On coordinate transformation and grid stretching for sparse grid pricing of basket options
نویسندگان
چکیده
We evaluate two coordinate transformation techniques in combination with grid stretching for pricing basket options in a sparse grid setting. The sparse grid technique is a basic technique for solving a high-dimensional partial differential equation. By creating a small hypercube sub-grid in the ‘composite’ sparse grid we can also determine hedge parameters accurately. We evaluate these techniques for multi-asset examples with up to five underlying assets in the basket.
منابع مشابه
Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation
This work presents reduced models for pricing basket options with the Black-Scholes and the Heston model. Basket options lead to multi-dimensional partial differential equations (PDEs) that quickly become computationally infeasible to discretize on full tensor grids. We therefore rely on sparse grid discretizations of the PDEs, which allow us to cope with the curse of dimensionality to some ext...
متن کاملAn efficient sparse grid Galerkin approach for the numerical valuation of basket options under Kou’s jump-diffusion model
We use a sparse grid approach to discretize a multi-dimensional partial integro-differential equation (PIDE) for the deterministic valuation of European put options on Kou’s jump-diffusion processes. We employ a generalized generating system to discretize the respective PIDE by the Galerkin approach and iteratively solve the resulting linear system. Here, we exploit a newly developed recurrence...
متن کاملOption Pricing in Hilbert Space-Valued Jump-Diffusion Models Using Partial Integro-Differential Equations
Hilbert space-valued jump-diffusion models are employed for various markets and derivatives. Examples include swaptions, which depend on continuous forward curves, and basket options on stocks. Usually, no analytical pricing formulas are available for such products. Numerical methods, on the other hand, suffer from exponentially increasing computational effort with increasing dimension of the p...
متن کاملGreen Energy Generation in Buildings: Grid-Tied Distributed Generation Systems (DGS) With Energy Storage Applications to Sustain the Smart Grid Transformation
The challenge of electricity distribution’s upgrade to incorporate new technologies is big, and electric utilities are mandated to work diligently on this agenda, thus making investments to ensure that current networks maintain their electricity supply commitments secure and reliable in face of disruptions and adverse environmental conditions from a variety of sources. The paper presents a new ...
متن کامل07 - 12 Multi - asset option pricing using a parallel Fourier - based technique
In this paper we present and evaluate a Fourier-based sparse grid method for pricing multi-asset options. This involves computing multidimensional integrals efficiently and we do it by the Fast Fourier Transform. We also propose and evaluate ways to deal with the curse of dimensionality by means of parallel partitioning of the Fourier transform and by incorporating a parallel sparse grids metho...
متن کامل