Question

A European call option and put option on a stock both have a strike price of $45 and an expiration date in six months. Both sell for $2. The risk-free interest rate is 5% p.a. The current stock price is $43. There is no dividend expected for the next six months. a) If the stock price in three months is $48, which option is in the money and which one is out of the money? b) As an arbitrageur, can you find any arbitrage opportunities from these two options? If so, please show the cash flows of your transactions carefully; if not, show your reason(s) carefully. c) How would your answers to b) change if the call option price is $1 and the put option price is $3?

Answer 1

a) If Stock Price in 3 months = 48, the call option will be "In the money", since Stock Price > Strike Price of 45

On the Contrary, the Put Option will be "Out of Money".

b)

To evaluate whether there is an arbitrage opportunity, we have to use the Put Call Parity equation :-

Price of Call + Present Value of Strike Price = Price of Put + Stock Price

Let us calculate the left hand side of equation :-

$2 + $45 / [ (1.05) ^ (1/2) ]

$2 + $43.92 = $45.92

Now, let us calculate the right hand side of equation :-

= $2 + $43 = $45

Since, both are not equal, arbitrage opportunity for $0.92 exists

c)

Let us use the revised values in the equation :-

Left hand side of equation :-

$1 + $45 / [ (1.05) ^ (1/2) ] = $1 + $43.92 = $44.92

Right hand side of equation :-

= $3 + $43 = $46

In this case, arbitrage profit for = (46 - 44.92) = $1.08