Question

a six month call on stock of abc ltd with an exercise proce of 100 rupees sold for rs 8. the stock price is 80. the risk free interest rate is 6% per annum. how much would u pay for a put option on the stock of abc ltd. with same maturity and exercise price? what would u do if the actual price is dfifferent from what u are willing to pay

Answer 1

As per the put-call parity equation, C + (K/(1 + r)^t) = P + S,

where C = price of call option,

P = price of put option,

S = current stock price

K = strike price of option

r = risk free rate

t = time to expiration in years

We plug in the values to find the price of the put option :

C + (K/(1 + r)^t) = P + S

8 + (100/(1 + 6%)^6/12) = P + 80

105.13 = P + 80

P = 25.13

Value of put option = Rs. 25.13

If the actual price is different, a put-call arbitrage can be undertaken to earn an arbitrage profit. If the actual price of the put option is higher than Rs.25.13, an arbitrage profit can be earned by buying the call option, selling the put option, short selling the stock and investing the proceeds in a bond at the risk free rate. If the actual price of the put option is lower than Rs.25.13, an arbitrage profit can be earned by selling the call option, buying the put option, buying the stock and borrowing the stock value at the risk free rate.