An empirical study on asymmetric jump diffusion for option and annuity pricing

Area of Science:

• Quantitative Finance
• Financial Modeling
• Econometrics

Background:

• Market price dynamics are often characterized by asymmetry, with different behaviors during uptrends versus downtrends.
• Existing models like Black-Scholes and symmetric jump diffusion may not fully capture these asymmetric price movements.
• Accurate estimation of market parameters (drift, volatility, jump intensity) is crucial for financial derivative pricing.

Purpose of the Study:

• To develop and present a novel asymmetric jump diffusion model for estimating market parameters.
• To capture the asymmetric nature of market price fluctuations in financial modeling.
• To compare the performance of the proposed model against conventional methods for option and annuity pricing.

Main Methods:

• The proposed method is based on Kou's jump diffusion model, extended to incorporate asymmetry.
• Market parameters estimated include drift, volatility, jump intensity, and rate of jump occurrence.
• Simulations were conducted to compare pricing estimates with the Black-Scholes model and Kou-Merton symmetric jump diffusion model.

Main Results:

• The asymmetric jump diffusion model effectively estimates market parameters, accounting for differing price behaviors in up and down markets.
• Simulation results demonstrate superior performance compared to the Black-Scholes and symmetric jump diffusion models.
• The model provides more accurate fair price estimations for European call options and annuities.

Conclusions:

• The asymmetric jump diffusion model offers a more robust framework for financial market parameter estimation.
• This approach enhances the accuracy of derivative pricing, particularly for options and annuities.
• The findings suggest the importance of incorporating asymmetry in financial diffusion models for improved predictive power.