We propose the use of a classical tool in PDE theory, the parametrix method, to build approximate solutions to generic parabolic models for pricing and hedging contingent claims. We obtain an expansion for the price of an option using as starting point the classical Black and Scholes formula....

We investigate the suitability of sparse grids for solving high-dimensional option pricing and interest rate models numerically. Starting from the partial differential equation, we try to - at least partially - break the curse of dimensionality through sparse grids which will result from a...

Option pricing model with non-constant volatility models are compared to stochastic volatility ones. The non-constant volatility models considered are the Dupire's local volatility and Hobson and Rogers path-dependent volatility models. These approaches have the theoretical advantage of...

This paper compares the goodness-of-fit and the stability of six methods used to extract risk-neutral probability density functions from currency option prices. We first compare five existing methods commonly employed to recover risk-neutral density functions from option prices. Specifically, we...

Krylov subspace methods have proven to be powerful methods for solving sparse linear systems arising in several engineering problems. More recently, these methods have been successfully applied in computational economics, for instance in the solution of forward-looking macroeconometric models...

This paper describes and analyses the use of the Filtered Historical Simulation algorithm in pricing spread options. Spread options are contracts whose payoff depends on the price difference (spread) between two or more underlying assets at a future date. Such kind of options are written in the...