Author(s)

Zhigang Tong^1*, Allen Liu²

¹Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada.
²Model Validation, Enterprise Risk and Portfolio Management, Bank of Montreal, Toronto, Canada.

In this paper, we introduce the stochastic correlation processes for modeling the credit spread. We first model the components of spread process as correlated Ornstein-Uhlenbeck processes and correlation as Jacobi process. Using the properties of Jacobi process, we are able to obtain the analytical solutions for the credit spread option prices. To further enhance the model’s ability to capture the abrupt changes in the observed correlation time series, we construct a new model where the correlation is modeled by a Jacobi process time change by Lévy subordinators. We employ the eigenfunction expansion methods to obtain the closed-form solutions for the option prices. Our empirical study indicates the time changed Jacobi process fits the correlation series significantly better than the Jacobi process.

Stochastic Correlation, Jacobi Process, Stochastic Time Change, Eigenfunction Expansion, Credit Spread Options

Tong, Z. and Liu, A. (2017) A Stochastic Correlation Model with Time Change for Pricing Credit Spread Options. Journal of Mathematical Finance, 7, 445-466. doi: 10.4236/jmf.2017.72024.