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516 Part FIVE Derivative Markets

Bond A Bond B
Annual coupon $80 $80
Maturity date 10 years 10 years
Quality rating Baa Baa
Conversion ratio 20 25
Stock price $30 $50
Conversion value $600 $1,250
Market yield on 10-year Baa-rated bonds 8.5% 8.5%
Value as straight debt $967 $967
Actual bond price $972 $1,255
Reported yield to maturity 8.42% 4.76%

Bond A has a conversion value of only $600. Its value as straight debt, in contrast, is $967.
This is the present value of the coupon and principal payments at a market rate for straight
debt of 8.5%. The bond™s price is $972, so the premium over straight bond value is only $5,
reflecting the low probability of conversion. Its reported yield to maturity based on scheduled
coupon payments and the market price of $972 is 8.42%, close to that of straight debt.
The conversion option on bond B is in the money. Conversion value is $1,250, and the bond™s
price, $1,255, reflects its value as equity (plus $5 for the protection the bond offers against stock
price declines). The bond™s reported yield is 4.76%, far below the comparable yield on straight
debt. The big yield sacrifice is attributable to the far greater value of the conversion option.
In theory, we could value convertible bonds by treating them as straight debt plus call op-
tions. In practice, however, this approach is often impractical for several reasons:
1. The conversion price frequently increases over time, which means the exercise price for
the option changes.
2. Stocks may pay several dividends over the life of the bond, further complicating the
option value analysis.
3. Most convertibles also are callable at the discretion of the firm. In essence, both the
investor and the issuer hold options on each other. If the issuer exercises its call option to
repurchase the bond, the bondholders typically have a month during which they still can
convert. When issuers use a call option, knowing that bondholders will choose to convert,
the issuer is said to have forced a conversion. These conditions together mean the actual
maturity of the bond is indeterminate.

Warrants are essentially call options issued by a firm. One important difference between calls
and warrants is that exercise of a warrant requires the firm to issue a new share of stock to sat-
An option issued by
isfy its obligation”the total number of shares outstanding increases. Exercise of a call option
the firm to purchase
requires only that the writer of the call deliver an already-issued share of stock to discharge
shares of the firm™s
stock. the obligation. In this case, the number of shares outstanding remains fixed. Also unlike call
options, warrants result in a cash flow to the firm when the warrant holder pays the exercise
price. These differences mean warrant values will differ somewhat from the values of call op-
tions with identical terms.
Like convertible debt, warrant terms may be tailored to meet the needs of the firm. Also like
convertible debt, warrants generally are protected against stock splits and dividends in that the
exercise price and the number of warrants held are adjusted to offset the effects of the split.
Warrants often are issued in conjunction with another security. Bonds, for example, may be
packaged together with a warrant “sweetener,” frequently a warrant that may be sold sepa-
rately. This is called a detachable warrant.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

14 Options Markets

Issue of warrants and convertible securities creates the potential for an increase in out-
standing shares of stock if exercise occurs. Exercise obviously would affect financial statistics
that are computed on a per-share basis, so annual reports must provide earnings per share fig-
ures under the assumption that all convertible securities and warrants are exercised. These fig-
ures are called fully diluted earnings per share.3

Collateralized Loans
Many loan arrangements require that the borrower put up collateral to guarantee the loan will
be paid back. In the event of default, the lender takes possession of the collateral. A nonre-
course loan gives the lender no recourse beyond the right to the collateral. That is, the lender
may not sue the borrower for further payment if the collateral turns out not to be valuable
enough to repay the loan.4
This arrangement gives an implicit call option to the borrower. Assume the borrower is ob-
ligated to pay back L dollars at the maturity of the loan. The collateral will be worth ST dollars
at maturity. (Its value today is S0.) The borrower has the option to wait until loan maturity and
repay the loan only if the collateral is worth more than the L dollars necessary to satisfy the
loan. If the collateral is worth less than L, the borrower can default on the loan, discharging
the obligation by forfeiting the collateral, which is worth only ST.
Another way of describing such a loan is to view the borrower as turning over collateral to
the lender but retaining the right to reclaim it by paying off the loan. The transfer of the col-
lateral with the right to reclaim it is equivalent to a payment of S0 dollars, less a simultaneous
recovery of a sum that resembles a call option with exercise price L. Basically, the borrower
turns over collateral and keeps an option to “repurchase” it for L dollars at the maturity of the
loan if L turns out to be less than ST. This is a call option.
A third way to look at a collaterized loan is to assume the borrower will repay the L dollars
with certainty but also retain the option to sell the collateral to the lender for L dollars, even if
ST is less than L. In this case, the sale of the collateral would generate the cash necessary to
satisfy the loan. The ability to “sell” the collateral for a price of L dollars represents a put op-
tion, which guarantees the borrower can raise enough money to satisfy the loan simply by
turning over the collateral.
Figure 14.14 illustrates these interpretations. Figure 14.14A is the value of the payment to
be received by the lender, which equals the minimum of ST or L. Panel B shows that this
amount can be expressed as ST minus the payoff of the call implicitly written by the lender and
held by the borrower. Panel C shows it also can be viewed as a receipt of L dollars minus the
proceeds of a put option.

Levered Equity and Risky Debt
Investors holding stock in incorporated firms are protected by limited liability, which means
that if the firm cannot pay its debts, the firm™s creditors may attach only the firm™s assets and
may not sue the corporation™s equityholders for further payment. In effect, any time the cor-
poration borrows money, the maximum possible collateral for the loan is the total of the firm™s

We should note that the exercise of a convertible bond need not reduce earnings per share (EPS). Diluted EPS will
be less than undiluted EPS only if interest saved (per share) on the converted bonds is less than the prior EPS.
In reality, of course, defaulting on a loan is not so simple. Losses of reputation are involved as well as considerations
of ethical behavior. This is a description of a pure nonrecourse loan where both parties agree from the outset that only
the collateral backs the loan and that default is not to be taken as a sign of bad faith if the collateral is insufficient to
repay the loan.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

518 Part FIVE Derivative Markets

F I G U R E 14.14 Payoff
Collateralized loan

Payoff to lender

When ST exceeds L, the loan is repaid and the collateral is reclaimed.
Otherwise, the collateral is forfeited and the total loan repayment is
worth only ST.


Payoff to call with exercise price L

ST dollars minus the payoff
to the implicit call option



Payoff to a put with
exercise price L
L dollars minus the payoff to
the implicit put option


assets. If the firm declares bankruptcy, we can interpret this as an admission that the assets of
the firm are insufficient to satisfy the claims against it. The corporation may discharge its ob-
ligations by transferring ownership of the firm™s assets to the creditors.
Just as is true for nonrecourse collateralized loans, the required payment to the creditors
represents the exercise price of the implicit option, while the value of the firm is the underly-
ing asset. The equityholders have a put option to transfer their ownership claims on the firm
to the creditors in return for the face value of the firm™s debt.
Alternatively, we may view the equityholders as retaining a call option. They have, in ef-
fect, already transferred their ownership claim to the firm to the creditors but have retained the
right to reacquire the ownership claim by paying off the loan. Hence, the equityholders have
the option to “buy back” the firm for a specified price, or they have a call option.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

14 Options Markets

The significance of this observation is that analysts can value corporate bonds using
option-pricing techniques. The default premium required of risky debt in principle can be
estimated using option valuation models. We will consider some of these models in the next

Investors clearly value the portfolio strategies made possible by trading options; this is re-
flected in the heavy trading volume in these markets and their tremendous success. Success
breeds imitation, and in recent years we have witnessed tremendous innovation in the range of
option instruments available to investors. Part of this innovation has occurred in the market for
customized options, which now trade in active over-the-counter markets. Many of these op-
tions have terms that would have been highly unusual even a few years ago; they therefore are
called “exotic options.” In this section, we will survey some of the more interesting variants
of these new instruments.

Asian Options
You already have been introduced to American and European options. Asian options are op-
tions with payoffs that depend on the average (rather than final) price of the underlying asset
during at least some portion of the life of the option. For example, an Asian call option may
have a payoff that is either equal to the average stock price over the last three months minus
the strike price, if that value is positive, or zero. These options may be of interest to firms that
wish to hedge a profit stream that depends on the average price of a commodity over some pe-
riod of time.

Barrier Options
Barrier options have payoffs that depend not only on some asset price at option expiration
but also on whether the underlying asset price has crossed through some “barrier.” For ex-
ample, a down-and-out option is one type of barrier option that automatically expires worth-
less if and when the stock price falls below some barrier price. Similarly, down-and-in
options will not provide a payoff unless the stock price does fall below some barrier at least
once during the life of the option. These options also are referred to as knock-out and
knock-in options.

Lookback Options
Lookback options have payoffs that depend in part on the minimum or maximum price of the
underlying asset during the life of the option. For example, a lookback call option might pro-
vide a payoff equal to the maximum stock price during the life of the option minus the exer-
cise price, as opposed to the closing stock price minus the exercise price. Such an option
provides (for a fee, of course) a form of perfect market timing, providing the call holder with
a payoff equal to the one that would accrue if the asset were purchased for X dollars and later
sold at what turns out to be its highest price.

Currency-Translated Options
Currency-translated options have either asset or exercise prices denominated in a foreign cur-
rency. A good example of such an option is the quanto, which allows an investor to fix in
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

520 Part FIVE Derivative Markets

advance the exchange rate at which an investment in a foreign currency can be converted back
into dollars. The right to translate a fixed amount of foreign currency into dollars at a given
exchange rate is a simple foreign exchange option. Quantos are more interesting, however, be-
cause the amount of currency that will be translated into dollars depends on the investment
performance of the foreign security. Therefore, a quanto in effect provides a random number


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