Question

Question 1. Given the price of a stock is \$21, the maturity time is 6 months,...

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.

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

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