Fi312 Ps1

FI 312, Fall 2014 - Problem Set 2

This problem set is due on September 16th in class. Sorry, no late problem sets are accepted! All students must submit problem sets individually. Please staple your homework, and write your name and student ID on the front page.

1

Put-Call parity

This exercise asks you to test put-call parity in the data.

(a) The chart above contains option quotes for Microsoft from September 3, 2009. Verify the put-call parity condition for the options with the strike price as $26. Use the bid prices for both 1

the call and put options, and assume that Rf = 0. Note, the price of Microsoft on September 3 was $24.11. Do you find the deviation from the put-call parity? What is your arbitrage portfolio for the options? (b) What is wrong with using the bid prices for both the put and the call? If you actually want to engage in the arbitrage trade for the option with strike $26 from (a), would you use the bid or the ask price for the put? For the call? Using the appropriate (bid or ask) prices, is your proposed arbitrage trade still making money?

2

One-period option valuation

The economy next year will be either in a boom or in a recession. We have the following data about the payoffs of the stocks and bonds of a company called Vitamin Co.: Vitamin stock t=1 t=0 State 1: Boom State 2: Recession Price 7 3 4 Vitamin bond 10 10 9

(a) Consider a portfolio of x shares of Vitamin stock and y shares of Vitamin bond. Express the payoff of this portfolio in state 1 and state 2 as a function of x and y. (b) In the two states, what are the payoffs of a European call option and a European put option on Vitamin stock that has strike price X = 5 and expires in one year? (c) Equate your expression for the portfolio payoffs from (a) with the corresponding payoffs of this option. Solve this system of two equations for x and y. By the LOOP, what is the price today of the call and put options in (b)? (d) What is the (net simple) rate of return Rf...