Dynamic programming for valuing American options under a variance‐gamma process
针对方差伽马模型下美式期权无解析解的问题，提出结合有限元的动态规划方法，数值实验验证了收敛性和效率，并应用于标普500期货期权。
Abstract Lévy processes provide a solution to overcome the shortcomings of the lognormal hypothesis. A growing literature proposes the use of pure‐jump Lévy processes, such as the variance‐gamma (VG) model. In this setting, explicit solutions for derivative prices are unavailable, for instance, for the valuation of American options. We propose a dynamic programming approach coupled with finite elements for valuing American‐style options under an extended VG model. Our numerical experiments confirm the convergence and show the efficiency of the proposed methodology. We also conduct a numerical investigation that focuses on American options on S&P 500 futures contracts.