164 The Management of Bond Investments and Trading of Debt
in the industrial sector, but the bond market was pricing-in profit risk. Quality
spreads for corporates were at levels normally seen on deep slowdowns. Therefore,
many analysts were of the opinion that the real problem with profits was deep-seated.
7.7 Modeling the volatility of interest rate premium
The last example in section 7.5 provided evidence on volatility of interest rates. Up
to a point, the volatility of interest rate premiums may be empirically mapped
through determinants of a structural model for valuing debt securities, particularly
those of higher risk. For instance, a model developed by the Deutsche Bundesbank
uses as proxies of crucial variables influencing interest rate behavior:
Volatility of equity prices
Interest rate level of risk-free investments, and
The company’s level of indebtedness.
Behind this approach is the Merton model, which looks at the payoff at maturity
from holding a corporate bond, being subject to the risk of default, as equal to hold-
ing a long riskless asset and a short put option on the market value of the firm. With
this approach, the strike price is equal to the nominal value of the bond. Say, for
instance, that firm A issues a zero-coupon bond (see Chapter 4) with B nominal value.
If the market value of firm A, VA, is greater than the nominal value of the bond at
maturity, which means VA B
Then bondholder(s) will get back the amount B.
By contrast, if As market value is lower than the nominal value B of the bond,
then bondholder(s) will receive only amount VA which, while being the full market
value of the company, is less than B (VA B). Therefore, the repayment C to the
bondholder(s) resembles the payoff from an option on the market value of the com-
pany, where the strike price is the nominal value of the bond. C is determined by the
algorithm:
C min (VA,B)
A different way of looking at this transaction is that the bondholder(s) grant(s) the
shareholder(s) a put option which the latter may exercise when the firm’s market
value is lower than the nominal value of the bond. Notice that a higher degree of the
firm’s indebtedness and a rise in the volatility of its market value,
Raises the price of the put option, and
Increases the interest rate spread of the bond relative to a risk-free asset.
In contrast to this, a higher riskless rate of interest lowers the value of the put
option and could raise the spread. Moreover, a higher share price lowers the value of
the put option, and by extension the interest rate minimum of non-investment grade

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