Credit Default Swaps and the mixed-fractional CEV model

TL;DR

This paper introduces a mixed-fractional CEV model driven by mixed-fractional Brownian motion to better capture default probabilities and CDS spreads, providing a more realistic framework for credit risk modeling.

Contribution

It extends the standard CEV model by incorporating mixed-fractional Brownian motion, enhancing its ability to model credit default swaps more accurately.

Findings

Increased default probability and CDS spreads under the mixed-fractional model.

Improved empirical performance over the standard CEV model.

More realistic modeling of credit events.

Abstract

This paper explores the capabilities of the Constant Elasticity of Variance model driven by a mixed-fractional Brownian motion (mfCEV) [Axel A. Araneda. The fractional and mixed-fractional CEV model. Journal of Computational and Applied Mathematics, 363:106-123, 2020] to address default-related financial problems, particularly the pricing of Credit Default Swaps. The increase in both, the probability of default and the CDS spreads under mixed-fractional diffusion compared to the standard Brownian case, improves the lower empirical performance of the standard Constant Elasticity of Variance model (CEV), yielding a more realistic model for credit events.