2. There is a non-dividend-paying stock with current price $45. There are currently two 4- month...

 

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2. There is a non-dividend-paying stock with current price $45. There are currently two 4- month European put options on this stock, with strike price $40 and $50, respectively. The current interest rate is 1.8% per annum, compounded continuously. (a) An investor forms a portfolio by longing one share of the option with strike $50, and shorting one share of the option with strike $40. Write out the payoff of this portfolio at maturity, as a function of stock price at maturity S(T). (3 points) (b) Using a no-arbitrage argument, is the current value of the portfolio in (a) positive or negative? Why? (2 points) (c) Suppose that the stock price follows a single-period binomial tree model. During this 4-month period, the total return of the stock is either 1.15 or 1/1.15. Find the current prices of these two options under this model. (3 points) (d) Under the binomial tree model specified in (c), what is the current value of the portfolio described in (a)? (2 points) 2. There is a non-dividend-paying stock with current price $45. There are currently two 4- month European put options on this stock, with strike price $40 and $50, respectively. The current interest rate is 1.8% per annum, compounded continuously. (a) An investor forms a portfolio by longing one share of the option with strike $50, and shorting one share of the option with strike $40. Write out the payoff of this portfolio at maturity, as a function of stock price at maturity S(T). (3 points) (b) Using a no-arbitrage argument, is the current value of the portfolio in (a) positive or negative? Why? (2 points) (c) Suppose that the stock price follows a single-period binomial tree model. During this 4-month period, the total return of the stock is either 1.15 or 1/1.15. Find the current prices of these two options under this model. (3 points) (d) Under the binomial tree model specified in (c), what is the current value of the portfolio described in (a)? (2 points)

Answer rating: 100% (QA)

SOLUTION a Let ST denote the stock price at maturity The payoff of the portfolio at maturity is given by Payoff Long Put with strike 50 Short Put with ... View the full answer