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Calibration of a path-dependent volatility model: Empirical tests

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  • Foschi, Paolo
  • Pascucci, Andrea

Abstract

The Hobson and Rogers model for option pricing is considered. This stochastic volatility model preserves the completeness of the market and can potentially reproduce the observed smile and term structure patterns of implied volatility. A calibration procedure based on ad-hoc numerical schemes for hypoelliptic PDEs is proposed and used to quantitatively investigate the pricing performance of the model. Numerical results based on S&P500 option prices are discussed.

Suggested Citation

  • Foschi, Paolo & Pascucci, Andrea, 2009. "Calibration of a path-dependent volatility model: Empirical tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2219-2235, April.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2219-2235
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    References listed on IDEAS

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    1. Sundaresan, S.M., 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Papers 00-03, Columbia - Graduate School of Business.
    2. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    3. Figa-Talamanca, Gianna & Guerra, Maria Letizia, 2006. "Fitting prices with a complete model," Journal of Banking & Finance, Elsevier, vol. 30(1), pages 247-258, January.
    4. Andrea Pascucci & Marco Di Francesco, 2005. "On the complete model with stochastic volatility by Hobson and Rogers," Finance 0503013, University Library of Munich, Germany.
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    6. Trifi Amine, 2006. "Issues of Aggregation Over Time of Conditional Heteroscedastic Volatility Models: What Kind of Diffusion Do We Recover?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-26, December.
    7. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(1), pages 13-32, May.
    8. Amendola, Alessandra & Storti, Giuseppe, 2008. "A GMM procedure for combining volatility forecasts," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3047-3060, February.
    9. Yu, Jun & Yang, Zhenlin & Zhang, Xibin, 2006. "A class of nonlinear stochastic volatility models and its implications for pricing currency options," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2218-2231, December.
    10. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
    11. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    12. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
    13. Sekine, Jun, 2008. "Marginal distribution of some path-dependent stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1846-1850, September.
    14. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, June.
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    16. Lindström, Erik & Ströjby, Jonas & Brodén, Mats & Wiktorsson, Magnus & Holst, Jan, 2008. "Sequential calibration of options," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2877-2891, February.
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    Cited by:

    1. Mauro Rosestolato & Tiziano Vargiolu & Giovanna Villani, 2013. "Robustness for path-dependent volatility models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 137-167, November.

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