral pricing, replicating portfolio. Black-Scholes option pricing model: lognormal model, Black-Scholes formula, historical volatility. Derivatives risk management: Greeks, hedging. Mean-variance portfolio theory: mean-variance setting, efficient frontier, capital market line. Asset pricing models: CAPM, factor models. Investment Risks: risk measures. Behavioral Finance: efficient market hypothesis (EMH), anomalies, behavioral biases. Question 4. [30 marks] Suppose that in a particular discrete-time stock market, the stock prices follow a binomial tree model with the time step taken to be 1 year. Let u= 0.15 and d = -0.05 be the one-step rates of return of stock prices, corresponding to the price going up and down respectively. The current stock price S(0) = 50 and the risk-free rate of return for one year is r = 5%. (i) Find the risk-neutral probability of the binomial tree model. (ii) Find the risk-neutral expectation of the stock price EQ [S(2)] after two time steps. (iii) Suppose that the stock price goes up to 55 after one year. What is the risk-neutral conditional expectation of the stock price EQ [S(2)|S(1)]?