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Analytical approximation of the transition density in a local volatility model [PDF]

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 ...
Pagliarani, Stefano, Pascucci, Andrea
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Pricing Discrete Barrier Options under Stochastic Volatility [PDF]

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively ...
Akihiko Takahashi, Kenichiro Shiraya, Toshihiro Yamada +2 more
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"On Approximation of the Solutions to Partial Differential Equations in Finance" [PDF]

This paper proposes a general approximation method for the solutions to second-order parabolic partial differential equations (PDEs) widely used in finance through an extension of Léandre's approach(Léandre (2006,2008)) and the Bismut identiy(e.g ...
Akihiko Takahashi, Toshihiro Yamada
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Option data and modeling BSM implied volatility [PDF]

This contribution to the Handbook of Computational Finance, Springer-Verlag, gives an overview on modeling implied volatility data. After introducing the concept of Black-Scholes-Merton implied volatility (IV), the empirical stylized facts of IV data are
Matthias Fengler
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Mean-Reverting SABR Models: Closed-form Implied Volatilities and Application to Stock Indices [PDF]

Volodymyr Perederiy
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Option pricing in the moderate deviations regime. [PDF]