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<p>This study addresses the pricing of defaultable bonds and credit default swaps (CDSs) within a mixed fractional intensity framework incorporating stochastic recovery. The default intensity is modeled using a mixed fractional Cox–Ingersoll–Ross (mfCIR) process, while the recovery rate is formulated as a function of the default intensity. The noise component of the mfCIR model combines fractional Brownian motion (fBm) and a standard Brownian motion, providing a more flexible representation of financial markets. By employing a variable separation technique, the pricing formulae for defaultable bonds and CDSs are derived under the mfCIR model. Specifically, a closed-form analytical solution for the mixed fractional intensity model is obtained by analytically solving a backward parabolic partial differential equation analytically, overcoming challenges caused by an additional stochastic factor. Numerical experiments are conducted to analyze the sensitivity of the model’s parameters on credit spreads and the swap premium of a CDS.</p>

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A novel analytical pricing of defaultable bonds and CDSs with stochastic recovery in a mixed fractional CIR model

  • 期刊论文

  • 发表日期：

    2025年7月7日

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  • Zhaoqiang Yang,
  • Chenglong Xu

摘要

This study addresses the pricing of defaultable bonds and credit default swaps (CDSs) within a mixed fractional intensity framework incorporating stochastic recovery. The default intensity is modeled using a mixed fractional Cox–Ingersoll–Ross (mfCIR) process, while the recovery rate is formulated as a function of the default intensity. The noise component of the mfCIR model combines fractional Brownian motion (fBm) and a standard Brownian motion, providing a more flexible representation of financial markets. By employing a variable separation technique, the pricing formulae for defaultable bonds and CDSs are derived under the mfCIR model. Specifically, a closed-form analytical solution for the mixed fractional intensity model is obtained by analytically solving a backward parabolic partial differential equation analytically, overcoming challenges caused by an additional stochastic factor. Numerical experiments are conducted to analyze the sensitivity of the model’s parameters on credit spreads and the swap premium of a CDS.