"The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. What is the price of a one-year European put option on the stock with a strike price of $50

The price of a one-year European put option on the stock with a strike price of $50 is $2.09

Explanation:

As, the call and the put option is of the same asset class, we apply call-put parity to find the price of the European put option.

The call-put parity function is:

C + PV(x) = P + S; in which:

C: Price of the call option = $6;

PV(x) : present value of strike price = Strike price in one year / e^6% = 50/e^6% = $47.09

P: price of the put option

S: spot price of the asset = $51

=> P = C + PV(x) - S = 6 + 47.09 - 51 = $2.09.

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