# Put Call Parity

Formula 15.11
c + PV(x) = p + s

Where:
c = the current price or market value of the European call
x = option strike price
PV(x) = the present value of the strike price ‘xeuropean’ discounted from the expiration date at a suitable risk-free rate
p = the current price or market value of the European put
s = the current market value of the underlying stock.

The put-call parity formula shows the relationship between the price of a put and the price of a call on the same underlying security with the same expiration date, which prevents arbitrage opportunities. A protective put (holding the stock and buying a put) will deliver the exact payoff as a fiduciary call (buying one call and investing the present value (PV) of the exercise price).

For the exam, you should know that a protective put = fiduciary call (asset + put = call + Bond)

Source : Investopedia.

Eg: Rearraging the above formula, if I buy a protective put and also sell call option, that results in equation

x = asset + put  – call. where x can be strike price of bond or cash, which will be a constant, thereby proving the put call parity.