Pricing Credit Default Swap under Fractional Vasicek Interest Rate Model

Abstract

This paper discusses the pricing problem of credit default swap in the fractional Brownian motion environment. As credit default swap is exposed to both the interest rate risk and the default risk, we assume that the default intensity of a firm depends on the stochastic interest rate and the default states of counterparty firms. The interest rate risk is reflected by the fractional Vasicek interest rate model. We model the firm's default intensity under the looping default model and derive the pricing formulas of risky bonds and credit default swap.

Maximum Likelihood Estimation in the Fractional Vasicek Model

“…Such processes appear in finance, hydrology, telecommunication, turbulence and image processing. In particular, various financial applications of the fractional Vasicek model (1.2) can be found in the articles [3][4][5][6][7][8][9]21]. The goal of the paper is to construct maximum likelihood estimators (MLEs) for the unknown parameters α and β and to establish their consistency and asymptotic normality.…”

Maximum Likelihood Estimation in the Mixed Fractional Vasicek Model

“…This model is now known as the Vasicek model and it was generalized to a fractional Vasicek model to study processes with long range dependence which appears in financial mathematics and other areas such as telecommunication networks, turbulence and image processing. Properties of fractional Vasicek model for modeling are investigated in Chronopoulu and Viens [2], Corlay et al [3], Hao et al [8], Song and Li [30] and Xiao et al [37] among others. Maximum likelihood estimation for fractional Vasicek model is investigated in Lohvinenko and Ralchenko [12,13,14,15] and Xiao and Yu [38,39].…”

Asymptotic Properties of Parameter Estimators in Fractional Vasicek Model

“…where B H is the fractional Brownian motion with Hurst index H ∈ (0, 1), and α, β and γ are positive constants. Recently this model has been used in various problems in mathematical finance, see [7,8,24]. When H = 1/2, the fractional Brownian motion is the Wiener process W , and the equation (1.1) becomes the well-known interest rate model dX t = (α − βX t ) dt + γ dW t ,…”