Question

The Put-Call Parity equation is shown below. Explain the logic of this equation from using a synthetic security based argument. P=C-S_0+Ke^(-rt)

Answer 1

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As per put-call parity (PCP)

P+ S = present value of X + C

P= value of put option.

S= current price of the share

X= strike price

C= value of call option. (PCP Call)

Present value of X = X/(1+r)

r = risk free rate.

The logic behind this equation is that buying the put option & current stock is same as buying a bond & a call.

If there is a mismatch between P & C, then put-call parity does not hold good.

Then there is a situation of Arbitrage.

We need to take benefit of this situation by conducting an arbitrage position.

Compare the value of Actual Call price in the market with that of PCP Call price.

If Actual Call< PCP Call then,

Arbitrage Strategy:

1. Buy Call.

2. Sell synthetic put option.

(Or 2. Buy Risk-free Asset.

2. Sell Put.

2. Sell Stock. )

[Note: Sell synthetic put option = Buy Risk-free Asset+ Sell Put+Sell Stock].  

If Actual Call> PCP Call then,

Arbitrage Strategy:

1. Sell Call

2. Buy synthetic put option.

or (2. Sell Risk-free Asset.

2. Buy Put.

2. Buy Stock. )

Arbitrage profit = difference between Actual Call price in the market and PCP Call price.

= Actual Price- PCP Price.