**Put-Call Parity Equation and Uses (European Calls and Puts) – Nick Krause**

From reading the text book, Financial Markets and Corporate Strategy, I've learned that Put-Call Parity allows us to see the relationship between the price of a call option and a put option, when they have identical strike prices and expiration periods. The put-call parity formula is one of the important tools for option pricing. This formula allows us to estimate what a put or call premium would be (with no dividends and no arbitrage) based on the exercise price of the stock, the risk free interest rate, the market price of the stock, and one of either the put or call premium. This formula is very helpful for option based interpretations of corporate securities as well as portfolio insurance.

The formula to show the relationship of put-call parity is: **c _{0} - p_{0} = S_{0} – PV(K)**. This equation can be formatted to solve either put or call premiums (as seen below).

To estimate for a call premium

**c _{0} = p_{0} + S_{0} – PV(K)**

To estimate for a put premium

**p _{0} = c_{0} – S_{0} + PV(K)**

p_{0} = current value of a put premium

c_{0} = current value of a call premium

S_{0} = market value of the stock

PV(K) = present value of the strike (exercise) price

**Examples based on questions from chapter tests:**

Use put-call parity relationship to estimate the **call premium** that is consistent with the following terms. Exercise price for both put and call = $100, Market price of stock = $110.76, Risk free interest rate = 8.3%, Put Premium = $1.63. The option expires in one year.

*The formula to use is: **c _{0} = p_{0} + S_{0} – PV(K)**

Find the amounts for the equation:

p_{0} = $1.63

c_{0} = ?

S_{0} = 110.76

PV(K) = $92.34 (Found by dividing the Strike price by 1 + risk free interest rate: 100/1.083)

**c _{0}** = $1.63 + $110.76 - $92.34 =

**$20.05**(The Premium you would have on a Call Option)

Use put-call parity relationship to estimate the **put premium** that is consistent with the following terms. Exercise price for both put and call = $150, Market price of stock = $137.50, Risk free interest rate = 6.7%, Call Premium = $2.35. The option expires in one year.

*The formula to use is: **p _{0} = c_{0} – S_{0} + PV(K)**

Find the amounts for the equation:

p_{0} = ?

c_{0} = $2.35

S_{0} = $137.50

PV(K) = 140.58 (Found by dividing the Strike price by 1 + risk free interest rate: 150/1.067)

**p _{0}** = $2.35 - $137.50 + 140.58 =

**$5.43**(The Premium you would have on a Put Option)