Lecture_10 - 10 Coupon Bonds The chapter studies coupon bonds from the perspective of the arbitrage-free pricing methodology This is in contrast to

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1 10 Coupon Bonds The chapter studies coupon bonds from the perspective of the arbitrage-free pricing methodology. This is in contrast to the classical approach to fixed income analysis or coupon bond pricing that was presented in Chapter 2. The differences between the two approaches are numerous.
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2 First, the arbitrage-free pricing methodology can be used to risk manage a portfolio of bonds given an arbitrary evolution for the term structure of interest rates. The classical approach can only hedge parallel shifts in the term structure of interest rates. Second, the arbitrage-free pricing approach can be used to price interest rate derivatives in a manner consistent with that used to price coupon-bonds. The classical approach cannot. Third, the arbitrage-free pricing approach can be extended to handle foreign currency risk and credit risk. The classical approach cannot.
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3 A A Coupon Bond as a Portfolio of Zero-Coupon Bonds This section studies the arbitrage-free pricing of noncallable coupon bonds. The valuation method of this section is independent of the particular evolution of the term structure of interest rates selected; in particular, it does not depend on the number or specification of the factors in the economy, either one, two, or three factors. We define a coupon bond with principle L, coupons C, and maturity T to be a financial security that is entitled to receive coupon payments of C dollars at times 1, …, T with a principal repayment of L at time T. The coupon rate on the bond is c = 1+C/L.
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4 Table 10.1: The Cash Flows to a Typical Coupon Bond with Price B (0), Principal L, Coupon C and Maturity T Time 012… T ||| | B (0) C C C Coupons LP r i n c i p a l coupon rate c = 1+C/L
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5 The coupon bond’s cash flows can be obtained from a portfolio of zero-coupon bonds. The duplicating portfolio consists of C zero-coupon bonds maturing at times = 1 , . .., T -1 and C+L zero-coupon bonds maturity at time T. Let the market price of the coupon bond be denoted B(t) . The cost of constructing the duplicating portfolio of zero-coupon bonds is: ) T , t ( LP T 1 t i ) i , t ( CP + + = . In constructing this portfolio, it is assumed that the construction occurs after the coupon payment has been paid at time t (i.e., it represents the ex-coupon value at time t ).
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6 Thus, the arbitrage-free price of the coupon bond is: ) T , t ( LP T 1 t i ) i , t ( CP ) t ( + + = = B . (10.1) Note that the arbitrage-free price for the coupon bond can be computed without any knowledge of the evolution of the term structure of interest rates. It depends solely on the initial zero-coupon bond price curve. We now illustrate this computation with an example.
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7 Table 10.2: An Example of a Time 0 Zero-Coupon Bond Price Curve P(0,4) = .923845 P(0,3) = .942322 P(0,2) = .961169 P(0,1) = .980392
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8 Table 10.3: An Example of the Cash Flows to a Coupon Bond 0 1 2 3 4 $5 $5 $100 time coupon principal
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9 EXAMPLE: COUPON BOND CALCULATION .
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This note was uploaded on 12/09/2008 for the course NBA 5550 taught by Professor Jarrow,robert during the Fall '08 term at Cornell University (Engineering School).

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Lecture_10 - 10 Coupon Bonds The chapter studies coupon bonds from the perspective of the arbitrage-free pricing methodology This is in contrast to

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