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Analytical approximation of the transition density in a local volatility model

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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.

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File URL: http://mpra.ub.uni-muenchen.de/31107/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 31107.

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Date of creation: 04 May 2011
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Handle: RePEc:pra:mprapa:31107

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Keywords: option pricing; analytical approximation; local volatility;

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  1. Luca Capriotti, 2006. "The Exponent Expansion: An Effective Approximation Of Transition Probabilities Of Diffusion Processes And Pricing Kernels Of Financial Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1179-1199.
  2. 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.
  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. 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.
  5. Sam Howison, 2005. "Matched asymptotic expansions in financial engineering," OFRC Working Papers Series 2005mf01, Oxford Financial Research Centre.
  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.
  7. Dennis Kristensen & Antonio Mele, 2009. "Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models," CREATES Research Papers 2009-14, School of Economics and Management, University of Aarhus.
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Cited by:
  1. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "Explicit implied vols for multifactor local-stochastic vol models," Papers 1306.5447, arXiv.org, revised Mar 2014.
  2. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "A family of density expansions for L\'evy-type processes," Papers 1312.7328, arXiv.org.
  3. 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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