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Analytical approximation of the transition density in a local volatility model

Author

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  • Pagliarani, Stefano
  • Pascucci, Andrea

Abstract

We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.

Suggested Citation

  • Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:31107
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    File URL: https://mpra.ub.uni-muenchen.de/31107/1/MPRA_paper_31107.pdf
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    References listed on IDEAS

    as
    1. Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, vol. 102(2), pages 390-415.
    2. Fabio Antonelli & Sergio Scarlatti, 2009. "Pricing options under stochastic volatility: a power series approach," Finance and Stochastics, Springer, vol. 13(2), pages 269-303, April.
    3. A. E. Whalley & P. Wilmott, 1997. "An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 307-324.
    4. Sam Howison, 2005. "Matched asymptotic expansions in financial engineering," OFRC Working Papers Series 2005mf01, Oxford Financial Research Centre.
    5. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
    6. Luca Capriotti, 2006. "The Exponent Expansion: An Effective Approximation of Transition Probabilities of Diffusion Processes and Pricing Kernels of Financial Derivatives," Papers physics/0602107, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. repec:spr:finsto:v:21:y:2017:i:3:d:10.1007_s00780-017-0330-x is not listed on IDEAS
    2. Matthew Lorig, 2014. "Indifference prices and implied volatilities," Papers 1412.5520, arXiv.org, revised Sep 2015.
    3. Weston Barger & Matthew Lorig, 2016. "Approximate pricing of European and Barrier claims in a local-stochastic volatility setting," Papers 1610.05728, arXiv.org, revised Apr 2017.
    4. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
    5. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion formulas for European quanto options in a local volatility FX-LIBOR model," Papers 1801.01205, arXiv.org, revised Apr 2018.
    6. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2014. "Asymptotics for $d$-dimensional L\'evy-type processes," Papers 1404.3153, arXiv.org, revised Nov 2014.
    7. repec:gam:jijfss:v:6:y:2018:i:2:p:39-:d:139355 is not listed on IDEAS
    8. repec:wsi:ijfexx:v:04:y:2017:i:02n03:n:s2424786317500189 is not listed on IDEAS
    9. Matthew Lorig & Ronnie Sircar, 2015. "Portfolio Optimization under Local-Stochastic Volatility: Coefficient Taylor Series Approximations & Implied Sharpe Ratio," Papers 1506.06180, arXiv.org.
    10. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "A family of density expansions for L\'evy-type processes," Papers 1312.7328, arXiv.org.
    11. Stefano, Pagliarani & Pascucci, Andrea & Candia, Riga, 2011. "Expansion formulae for local Lévy models," MPRA Paper 34571, University Library of Munich, Germany.

    More about this item

    Keywords

    option pricing; analytical approximation; local volatility;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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