Commodity Asian option pricing and simulation in a 4-factor model with jump clusters.

Area of Science:

• Quantitative Finance
• Econometrics
• Financial Modeling

Background:

• Commodity markets exhibit distinct features: mean reversion, stochastic volatility, convenience yield, and jump clustering.
• Asian options are a popular derivative instrument in these markets.

Purpose of the Study:

• To develop a comprehensive model for commodity markets that integrates key stylized features.
• To derive methods for pricing geometric and arithmetic Asian options within this model.

Main Methods:

• Formulation of a model under the historical measure.
• Introduction of a structure-preserving change of measure to obtain a risk-neutral version.
• Derivation of semi-closed formulas for geometric Asian options.
• Development of an efficient simulation scheme for price processes.
• Application of the control variate technique for pricing arithmetic Asian options.
• Econometric experiments to validate jump clustering and simulation performance.

Main Results:

• A novel model capturing salient commodity market features is proposed.
• Semi-closed pricing formulas for geometric Asian options are derived.
• An efficient simulation scheme enables pricing of arithmetic Asian options.
• Econometric analysis confirms the presence of jump clusters in commodity prices.

Conclusions:

• The proposed model effectively integrates complex commodity market dynamics.
• The developed pricing methodologies offer computational efficiency for Asian options.
• The study validates the model's performance using real-world calibrated data.