Introduction to Corporate Finance

ParT 2: ValuaTION, rISk aNd reTurN

example

Suppose you are tracking two shares. One exhibits

much more volatility than the other. Let’s call the

more volatile shares Extreme Pty Ltd and the less

volatile shares Steady Corporation. At present, shares

of both companies sell for about $40. At-the-money

put and call options are available on both shares,

with an expiration date in three months. Based on

the historical volatility of each share, you estimate a

range of prices that you think the shares may attain

by the time the options expire. Next to each possible

share price, you write down the option payoff that

will occur if the shares actually reach that price on

the expiration date (the strike price is $40 for both

options). The numbers appear in Table 8.5.

The payoffs of puts and calls for both companies

are zero exactly half the time. But when the payoffs

are not zero, they are much larger for Extreme Pty

Ltd than they are for Steady Corporation. That

makes options on shares in Extreme Pty Ltd much

more valuable than options on shares in Steady

Corporation.

Summing up, we now know that option prices usually increase as time to expiration increases. Option

values also rise as the volatility of the underlying asset increases. Call option prices increase as the

difference between the share price and the strike price (S–X) grows larger, whereas put prices increase

as this difference decreases. We are finally ready to tie all this together and calculate market price of puts

and calls. Fortunately, simple but powerful tools exist for valuing options. We examine two approaches

for valuing options, the binomial model and the Black–Scholes model.

8 Throughout most of this book, we have shown that if an asset’s risk increases, its price declines.

Why is the opposite true for options?

9 Put options increase in value as share prices fall, and call options increase in value as share prices

rise. How can the same movement in an underlying variable (for example, an increase either in time

before expiration or in volatility) cause both put and call prices to rise at the same time?

CONCEPT REVIEW QUESTIONS 8-3

8-4 OPTION PrICING MOdelS

Earlier in this chapter, we studied an important relationship linking the prices of puts, calls, shares and

risk-free bonds. Put–call parity establishes a direct link between the prices of these assets, a link that

must hold to prevent arbitrage opportunities. A similar logic drives the binomial option pricing model. We

shall discuss this model in section 8-4a below.

TaBle 8.5 POSSIBLE OPTION PAYOFFS FOR

EXTREME PTY LTD AND STEADY

CORPORATION

Shares Potential prices

in three months

Call

payoff

Put

payoff

Extreme Pty Ltd $15 $0 $25

35 0 5

45 5 0

65 25 0

Steady Corporation $30 0 $10

38 0 2

42 2 0

50 10 0