Question

A two-month European put option on a non-dividend-paying stock has a strike price of $65. The risk-free interest rate is 5% per annum and the stock price is $58. a) What is the lower bound for this put option? b) If the market price of this put option is $3, is there an arbitrage opportunity? c) If so, define the arbitrage strategy.

Answer 1

a. For an In the money Put option, lower bound = Strike price - Stock Price = 65e ^ (-0.05*2/12) - 58 = 6.46 $

b. If the put option can be bought for 3$, which is less than the lower bound price of 6.46$, then there is an arbotrage opportunity.

c. Investor will borrow 61$ at risk free rate for 2 months, and buy the put option for 3$, and buy the stock for 58$.

This generates a profit in all circumstances. If the stock price is above $65 in one month, the option expires worthless, but the stock can be sold for at least $65. A sum of $65 received in two month has a present value of $64.46 today. The strategy therefore generates profit with a present value of at least $3.46 (6.46 - 3). If the stock price is below $65 in two month the put option is exercised and the stock owned is sold for exactly $65 (or $64.46 in present value terms). The trading strategy therefore generates a profit of exactly $3.46 in present value terms.