Quinn Headington

Put-call Parity Generally speaking, put-call parity is a basic method, or formula, that compares the value of a put option to that of a call option when given the same strike (exercise) price and expiration date. Using this formula, one can calculate a potential premium that can be realized upon exercising an option.

Because the methodology for put-call parity requires the option to be exercised on the expiration date, European options are typically considered as they cannot be exercised prematurely. American options have the ability to be exercised prior to the expiration date but should not be done so unless a dividend payout makes an early exercise financially beneficial. It should also be noted that the put-call parity formula prohibits arbitrage. The put-call parity formula follows:

c - p = S - PV(K)
c = call premium p = put premium
S = spot (current) market price
PV(K) = present value of the strike (exercise) price for the call and put options

In solving the put-call parity formula, one might need to first establish PV(K). The formula for accomplishing this, which is similar to a typical present value calculation, is as follows:

PV(K) = K / (1 + rf) where K = strike (or exercise) price and rf = risk-free rate

An sample question for using the put-call parity formula to calculate an option's premium follows:

The current market price for a stock is $75. Given an exercise price for a put and call option on this stock of $70, a risk-free interest rate of 5.0% and a put premium of $1.25, what is the call premium?

We would first attempt to solve this problem by establishing the present value of the exercise price: PV(K). The exercise price is listed to be $70 and the risk-free rate is 5%, thus:

PV(K) = K / (1 + rf) = $70 / (1 + 5%) = $70 / 1.05 = $66.67

We then use this figure, along with the other previously provided information, to solve the put-call parity formula for the call option premium, c:

c - p = S - PV(K): c - $1.25 = $75 - $66.67: c = $9.58