高斯積分法在跳躍擴散過程下評價美式與新奇選擇權

Gaussian Quadrature Method for Pricing American and Exotic Options in a Jump-Diffusion Process

本研究採用高斯積分法在跳躍擴散模型的設定下來評價美式與新奇選擇權。我們的數值分析結果顯示，此高斯積分法相較於過往文獻上使用的其他方法，包含快速高斯轉換法（Broadie and Yamamoto, 2003）、二項樹法（Hilliard and Schwartz, 2005），以及外插法（Feng and Linetsky, 2008）等，在評價美式選擇權上具有一定的精確度。除了美式選擇權，我們也將此法應用在新奇選擇權評價，亦有不錯的表現。整體而言，高斯積分法具有高精確度且適合用於跳躍擴散過程下具有提早履約性質的選擇權評價。

In this paper we propose a Gaussian quadrature method to study American and exotic option pricing under the jumpdiffusion model of Merton (1976). Our numerical experiments show that the Gaussian quadrature method, compared to several existing methods in the literature, including the fast Gauss transform method (Broadie and Yamamoto, 2003), the bivariate tree approach (Hilliard and Schwartz, 2005), and the extrapolation approach (Feng and Linetsky, 2008), is accurate for valuing American options. In addition to American options, we also show that the Gaussian quadrature method performs well for the valuation of exotic options under the jump-diffusion model. Overall, the Gaussian quadrature method is highly accurate and suitable for the valuation of price options with early exercise features under a jump-diffusion process.