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Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method

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  • Xu, Guoping
  • Zheng, Harry

Abstract

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with the basket value process. The numerical tests show that the suggested method is fast and accurate in comparison with the Monte Carlo and other methods in most cases.

Suggested Citation

  • Xu, Guoping & Zheng, Harry, 2010. "Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 415-422, December.
  • Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:415-422
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    References listed on IDEAS

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    1. Xu, Guoping & Zheng, Harry, 2009. "Approximate basket options valuation for a jump-diffusion model," Insurance: Mathematics and Economics, Elsevier, pages 188-194.
    2. Vanmaele, Michele & Deelstra, Griselda & Liinev, Jan, 2004. "Approximation of stop-loss premiums involving sums of lognormals by conditioning on two variables," Insurance: Mathematics and Economics, Elsevier, pages 343-367.
    3. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, pages 231-262.
    4. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Atsushi Kawai, 2003. "A new approximate swaption formula in the LIBOR market model: an asymptotic expansion approach," Applied Mathematical Finance, Taylor & Francis Journals, pages 49-74.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
    8. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
    9. Michèle Vanmaele & Griselda Deelstra & Jan Liinev, 2004. "Approximation of stop-loss premiums involving sums of lognormals by conditioning on two variables," ULB Institutional Repository 2013/7604, ULB -- Universite Libre de Bruxelles.
    10. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, pages 1705-1711.
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    Citations

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    Cited by:

    1. Kenichiro Shiraya & Akihiko Takahashi, 2015. "An Approximation Formula for Basket Option Prices under Local Stochastic Volatility with Jumps: an Application to Commodity Markets," CIRJE F-Series CIRJE-F-973, CIRJE, Faculty of Economics, University of Tokyo.
    2. Akihiko Takahashi & Toshihiro Yamada, 2014. "This paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its Greeks (sensitivities) under a stochastic volatility model. More gene," CARF F-Series CARF-F-347, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2014.
    3. Kenichiro Shiraya & Akihiko Takahashi, 2015. "An approximation formula for basket option prices under local stochastic volatility with jumps: an application to commodity markets," CARF F-Series CARF-F-361, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    4. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    5. Stefano, Pagliarani & Pascucci, Andrea & Candia, Riga, 2011. "Expansion formulae for local Lévy models," MPRA Paper 34571, University Library of Munich, Germany.

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