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Chapter 23

Chapter 23 Notes

Course Code
Derek Chau

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Chapter 23 Options and Corporate Finance: Basic Concepts Notes
23.1 Options
an option is a contact giving its owner the right to buy or sell an asset at a fixed price on or before a given date
some important definitions related to options are:
1) Exercising the option. The act of buying or selling the underlying asset via the option contract.
2) Strike or exercise price. The fixed price in the option contract at which the holder can buy or sell the underlying asset.
3) Expiration date. The maturity date of the option. After this date, the option is dead.
4) American and European options. An American option may be exercised at any time up to and including the expiration
date. A European option differs in that it can be exercised only on the expiration date.
23.2 Call Options
the most common type of option is called a call option
a call option gives the owner the right to buy an asset at a fixed price during a particular time period
there is no restriction on the kind of asset, but the most common options traded on exchanges are on stocks and bonds
23.3 Put Options
a put option can be viewed as the opposite of a call option
just as a call gives the holder the right to buy the stock at a fixed price, a put gives the holder the right to sell the stock for a fixed
exercise price during the life of the option
23.6 Combination of Options
investor gets same payoff from (1) buying a put and buying underlying stock; (2) buying a call and buying a zero-coupon bond
if investors have the same payoffs from the two strategies, the two strategies must have the same cost
this leads to the result that: cost of first strategy = cost of second strategy
price of underlying stock + price of put = price of call + present value of exercise price
this relationship is known as put-call parity and is one of the most fundamental relationships concerning options
23.8 An Option Pricing Formula
the value of a call option is a function of 5 variables—(1) the current price of the underlying asset, which for stock options is the
price of the shares of common stock; (2) the exercise price; (3) the time to the expiration date; (4) the variance of the underlying
asset; and (5) the risk-free interest rate
The Black-Scholes Model
C = SN (d1) – E e–rt N(d2)
where d1 = [ln (S/E) + (r + ½ σ2) t] / √σ2t and d2 = d1 - √σ2t
this formula for the value of a call, C, involves 5 parameters and a statistical concept:
1) S = current stock price
2) E = exercise price of call
3) r = continuously compounded risk-free rate of return (annualized)
4) σ2 = variance (per year) of the continuous return on the stock
5) t = time (in years) to expiration date
6) N(d) = probability that a standardized, normally distributed, random variable will be less than or equal to d
23.13 Summary and Conclusions
1. The most familiar options are puts and calls. These options give the holder the right to sell or buy shares of common stock at a
given exercise price. American options can be exercised at any time up to and including the expiration date. European options
can be exercised only at the expiration date.
2. Options can be held either in isolation or in combination. We focused on the strategy of buying a put, buying the stock, selling a
call where the put and call have both the same exercise price and the same expiration date. This strategy yields a riskless return
because the gain or loss on the call precisely offsets the gain or loss on the stock-and-put combination. In equilibrium, the return
on this strategy must be exactly equal to the riskless rate. From this, the put-call parity relationship was established:
Value of stock + Value of put – Value of call = Present value of exercise price
3. The value of an option depends on 5 factors—(1) the price of the underlying asset; (2) the exercise price; (3) the expiration date;
(4) the variability of the underlying asset; and (5) the interest rate on risk-free bonds.
The Black-Scholes model can determine the intrinsic price of an option from these five factors.
4. Much of corporate financial theory can be presented in terms of options. It was pointed out that
a. Common stock can be represented as a call option on the firm.
b. Shareholders enhance the value of their call by increasing the risk of their firm.
c. Real projects have hidden options that enhance value.
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