Question

Question 1. Given the price of a stock is $21, the maturity time is 6 months, the strike price is $20 and the price of European call is $4.50, assuming risk-free rate of interest is 3% per year continuously compounded, calculate the price of the European put option?

Hint: Use put-call parity relationship.

Note: Bull spreads are used when the investor believes that the price of stock will increase. A bull spread on calls consists of going long in a call with strike price K1 and going short on a call with strike price K2, with K2 > K1, and the expiration is the same for both options.

Answer 1

Computation of price of the European put option using put-call parity:
Put-call parity formula: Value of call option+Present value of strike price = Value of put option+Current price of a stock

Given, Value of call option = $4.50, Current price of a stock = $21, Strike price (k) = $20, risk free rate(r) = 3%pa, Maturity time (t) = 6months/12 = 0.5years

Present value of strike price = k*[e^(-r*t)] = 20*[2.718^(-0.03*0.5)] = 20*[2.718^(-0.015)] = 20*0.9851 = $19.70

Value of put option = Value of call option+Present value of strike price-Current price of a stock = $4.50+$19.70-$21 = $3.20

Price of the European put option = $3.20