Lecture_09

Lecture_09 - 9 Contingent Claims Valuation-Theory A...

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1 9 Contingent Claims Valuation---Theory A Motivation The purpose of this chapter is to price interest rate options given the market prices of the entire zero-coupon bond price curve and its stochastic evolution. We do not ascertain whether these zero-coupon bond prices are correct relative to each other, as in arbitraging the yield curve. We therefore need to impose conditions on the zero-coupon bond price curve’s evolution, given the current market prices, so that it is arbitrage-free. Options are priced relative to this evolution.
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2 This change in perspective is dictated by the circumstances surrounding the application. If the initial zero-coupon bond price curve is not taken as given, and the techniques of chapters 7 and 8 applied, then mispricings observed in interest rate options could be due to either mispriced zero-coupon bonds or mispriced options. Trading any zero-coupon bond mispricings using options is an indirect and highly levered strategy that is sensitive to model risk.
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3 A better approach is to trade these zero-coupon bond mispricings directly, using the bond trading strategies of Chapters 7 and 8. The techniques of this chapter therefore seek mispricings of interest rate options relative to the market prices of the entire zero-coupon bond price curve (not just the prices of a few bonds). Then, one is guaranteed that the arbitrage opportunities discovered are due to the options themselves.
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4 B The One-Factor Economy The key insight to be understood in this chapter is how to determine when a given zero-coupon bond price curve evolution is arbitrage-free. EXAMPLE: AN ARBITRAGE FREE ZERO- COUPON BOND PRICE CURVE EVOLUTION
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5 .923845 .942322 .961169 .980392 1 .947497 .965127 .982699 1 .937148 .957211 .978085 1 .967826 .984222 1 .960529 .980015 1 .962414 .981169 1 .953877 .976147 1 .985301 1 .981381 1 .982456 1 .977778 1 .983134 1 .978637 1 .979870 1 .974502 1 1 1 1 1 1 1 1 1 P(0,4) P(0,3) P(0,2) P(0,1) P(0,0) = time 0 1 2 3 4 Figure 9.1: An Example of a One-Factor Bond Price Curve Evolution.
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In practice the initial zero-coupon bond price curve is based on available market quotes. From this evolution we can compute the spot rate
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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.

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Lecture_09 - 9 Contingent Claims Valuation-Theory A...

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