Time-adaptive high-order compact finite difference schemes for option pricing in a family of stochastic volatility models

High-order compact finite difference scheme for option pricing in stochastic volatility models

We derive a new compact high-order finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. To prove results on the unconditional stability in the sense of von Neumann we perform a thorough Fourier analysis of the problem and deduce convergence of our scheme. We present results of numerical exper...

High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids

We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and secondorder accurate in time for vanishing correlation. In our numerical study we obtain highorder numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all ...

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

Finite Difference Methods in Derivatives Pricing under Stochastic Volatility Models

High-order ADI scheme for option pricing in stochastic volatility models

We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer’s ADI time...