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5.1 Discound bonds

Dealing with stock options, the small uncertain changes in the short term interest (or the spot rate) have been neglected in comparison with the much larger random changes in the price of the underlying share. As a consequence, the Black-Scholes model accounts only for the volatility of the underlying and is only applicable over a relatively short period of time with typically less than one year to the expiry. In contrast to stock options, bonds do not depend on an underlying and mature over time intervals as long as 30 years. The uncertain evolution of the spot rate is then the dominant factor that drives the bond price if the credit rating of the bond issuer doesn't change: a bond that pays a fixed annual coupon of 5% during the next 10 years is more valuable if the spot rate is forecasted to drop to 2% rather than if it is to rise to 6%... This chapter examines the effect of volatile interest rates on a variety of credit market securities, using the VMARKET to develop your intuition with numerical experiments for a number of standard models used for the credit market.



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