State-dependent jump risks for American gold futures option pricing

• We model the gold futures price through a regime-switching jump-diffusion model.
• The model captures the leptokurtic returns, jump intensity switching and clustering.
• The risk-neutral gold futures price dynamics are derived under different jump risks.
• We evaluate American gold futures options using the least-squares Monte Carlo method.
• Empirical results show the importance of incorporating state-dependent jump risks.

In this study, we investigate the valuation of American-style options when the underlying gold futures price follows a pure diffusion structure with state-dependent jump dynamics. Under such dynamics, the jump events are described as a compound Poisson process with a log-normal jump amplitude, and the regime-switching arrival intensity is captured by a hidden Markov chain whose states represent the economic states. Considering the different jump risk assumptions, we use the Merton measure and Esscher transform to derive risk-neutral gold futures price dynamics under an incomplete market setting. To achieve a desired accuracy level, the least-squares Monte Carlo method is used to approximate the values of American gold futures options. Our empirical and numerical results based on actual market data are provided to illustrate the importance of incorporating state-dependent jump risks when pricing American put options on gold futures.