673_Bonds_and_Swaps_examples - NBA 673 Spring 2006 Bonds...

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NBA 673 Spring 2006 Bonds and Swaps 1. Bonds : Consider a coupon bond like the one illustrated in Figure 1: T 2T 3T Price c c c P=1 Typically T = 6 months , and the coupon is expressed as a per-year payment. For example, if c = 7 : 5% per year and the bond pays two coupons per year, then each coupon payment will be worth 0 : 075 2 = $0 : 0375 . In the case of semi-annual coupon payments we often assume that coupon payments occur exactly : 5 years apart. The coupon is always expressed as a percentage of the principal, so if the principal is not equal to 1 , the coupon payments increase proportionally. You can now understand the meaning of a "zero-coupon" bond - it is just a bond that pays no coupons ( c = 0 ). Valuation formulas for bonds are simpler if we assume that we are just at the beginning of a coupon-period; and this is what we will do in this class. We note in passing, however, that it is possible - and often necessary in practice - to value bonds at other times than at the beginning of the coupon period. Let us assume that we have a bond with principal P = $1000 : 00 , c = 5% (paid semi-annually), and maturity in 1 : 5 years. What is the value of the bond? This is not a trivial question. The answer depends on both the level of interest rates and Let us address riskiness ²rst. If default can occur, then the value of the bond can risk of default, the lower the value of the bond should be, since our expectation of actually receiving the promised money decreases proportionally. Clearly, if the probability of default is 100%, then the bond is worthless. Determining the probability of default for a bond issuer (in general, the "credit risk") is an active area of research. We avoid this topic entirely by assuming either that the bond is default-free (like the usual zero-coupon bond), or that the risk of default has 1
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already been priced in. We are in the latter case when we deal with LIBOR-based zeros, since issuers of LIBOR debt can default. Assuming that the bond is not risky, we are left with determining the price of the bond based on prevailing interest rates. For now, we will assume that interest rates are constant in time. Let the constant interest rate be r = 8% , compounded semiannually. What is the value of the bond?
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This note was uploaded on 09/28/2008 for the course NBA 6730 taught by Professor Janosi,tibor during the Spring '06 term at Cornell University (Engineering School).

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673_Bonds_and_Swaps_examples - NBA 673 Spring 2006 Bonds...

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