A0330
Title: Pricing spread options with bivariate Gil-Pelaez inversion
Authors: Daniel Miao - National Taiwan University of Science and Technology (Taiwan) [presenting]
Abstract: Pricing spread options remains challenging due to their dependency on the difference between two underlying asset prices. Existing numerical approaches, notably the two-dimensional FFT method introduced by another study, are widely applied but sensitive to grid and damping parameter choices. To address these limitations, a pricing method based on the bivariate Gil-Pelaez inversion formula is proposed, leveraging the joint characteristic function of the asset distributions to directly evaluate a two-dimensional integral without extensive parameter tuning. Numerical experiments across diverse models, including geometric Brownian motion (GBM), jump-diffusion (JD), variance gamma (VG), stochastic volatility (SV), and stochastic volatility with jumps (SVJ), demonstrate the method's superior accuracy and numerical stability compared to FFT-based approaches. Additionally, cubic spline interpolation is integrated to significantly reduce computational complexity. The interpolation approach achieves equivalent accuracy to dense numerical grids but requires substantially fewer integration points, thereby notably shortening computation time. Results underline the effectiveness and computational advantages of the bivariate Gil-Pelaez inversion method, particularly for complex financial models involving heavy tails and jumps.
