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Analytical approximation of the transition density in a local volatility model


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).

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  • 91Gxx
  • 35K10
  • 60J70


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