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erating an OAS is the rationale that the precise nature of the non-Treasury
yield curve may not have the same slope characteristics of the Treasury par
bond curve. For example, it is commonplace to observe that credit yield
spreads widen as maturities lengthen among non-Treasury bonds. An exam-
ple of this is shown in Figure 2.20. This nuance of curve evolution and
makeup can have an important bearing on any OAS output that is gener-
ated and can be a very good reason not to use a Treasury par bond curve.
We conclude this section with two around-the-triangle reviews of the
spreads presented thus far. Comments pertaining to OAS are relevant for a
bond embedded with a short call option (see Figure 2.21).
And for our second triangle review, consider Figure 2.22. As presented,
nominal spread is suggested as being the best spread for evaluating liquid-
ity or credit values, forward spread is suggested as being the best spread to
capture the information embedded in an entire yield curve, and OAS is sug-
gested as being the best spread to capture the value of optionality.
Accordingly, if there is no optionality in a bond or if volatility is zero, then
only a forward and a nominal spread offer insight. And if volatility is zero
and the term structure of interest rates is perfectly flat, only a nominal spread
offers insight.

Sample non-Treasury par bond curve

Sample Treasury par
bond curve

The slope of the non-Treasury par
bond curve widens as maturities


FIGURE 2.20 Credit yield spreads widen as maturities lengthen among non-Treasury bonds.

Cash Flows

• FS > 0 when par bond curves
are upward sloping.
• FS < 0 when par bond curves
are downward sloping.
• FS = NS when par bond
curves are flat.

Nominal Forward


• OAS > or = 0 regardless of par bond curve shapes.
• OAS = FS when volatility value is zero.
• OAS = FS = NS when T = 0 (settlement is immediate), or when there is
no optionality and the par bond curves are flat.

FIGURE 2.21 Nominal spreads (NS), forward spreads (FS), and option-adjusted
spreads (OAS).

If the par bond curve is flat then
there is no use for a forward
spread analysis for bonds
without optionality; the nominal
spread will suffice.
Useful to identify
liquidity and credit
spread values
Useful to identify an
Nominal embedded curve value


Useful to identify embedded
option value
If there is no embedded
optionality, or if key option
variables effectively reduce
the value of the embedded
option(s) to that of a forward
(as when volatility value is
zero), then there is no use for
an OAS; the forward spread
will suffice.

FIGURE 2.22 Interrelationships among nominal, forward, and option-adjusted spreads.


Sometimes forwards and futures and options are referred to as derivatives.
For a consumer, bank checks and credit cards are derivatives of cash. That
is, they are used in place of cash, but they are not the same as cash. By
virtue of not being the same as cash, this may either be a positive or neg-
ative consideration. Being able to write a check for something when we
have no cash with us is a positive thing, but writing a check for more
money than we have in the bank is a negative thing. Similarly, forwards
and futures and options as derivatives are easily traced back to a particu-
lar security type, and they can be used and misused by investors. In every-
day usage, if something is referred to as being a derivative of something
else, generally there is a common link. This is certainly the case here. Just
as a plant is derived from a seed, earth, and water, spot is incorporated in
both forward and future calculations as well as with option calculations.
Thus, forwards and futures and options are all derivatives of spot; they
incorporate spot as part of their valuation and composition, yet they also
are different from spot.
It sometimes is said that derivatives provide investors with leverage.
Again, in everyday usage, “leverage” can connote an objective of maxi-
mizing a given resource in as many ways as possible. If we think of cash as
a resource, one way to maximize our use of it is to manage the way it works
for us on a day-to-day basis. For example, when we pay for our groceries
with a personal check instead of cash, the cash continues to earn interest
in our interest-bearing checking account up until the time the check clears
(perhaps even several days after we have eaten the groceries we purchased).
We leveraged our cash by allowing its existence in a checking account to
enable us to purchase food today and continue to earn interest on it for days
Similarly, when a forward is used to purchase a bond, no cash is paid
up front; no cash is exchanged at all until the bond actually is received in
the future. Since this frees up the use of our cash until it is actually
required sometime later, the forward is said to be a leveraged transaction.
However, whatever investors may do with their cash until such time that
the forward expires, they have to ensure that they have the money when
the expiration day arrives. The same is true for a futures contract that is
held to expiration.
In contrast to the case with a forward or future, investors actually pur-
chase an option with money paid at the time of purchase. However, this is
still considered to be a leveraged transaction, for two reasons.

Cash Flows

1. The option™s price is not the price that would be paid for spot; the
option™s price (if it is a call option) is F K V, and for an at-the-
money option, F K V is typically much less than S17.

2. The presence of F within the option™s price formula means that no
exchange of cash for goods will take place until the option expires. In
the case of a futures option where the option trades to an underlying
futures contract as opposed to spot, there is an additional delay from
when the option expires until the time that cash is exchanged for the
spot security.

Leverage is usually the reason behind much of the criticism of deriva-
tives voiced by market observers. A common complaint is that the very exis-
tence of derivatives allows (perhaps even encourages) irresponsible
risk-taking by permitting investors to leverage a little cash into a lot of risk
via security types that do not require the same initial cash outlay as spot.
The implication is that when investors take on more risk than they should,
they endanger themselves as well as possibly others who are party to their
trading. Just as it is hard to argue for irresponsible consumers who spend
the cash in their checking accounts before the grocery check has cleared, it
is hard to argue for irresponsible investors who have no cash to honor a
derivative transaction in the financial marketplace. Various safeguards exist
to protect investors from themselves and others (as with credit and back-
ground checks as well as the use of margins, etc.). Indeed, larger financial
institutions have entire risk management departments responsible for ensur-
ing that trading guidelines are in place, are understood, and are followed.
Even with the presence of these safeguards there are serious and adverse
events that nonetheless can and do occur.
In sum, derivatives can most certainly be dangerous if misused, as can
just about any financial instrument. Understanding the fundamental risks of
any security ought to be prerequisite before, during, and after any purchase
or sale.

An at-the-money option is an option where K is equal to S. An in-the-money call
option exists when S is greater than K, and an out-of-the-money call option exists
when S is less than K. An in-the-money put option exists when S is less than K, and
an out-of-the-money put option exists when S is greater than K.
If time to expiration is a long period (many years), F K + V could be greater
than S.


For bonds, equities, and currencies, the formula for an option™s valuation is
the same. For a call option it is F K V, and for a put option it is K F
V. In either case, the worst-case scenario for an option™s value is zero, since
there is no such thing as a negative price. Although the variable labels are
the same (F, K, and V), the inputs used to calculate these variables can dif-
fer appreciably. With regard to F, for example, F for a Treasury bill is as sim-
ple as S (1 RT) while for a currency it is S (1 T (Rh Ro)). And with
regard to V, volatility value is a function of time, the standard deviation of
the underlying spot, and R.

This chapter outlined the principal differences and similarities among the
three basic cash flow types in the market. Figure 2.23 reinforces the inter-
relationships among spot, forwards and futures, and options.
Chapter 3 adds the next layer of credit and shows how credit is greatly
influenced by products (Chapter 1) and cash flows (Chapter 2).

Cash Flows

2-year Treasury



2-year Treasury
one year forward


The fact that the forward does not
require an upfront payment and that
the option costs a fraction of the
upfront cost of spot is what contributes
to forwards and options being referred


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