Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads

Abstract

Most important financial models assume randomness is explained through a normal random variable because, in general, use of alternative models is obstructed by the difficulty of calibrating and simulating them. Here we empirically study credit default swap pricing models under a reduced-form framework assuming different dynamics for the default intensity process. We explore pricing performance and parameter stability during the highly volatile period from June 30, 2008 to December 31, 2010 for different classes of processes driven by Brownian motion, three non-Gaussian Lévy processes, and a Sato process. The models are analyzed from both a static and dynamic perspective.

Exact simulation of gamma-driven Ornstein–Uhlenbeck processes with finite and infinite activity jumps

“…Moreover, Nicolato and Venardos (2003) further applied the Γ-OU stochastic volatility model to pricing European options. Schoutens and Cariboni (2010) and Bianchi and Fabozzi (2015) adopted the Γ-OU process as a stochastic intensity process for modelling credit default risk and pricing credit default swaps (CDSs). Cartea et al (2015, p.220) used it for modelling the stochastic mean-reverting volume rate of trading, see also Cartea and Jaimungal (2016).…”

Disentangling the Information Content of Government Bonds and Credit Default Swaps: An Empirical Analysis on Sovereigns and Banks

“…Furthermore, it is taken into account that if default occurs between some payment dates, the fee has to be paid only for the portion between the last payment date and the time of default as the insurance buyer is protected only for that period. In this paper, to calibrate the model instead of directly considering the formula in Equation (2.4) as done in Bianchi and Fabozzi [16], we bootstrap the default probability curves from CDS market quotes. That is, for each given point in time and for each maturity, after having fixed a constant recovery rate (we assume 40 per cent for both sovereign and bank CDS), we find the constant default intensity λ such that the CDS quote coincides with the right-hand side of the equality (2.4).…”

“…As far as the implementation is concerned, we cast the bond and CDS default term structure into a state-space form and calibrate it with a filter as similarly done by Chen et al [11], Jarrow et al [12], Carr and Wu [13], Chen et al [14], Ang and Longstaff [15], Bianchi and Fabozzi [16], and Li and Zinna [17,18]. The Kalman filter algorithm together with a maximum likelihood estimation method are considered to fit the model in the period from June 2008 to December 2014.…”

American option valuation under time changed tempered stable Lévy processes

“…Itkin [20] and Carr [21] applied time varying Lévy process to volatility derivatives. Bianchi [22] investigated the pricing performance of credit default swap spreads assuming stochastic non-Gaussian Lévy process dynamics for the default intensity model. Kim [23] derived the analytic solution for quanto option pricing under the NTS model.…”