Question

One stock is selling for $54 per share. Calls and puts with a $55 strike and 360 days until expiration are selling for $8 and $4, respectively. What is the arbitrage profit, if we trade on one call and one put? Suppose a risk-free rate is 10%.

Answer 1

According to put call parity Theorm

Value of call + PV of strike price = Value of Put + Stock price

8 + 55 * e^-(0.1)(1) = 4 + 54

8 + 55* e^-0.1 = 58

55 * e^-0.1 = 58 - 8

55 * e^-0.1 = 50

e^-0.1 = 50 / 55

e^-0.1 = 0.909

0.09048 = 0.909

as the Value of call + PV of strike price is not equal to  Value of Put + Stock price, arbitrage exists

Strategy:

Hold a call option, Write a put option and short sell a stock

Net proceeds today = sale value of stock + premium received from put option - Premium paid for call option

= 54 + 4 - 8

= 50

Invest these proceedings for a period of one year and realize the maturity

Maturity value = Deposit value * e^rt

= 50 * e^0.1*1

= 50 *e^0.1

= 50 * 1.1052

= 55.26

buy a stock at $ 55 either using call option or put option as the case may be and clear off the short position

Net profit = maturity value - 55

= 55.26 - 55

= 0.26

risk less profit will be earned in 1 year is $ 0.26

Pls do rate, if the answer is correct and comment, if any further assistance is required.