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Delta Hedging in Discrete Time under Stochastic Interest Rate

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  • Flavio ANGELINI
  • Stefano HERZEL

Abstract

We examine the e?ect of stochastic interest rate on the Delta hedging strategy in discrete time when hedging a contingent claim written on a risky asset. The performance of the hedging is mainly measured by the variance of the error. We consider a simple two-dimensional model of the type Black-Scholes combined with the Vasicek model, allowing for correlation between the stock and the interest rate. Within this model, we perform the Delta hedging ?rst by implementing the strategy by taking into account the stochasticity of interest rate and then by using a plain Black-Scholes Delta with deterministic rate. The di?erences between the two performances can be relevant, mainly depending on the correlation and on the relation between the standard deviation of the risky asset and that of the interest rate. We also consider Delta hedging for an interest rate option in the Cox-Ingersoll and Ross model. The analysis is done by applying a general result for the e?cient computation of expected value and variance of the hedging error of a certain class of strategies, which include the Delta strategy.

Suggested Citation

  • Flavio ANGELINI & Stefano HERZEL, 2012. "Delta Hedging in Discrete Time under Stochastic Interest Rate," Quaderni del Dipartimento di Economia, Finanza e Statistica 110/2012, Università di Perugia, Dipartimento Economia.
    • Handle: RePEc:pia:wpaper:110/2012
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    References listed on IDEAS

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    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. van Haastrecht, Alexander & Lord, Roger & Pelsser, Antoon & Schrager, David, 2009. "Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 436-448, December.
    5. Flavio Angelini & Stefano Herzel, 2015. "Evaluating discrete dynamic strategies in affine models," Quantitative Finance, Taylor & Francis Journals, vol. 15(2), pages 313-326, February.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Aleš Černý, 2007. "Optimal Continuous‐Time Hedging With Leptokurtic Returns," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 175-203, April.
    8. Duan, Jin-Chuan & Simonato, Jean-Guy, 1999. "Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter," Review of Quantitative Finance and Accounting, Springer, vol. 13(2), pages 111-135, September.
    9. Flavio Angelini & Stefano Herzel, 2007. "Measuring the error of dynamic hedging: a Laplace transform approach," Quaderni del Dipartimento di Economia, Finanza e Statistica 33/2007, Università di Perugia, Dipartimento Economia.
    10. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    11. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    12. Aleš Černý & Jan Kallsen, 2008. "Mean–Variance Hedging And Optimal Investment In Heston'S Model With Correlation," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 473-492, July.
    13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    14. Toft, Klaus Bjerre, 1996. "On the Mean-Variance Tradeoff in Option Replication with Transactions Costs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(2), pages 233-263, June.
    15. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
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    Cited by:

    1. Peter A. Forsyth & George Labahn, 2017. "$\epsilon$-Monotone Fourier Methods for Optimal Stochastic Control in Finance," Papers 1710.08450, arXiv.org, revised Apr 2018.

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