Question

A four-month call option with $60 strike price is currently selling at $5. The underlying stock price is $59. The risk-free rate is 12% p.a. The put with same maturity and strike price is selling at $3.5. Can an arbitrageur make riskless profit? If ‘YES’ what strategies an arbitrageur should take to make this profit?

If your answer above is ‘YES’, calculate the arbitrage profit by completing the following table showing strategy (i.e., whether buying or selling put/call portfolio); position, immediate cash flows and cash flows at expiry (i.e., in 4 months)

Strategy	Position	Immediate cash flows	Cash flow in 4 months
			ST < $60	ST ≥ $60
Total

Answer 1

Strike Price = $60
Rf Rate = 12% p.a.
Maturity = 4 months
Call Option Premium = $5
Put Option Premium = $3.5
Current Stock Price = $59

Put-Call Parity

Stock + Put Option Premium = Call Option Premium + [Strike Price / (1+Rf)ⁿ]

Stock + Put Premium = 59 + 3.5 = 62.5
Call Option Premium + [Strike Price / (1+Rf)ⁿ] = 5 + [60/(1+0.12)^(4/12)]
= 5 + 57.78
= 62.78

Since a portfolio consisting of Call option + Zero-coupon bond representing the present value of strike price is overvalued, therefore we need to short the portfolio and we need to go long on the other portfolio which is undervalued i.e. of stock + put option.

The strategy used is called conversion strategy where we long the put and short the call option

Combine the two portfolios

We will buy the Put Option + Stock and hence our outflow is $62.5 ($3.5 + $59)
We will short the call option + Zero Coupon bond and hence our inflow is $62.78 ($5 + $57.78)
Hence our net inflow is $62.78 - $62.5 = $0.28

Immediate cash flow = net inflow = $0.28