In: Finance
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%.
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.