35 research outputs found
BENCHOP - The BENCHmarking project in Option Pricing
The aim of the BENCHOP project is to provide the finance community with a common suite of benchmark
problems for option pricing. We provide a detailed description of the six benchmark problems together
with methods to compute reference solutions. We have implemented fifteen different numerical methods
for these problems, and compare their relative performance. All implementations are available on line and can be used for future development and comparison
BENCHOPâSLV: the BENCHmarking project in Option PricingâStochastic and Local Volatility problems
In the recent project BENCHOPâthe 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 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 to solve these problems. Comparisons are made with respect to time to reach a certain error level in the computed solution for the different methods. The implemented Fourier method was superior to all others for the two problems where it was implemented. Generally, methods targeting the PDE formulation of the problem outperformed the methods for the SDE formulation. Among the methods for the PDE formulation the ADI method stood out as the best performing one
Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts
In this paper, we study the benefits of using polyharmonic splines and node
layouts with smoothly varying density for developing robust and efficient
radial basis function generated finite difference (RBF-FD) methods for pricing
of financial derivatives. We present a significantly improved RBF-FD scheme and
successfully apply it to two types of multidimensional partial differential
equations in finance: a two-asset European call basket option under the
Black--Scholes--Merton model, and a European call option under the Heston
model. We also show that the performance of the improved method is equally high
when it comes to pricing American options. By studying convergence,
computational performance, and conditioning of the discrete systems, we show
the superiority of the introduced approaches over previously used versions of
the RBF-FD method in financial applications
A comparison of the Fourier-Gauss-Laguerre and Fourier cosine series method in option pricing
We describe the Fourier-Gauss-Laguerre and Fourier cosine series method and test them extensively in four models: Black- Scholes, Black-Scholes with discrete dividends, Heston and Bates. While both methods mostly achieve good accuracy and high computational speed, problems may arise with respect to the optimal choice of the method-specific parameters and the extension of the methods to other models and financial products
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
European options can be priced by solving parabolic partial(-integro)
differential equations under stochastic volatility and jump-diffusion models
like Heston, Merton, and Bates models. American option prices can be obtained
by solving linear complementary problems (LCPs) with the same operators. A
finite difference discretization leads to a so-called full order model (FOM).
Reduced order models (ROMs) are derived employing proper orthogonal
decomposition (POD). The early exercise constraint of American options is
enforced by a penalty on subset of grid points. The presented numerical
experiments demonstrate that pricing with ROMs can be orders of magnitude
faster within a given model parameter variation range