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Implied Calibration of Stochastic Volatility Jump Diffusion Models

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Author Info
Stefano Galluccio (BNP Paribas)
Yann Le Cam (University of Evry Val d'Essonne)
Abstract

In the context of arbitrage-free modelling of financial derivatives, we introduce a novel calibration technique for models in the affine- quadratic class for the purpose of contingent claims pricing and risk- management. In particular, we aim at calibrating a stochastic volatility jump diffusion model to the whole market volatility surface at any given time. We numerically implement the algorithm and show that the proposed approach is both stable and accurate.

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Paper provided by EconWPA in its series Finance with number 0510028.

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Length: 40 pages
Date of creation: 25 Oct 2005
Date of revision:
Handle: RePEc:wpa:wuwpfi:0510028

Note: Type of Document - pdf; pages: 40
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Web page: http://129.3.20.41

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Related research
Keywords: Affine-quadratic models; Option pricing; Model Calibration;

Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 1999. "A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation," CIRANO Working Papers 99s-48, CIRANO. [Downloadable!]
  2. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06. [Downloadable!] (restricted)
  3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  4. 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. [Downloadable!] (restricted)
  5. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224. [Downloadable!] (restricted)
  6. Matthias R. Fengler, 2005. "Arbitrage-Free Smoothing of the Implied Volatility Surface," SFB 649 Discussion Papers SFB649DP2005-019, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  7. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 4(4), pages 727-52. [Downloadable!] (restricted)
  8. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics. [Downloadable!]
    Other versions:
  9. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
  10. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  11. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, 06. [Downloadable!] (restricted)
    Other versions:
  12. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October. [Downloadable!] (restricted)
  13. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA. [Downloadable!]
  14. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  15. Monika Piazzesi, 2001. "An Econometric Model of the Yield Curve with Macroeconomic Jump Effects," NBER Working Papers 8246, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  16. Olivier Scaillet., 2003. "Linear-Quadratic Jump-Diffusion Modelling with Application to Stochastic Volatility," THEMA Working Papers 2003-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise. [Downloadable!]
    Other versions:
  17. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Giacomo Bormetti & Valentina Cazzola & Danilo Delpini, 2009. "Option Pricing Under Ornstein-Uhlenbeck Stochastic Volatility," Quantitative Finance Papers 0905.1882, arXiv.org. [Downloadable!]
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