Commodity Asian option pricing and simulation in a 4-factor model with jump clusters
针对商品市场均值回复、随机波动、便利收益和跳跃簇等特征，提出四因子模型，推导几何亚式期权半封闭解，并设计高效模拟方案定价算术亚式期权，通过实证检验跳跃簇存在性。
Mean reversion, stochastic volatility, convenience yield and presence of jump clustering are well documented salient features of commodity markets, where Asian options are very popular. We propose a model which takes into account all these stylized features. We first state our model under the historical measure, then, after introducing a structure preserving change of measure, we provide a risk-neutral version of the same model and we show how to price geometric and arithmetic Asian options. To this end, we derive semi-closed formulas for the geometric Asian options price and develop a computationally efficient simulation scheme for the price process, allowing to price the arithmetic counterparts using control variate technique. Finally, we propose a simple econometric experiment to document presence of jump clusters in commodity prices and evaluate the performances of the proposed simulation scheme on some parameter sets calibrated on real data.