Question

A six month call option on Harkonnen BioSands stock with a strike of 50 currently sells for 3. A put option with the same strike and expiration date sells for 2. The interest rate is 2.5 percent. Harkonnen currently sells for 52 per share.

Given all this, explain your arbitrage strategy and how much money you expect to make.

Answer 1

S = Stock price =	52
K = Strike price =	50
r = rate =	2.5%
e = exponential value = exp(.) =	2.718282
t = time =	0.5
P = Put option price =	3.0
C = Call option price =	2.0
Using put call parity formula:
C = P + S - K*exp(-r*t)
C = 2 + 52 - 50*EXP(-0.025*0.5)
C = 4.62111

Given call option price is 3 but as we calculated call option price through put-call parity equation we can see the value of call option is 4.62111.

Hence, we can buy cheap call option selling at 3 and later when market corrects according to put call parity equation then we can sell put at higher rate of 4.62111 and that will be clear arbitrage. We can make arbitrage profit of 1.62111 (4.62111 - 3)

Assuming, put-call parity holds.