Numerical valuation of European options under two-asset infinite-activity exponential Lévy models
This work provides an efficient numerical method for option pricing in multi-asset Lévy models, which is incremental as it extends an existing 1D method to 2D.
The paper extends a numerical method for pricing European options under two-asset infinite-activity exponential Lévy models, achieving second-order convergence for finite-variation processes, as demonstrated for put-on-the-average options under Normal Tempered Stable dynamics.
We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional case to the 2-dimensional setting and is applicable for general Lévy measures under mild assumptions. A tailored discretization of the non-local integral term is developed, which can be efficiently evaluated by means of the fast Fourier transform. For the temporal discretization, the semi-Lagrangian theta-method is employed in a convenient splitting fashion, where the diffusion term is treated implicitly and the integral term is handled explicitly by a fixed-point iteration. Numerical experiments for put-on-the-average options under Normal Tempered Stable dynamics reveal favourable second-order convergence of our method whenever the exponential Lévy process has finite-variation.