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Explain why the value of put option on a non-dividend paying stock is equal to the...

Explain why the value of put option on a non-dividend paying stock is equal to the call value plus the present value of the exercise price minus the stock price

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Answer #1

We consider a non-dividend paying stock, existence of call and put option, existence of a bond with face value of 1

Let the price of S be S(t) at time t.

Portfolio 1: Buy 1 call option C & sell 1 put option P of the same expiry T and strike K. The payoff is S(T) - K.

Portfolio 2: Buy 1 share and borrowing K bonds. The payoff is also S(T) - K at time T, since our share bought for S(t) will be worth S(T) and the borrowed bonds will be worth K.

Assuming no arbitrage opportunities, two portfolios having same payoff at time T must have same price:

This is known as put call parity

Hence, P=C-S+PV of K

i.e.,

Value of put option on a non-dividend paying stock is equal to the call value plus the present value of the exercise price minus the stock price

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