A Closed Form Solution for Pricing Variance Swaps Under the Rescaled Double Heston Model.

Area of Science:

• Quantitative Finance
• Financial Modeling
• Derivative Pricing

Background:

• Multi-factor stochastic volatility models are crucial for accurate financial derivative pricing.
• Complex models like the double Heston model present challenges in parameter calibration and lack analytic pricing formulas.
• Efficient calibration and analytic solutions are vital for practical financial modeling.

Purpose of the Study:

• To rescale the double Heston model to reduce parameter complexity.
• To derive a closed-form analytic solution for variance swaps using the rescaled model.
• To evaluate the efficiency and accuracy of the rescaled model compared to the original double Heston model.

Main Methods:

• Rescaling the double Heston model to decrease the number of parameters.
• Derivation of a closed-form analytic solution for variance swaps.
• Empirical analysis fitting the models to VIX market data.

Main Results:

• The rescaled double Heston model requires fewer parameters and offers significantly reduced computation time.
• The rescaled model demonstrates comparable effectiveness to the original double Heston model in fitting VIX data under stable market conditions.
• Both the original and rescaled double Heston models exhibit limitations in accurately capturing market dynamics during highly turbulent periods, such as the post-COVID-19 pandemic era.

Conclusions:

• The rescaled double Heston model provides a more computationally efficient alternative for derivative pricing and variance swap analysis.
• While effective in stable markets, the model's performance degrades in extreme volatility scenarios.
• Further research is needed to enhance stochastic volatility models for capturing extreme market events.