BENCHOP-SLV: The BENCHmarking project in Option Pricing - Stochastic and Local Volatility problems
In the recent project BENCHOP - the BENCHmarking project in Option Pricing we found that Stochastic and Local Volatility problems were particularly challenging. Here we continue the effort by introducing a set of benchmark problems for this type of problems. Eight different numerical methods have been implemented to solve these problems and comparisons are made with respect to CPU-time to reach a certain error level in the computed solution. Both methods targeted for the Stochastic Differential Equation (SDE) formulation and the Partial Differential Equation (PDE) formulation of the problem, as well as Fourier methods making use of the characteristic function were implemented and compared.
An article with results from the project has been submitted for publication.
Below you find problem formulations, unit tests, and p-codes of the implementations. Any use of the code in the future is expected to be adequately cited.
Problem formulations and unit tests
p-codes
Methods for SDE formulation
- Monte Carlo simulation with Control and Antithetic variables MCA.zip
- Multi Level Monte Carlo MLMC.zip
- Stochastic Grid Bundling Method SGBM.zip
- The multi-step Monte Carlo Simulation of the SABR model mSABR.zip
Fourier methods
- Fourier method with Gauss-Laguerre quadrature FGL.zip
Methods for PDE formulation
- Alternating Direction Implicit method ADI.zip
- Radial Basis Function generated Finite Differences RBFFD.zip
- Radial Basis Function Partition of Unity Methods RBFPUM.zip