Testing the Closed-Form Spread Option Pricing Formula Based on Gauss-Hermite Quadrature for a Jump-Diffusion Model

In this paper we develop a closed-form spread option pricing formula based on Gauss-Hermite quadrature (GHQ) and show that the proposed method is a competitive method for the Black-Scholes model and is best-suited for the jump-diffusion model. The GHQ method turns the integral of spread option pricing formula into a summation of call option pricing formulas with adjusted parameters, and therefore the final formula remains in closed-form which ensures its computational advantage. Under the basic Black-Scholes model, the proposed GHQ formula provides equally nice accuracy compared to the best-performing LDZ formula in the literature. But for the extended jump-diffusion model, the LDZ formula sees a significant loss of accuracy due to the multi-layered summation, whereas the GHQ formula is still able to achieve very high accuracy at only slightly increased computing costs. Various closed-form formulas are tested in our numerical analysis which demonstrates that the proposed GHQ formula is the most recommended for pricing spread options under the jump-diffusion model.