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Analytical approximation of the transition density in a local volatility model

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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Correspondence to Stefano Pagliarani.

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Pagliarani, S., Pascucci, A. Analytical approximation of the transition density in a local volatility model. centr.eur.j.math. 10, 250–270 (2012). https://doi.org/10.2478/s11533-011-0115-y

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  • DOI: https://doi.org/10.2478/s11533-011-0115-y

MSC

  • 91Gxx
  • 35K10
  • 60J70

Keywords

  • Local volatility
  • Analytical approximation
  • Heat kernel expansion
  • Black-Scholes formula
  • Transition density