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Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives

The effect of model and parameter misspecification on the effectiveness of Gaussian hedging strategies for derivative financial instrumens is analyzed, showing that Gaussian hedges in the "natural" hedging instruments are particularly robust. This is true for all models that imply Balck/Scholes - type formulas for option prices and hedging strategies. In this paper we focus on the hedging of fixed income derivatives and show how to apply these results both within the framework of Gaussian term structure models as well as the increasingly popular market models where the prices for caplets and swaptions are given by the corresponding Black formulas. By explicitly considering the behaviour of the hedging strategy under misspecification we also derive the El Karoui, Jeanblanc-Picque and Shreve (1995, 1998) and Avellaneda, Levy and Paras (1995) results that a superhedge is obtained in the Black/Scholes model if the misspecified volatility dominates the true volatility. Furthermore, we show that the robustness and superhedging result do not hold if the natural hedging instruments are unavailable. In this case, we study criteria for the optimal choice from the instruments that are available.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 19.

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Length: 24 pages
Date of creation: 01 Aug 1999
Handle: RePEc:uts:rpaper:19
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  1. Frey, Rüdiger & Carlos A. Sin, 1997. "Bounds on European Option Prices under Stochastic Volatility," Discussion Paper Serie B 405, University of Bonn, Germany.
  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  3. 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, vol. 60(1), pages 77-105, January.
  4. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
  5. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
  6. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
  7. Nicole El Karoui & Monique Jeanblanc-Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126.
  8. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
  9. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Rudiger Frey & Daniel Sommer, 1996. "A systematic approach to pricing and hedging international derivatives with interest rate risk: analysis of international derivatives under stochastic interest rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 295-317.
  11. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
  12. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
  13. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
  14. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
  15. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
  16. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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