This paper presents new approximation formulae for European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models [<italic>Int. J. Theor. Appl. Finance</italic>, 2010, <bold>13</bold>(4), 603--634] for the case of...

Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion,...

A wide class of hybrid products are evaluated with a model where one of the underlying price follows a local volatility diffusion and the other asset value a log-normal process. Because of the generality for the local volatility function, the numerical pricing is usually much time consuming....

In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black--Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal...

We relate the Lp-variation, 2≤p∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in...