Please answer 7

Plot the payoff of the portfolio at the expiration date of the options. Which option must cost more and why? Make your argument using no-arbitrage reasoning. On the same graph, plot how the profit of the portfolio would appear relative to its payoff. A stock has a price of 100. It is expected to pay a dividend of $2 per share at year-end. An at-the-money European put option with I year maturity sells for $7. If the annual interest rate is 5%, what must be the price of an at-the-money European call option on the stock with 1 year maturity. Yon buy a share of stock, write a 1-year call option with strike price X = $100 and buy a 1-year put option with strike price X = $100. The net outlay required to establish this portfolio is $97. The stock pays no dividends. What is the risk-free interest rate? Suppose today's stock price of Book.com is $100. With probability 60% the price will rise to $130 in one year and with probability 40% it will fall to $80 in one year. A European put option with a strike price of $90 and a time to expiration of one year sells at $4. What is the one-year risk free rate implied by no-arbitrage (draw a binomial tree as we did in class)? What would Ik1 the no-arbitrage risk free rate if with a probability of 50% the price increases and with a probability of 50% it decreases, keeping all other values constant? Explain! Excel Question. Use the Black and Scholes file posted on Classes (under Excel files). We want to explore the effort of changing the time to expiration T from 1 to 2 years on the value of an in-the-money put option. Throughout this exercise we keep the stock price at S_0 = 40, the strike price at X = 70, the dividend rate at delta = 0, and the stock price volatility at sigma = 35%. For the interest rate r, consider various values. Show how the effect on the put price for T = 1 rightarrow 2 depends on the interest rate and explain intuitively why this happens. Confirm that the call price is always increasing in the time to expiration T