An analytical GARCH valuation model for spread options with default risk

In this paper, an analytical pricing formula for spread options with credit default risk is derived. Assets are set within discrete-time CAPM markets and Heston-Nandi GARCH processes are adopted for capturing the variance dynamics of asset returns. The proposed model decomposes the risk of all assets into idiosyncratic and systematic parts, and considers the impacts on the default intensity of market fluctuations. A corresponding theoretical framework of discrete -time credit risk modeling in reduced-form is also provided. We incorporate the credit risk and systematic factor into an affine-GARCH valuation model and utilize Fourier transform techniques to obtain the analytic spread option prices. Finally, the empirical results and numerical analysis for different model parameters are displayed.

Automated summary

This paper derives an analytical pricing formula for spread options with credit default risk. The model utilizes discrete-time CAPM markets and Heston-Nandi GARCH processes to capture the variance dynamics of asset returns. The study proposes a model that decomposes the risk of all assets into idiosyncratic and systematic parts, considering the impacts of market fluctuations on default intensity. It also provides a theoretical framework for discrete-time credit risk modeling in reduced-form. The proposed model incorporates credit risk and systematic factors into an affine-GARCH valuation model and uses Fourier transform techniques to obtain analytic spread option prices. The empirical results and numerical analysis for different model parameters are displayed.