Introduction to Corporate Finance

ParT 2: ValuaTION, rISk aNd reTurN

one share and one put option, with X = $75. No matter what happens to the share price over the next

year, these portfolios have equal payoffs on the expiration date. Therefore we can write:

Payoff on bond + Payoff on call = Payoff on share + Payoff on put

This equation applies to payoffs that occur one year in the future, when the put and call options

expire and the bond matures. However, an important principle in finance says that if two assets have

identical cash flows in the future, then they must sell for the same price today. If that were not true, then

investors could earn unlimited risk-free profits by engaging in arbitrage, simultaneously buying the asset

with the lower price and selling the asset with the higher price. To prevent arbitrage opportunities, the

price of the portfolio consisting of a bond and a call option must equal the price of the portfolio consisting of

one share and one put option.

In making the previous statement, we took a subtle, but important, step forward in understanding

options. Notice that the last sentence of the previous paragraph used the word ‘price’ rather than the

word ‘payoff.’ Because the future payoffs on these two portfolios will be identical on the expiration date,

then the prices of the portfolios must be equal on the expiration date and on any date prior to expiration.

We can express this idea algebraically as follows:

Eq. 8.1 S + P = B + C

In this equation, S stands for the current share price, P and C represent the current market prices

(premiums) of the put and call options, respectively, and B equals the current price of the risk-free, zero-

coupon bond. Equation 8.1 describes one of the most fundamental ideas in option pricing, known as

put−call parity. Put–call parity says that the prices of put and call options on the same underlying share,

with the same strike price and the same expiration date, must be related to each other.

example

Mototronics Pty Ltd shares currently sell for $28 per

share. Put and call options on Mototronics shares are

available, with a strike price of $30 and an expiration

date of one year. The price of the Mototronics call

option is $6, and the risk-free interest rate equals 5%.

What is the appropriate price for the Mototronics

put option? In other words, what price would satisfy

put–call parity?

Examine Equation 8.1. We know that the share

price equals $28 and the call price is $6. To find the

put price, we also need to know the market price

of a risk-free bond. Refer once again to Figure 8.6.

In that example, the face value of the bond is

$75, equal to the strike price of the option. To

apply put–call parity to value the Mototronics put

option, we must recognise that B, in Equation 8.1,

represents a risk-free bond with a face value of

$30, the same value as the option’s strike price.

The face value of the bond must equal the option’s

strike price because on the right-hand side of

Equation 8.1, it is the bond that provides the ‘floor’

on the portfolio value. On the left-hand side of

Equation 8.1, the put option creates a floor on the

portfolio value, and that floor is equal to the strike

price of the put. That is, if the put option’s strike

is $30, then the left-hand side of Equation 8.1 can

never be less than $30. For the right-hand side of

Equation 8.1 to have the same floor, the bond’s

face value must equal $30.

If a risk-free bond pays $30 in one year, then the

current market price of the bond equals

B = $30 ÷ (1.05) = $28.57

Plug this and the other known values into

Equation 8.1 to solve for the put price:

S + P = B + C

$28 + P = $28.57 + $6

P = $6.57

Put−call parity
A relationship that links the
market prices of shares, risk-
free bonds, call options and
put options