Market Price of Risk and Random Field Driven Models of Term Structure: A Space-Time Change of Measure Look
AbstractNo-arbitrage models of term structure have the feature that the return on zero-coupon bonds is the sum of the short rate and the product of volatility and market price of risk. Well known models restrict the behavior of the market price of risk so that it is not dependent on the type of asset being modeled. We show that the models recently proposed by Goldstein and Santa-Clara and Sornette, among others, allow the market price of risk to depend on characteristics of each asset, and we quantify this dependence. A key tool in our analysis is a very general space-time change of measure theorem, proved by the first author in earlier work, and covers continuous orthogonal local martingale measures including space-time white noise.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1005.3799.
Date of creation: May 2010
Date of revision:
Publication status: Published in Finite and infinite dimensional analysis in honor of Leonard Gross (New Orleans, LA, 2001), 37-44, Contemp. Math., 317, Amer. Math. Soc., Providence, RI, 2003
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-29 (All new papers)
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- Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 13(2), pages 365-84.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 77-105, January.
- Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 14(1), pages 149-85.
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