Question

The price of a non-dividend paying stock is $45 and the price of a six-month European call option on the stock with a strike price of $46 is $1. The risk-free interest rate is 6% per annum. The price of a six-month European put option is $2. Both put and call have the same strike price. Is there an arbitrage opportunity? If yes, what are your actions now and in six months? What is the net profit in six months?

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

As per put-call parity

P+ S = present value of X + C

P= value of put option.

S= current price of the share

X= strike price

C= value of call option.

Present value of X = X/e^r

r = risk free rate.

Given:

P= value of put option = 2

S= current price of share= 45

X= strike price = 46

Present value of X = 46/e^(0.06*0.5)

r = risk free rate. 6%

2+45 =46/e^(0.06*0.5) +C

C= 2.36

Value/Price of call option =$2.36

b. If the value of the call option is $2.36, then put-call parity is violated as the actual call price is $1.

And there is an arbitrage opportunity.

Arbitrage Opportunity:

Now,

Buy Call

Buy Risk-Free Asset.

After 6 months.

Sell Put,

Sell Stock.

To utilise the opportunity.

Profit is equal to the difference between the call price. = Should be as per PCP-Actual

= 2.36-1

= $1.36 (Answer).