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A Note on the Malliavin differentiability of the Heston Volatility

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Author Info
Elisa Alòs ()
Christian-Olivier Ewald

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Abstract

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the Cox-Ingersoll-Ross model for interest rates.

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File URL: http://www.econ.upf.edu/docs/papers/downloads/880.pdf
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Publisher Info
Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 880.

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Date of creation: Aug 2005
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Handle: RePEc:upf:upfgen:880

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Web page: http://www.econ.upf.edu/

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Related research
Keywords: Malliavin calculus; stochastic volatility models; Heston model; Cox-Ingersoll-Ross process;

Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G19 - Financial Economics - - General Financial Markets - - - Other
C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Other
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates

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  1. Bruno Bouchard & Ivar Ekeland & Nizar Touzi, 2004. "On the Malliavin approach to Monte Carlo approximation of conditional expectations," Finance and Stochastics, Springer, vol. 8(1), pages 45-71, January. [Downloadable!] (restricted)
  2. Christian-Oliver Ewald, 2005. "Optimal Logarithmic Utility And Optimal Portfolios For An Insider In A Stochastic Volatility Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 301-319. [Downloadable!] (restricted)
  3. Nicolas Bouleau, 2003. "Error Calculus and Path Sensitivity in Financial Models," Mathematical Finance, Blackwell Publishing, vol. 13(1), pages 115-134. [Downloadable!] (restricted)
  4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  5. Eric Benhamou, 2003. "Optimal Malliavin Weighting Function for the Computation of the Greeks," Mathematical Finance, Blackwell Publishing, vol. 13(1), pages 37-53. [Downloadable!] (restricted)
  6. Christian-Oliver Ewald & Aihua Zhang, 2006. "A new technique for calibrating stochastic volatility models: the Malliavin gradient method," Quantitative Finance, Taylor and Francis Journals, vol. 6(2), pages 147-158, April. [Downloadable!] (restricted)
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