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Local Stochastic Volatility With Jumps: Analytical Approximations

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  • STEFANO PAGLIARANI

    (Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova, Italy)

  • ANDREA PASCUCCI

    (Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy)

Abstract

We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function, which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.

Suggested Citation

  • Stefano Pagliarani & Andrea Pascucci, 2013. "Local Stochastic Volatility With Jumps: Analytical Approximations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-35.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:08:n:s0219024913500507
    DOI: 10.1142/S0219024913500507
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    2. Sun-Yong Choi & Jean-Pierre Fouque & Jeong-Hoon Kim, 2013. "Option pricing under hybrid stochastic and local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1157-1165, July.
    3. Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
    4. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    5. Kilin, Fiodar, 2007. "Accelerating the calibration of stochastic volatility models," CPQF Working Paper Series 6, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
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    Citations

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    Cited by:

    1. Kenichiro Shiraya & Akihiko Takahashi, 2015. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models," CARF F-Series CARF-F-365, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Recchioni, Maria Cristina & Iori, Giulia & Tedeschi, Gabriele & Ouellette, Michelle S., 2021. "The complete Gaussian kernel in the multi-factor Heston model: Option pricing and implied volatility applications," European Journal of Operational Research, Elsevier, vol. 293(1), pages 336-360.
    3. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility," Papers 2308.15672, arXiv.org, revised Feb 2024.
    4. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2014. "Asymptotics for $d$-dimensional L\'evy-type processes," Papers 1404.3153, arXiv.org, revised Nov 2014.
    5. Dan Pirjol & Xiaoyu Wang & Lingjiong Zhu, 2024. "Short-maturity asymptotics for VIX and European options in local-stochastic volatility models," Papers 2407.16813, arXiv.org.
    6. Colin Turfus, 2018. "Quantifying Correlation Uncertainty Risk in Credit Derivatives Pricing," IJFS, MDPI, vol. 6(2), pages 1-20, April.
    7. Kenichiro Shiraya & Akihiko Takahashi, 2015. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models," CIRJE F-Series CIRJE-F-980, CIRJE, Faculty of Economics, University of Tokyo.
    8. Kenichiro Shiraya & Akihiko Takahashi, 2017. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models (Revised version of CARF-F-365 : Subsequently published in Mathematics of Operations Research)," CARF F-Series CARF-F-426, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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