Question

1. The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. The term structure is flat, with all risk-free interest rates being 10%.

1. What is the price of a European put option that expires in six months and has a strike price of $30? (20 points)

Explain carefully the arbitrage opportunities if the European put price is $2.

Answer 1

Call Option Value = $2

Strike Price = $30

Underlying Stock Price = $29

Dividend = $0.50

Risk free Interest = 10%

Put Option Price = Call Option Price - Underlying Stock Price + Strike Price * exp(-r*t) + Dividend Amount

= $2.51

FOR ARBITRAGE OPPORTUNITY

we have 2 portfolios,

Portfolio A consist of call option and cash

call option price + Strike Price*exp(-r*t)

Portfolio B consist of put option and share

Put Option Price + Underlying stock price - Dividend

Value of Portfolio A;

=Call option price + Strike Price*exp(-r*t)

= $30.54

Value of Portfolio B:

= Put Option Price + Underlying stock price - Dividend

= $30.03

As, Portfolio A is overpriced relative to Portfolio B. An arbitrageur can buy the securities in Portfolio B and sell the securities in Portfolio A.