A comparison study of pricing credit default swap index tranches with convex combination of copulae

Abstract

This dissertation focuses on the high dimensional financial engineering, especially in dependence modeling and sequential surveillance.In aspect of dependence modeling, an introduction of high dimensional copula concentrating on state-of-the-art research in copula is presented. Factor copula, hierarchical Archimedean copula and vine copula are explicated, including their statistical inference.An empirical study in risk management by employing the introduced copulas is given.A more complex application in financial engineering using high dimensional copula is concentrated on the pricing of the portfolio-like credit derivative, i.e. credit default swap index (CDX) tranches. In this part, the convex combination of copulas is proposed in CDX tranche pricing with components stemming from elliptical copula family (Gaussian and Student-t), Archimedean copula family (Frank, Gumbel, Clayton and Joe) and hierarchical Archimedean copula family used in some publications. By comparison of two diverse credit derivatives, one can find that the convex combination of copulas has cutting edge in pricing CDX and CDO with components from Archimedean copula family with asymmetric tail dependence structures, e.g. Clayton, Gumbel and Joe copulas.In financial surveillance part, the chapter focuses on the monitoring of high dimensional portfolios (in 5, 29 and 90 dimensions) by development of a nonparametric multivariate statistical process control chart, i.e. energy test based control chart (ETCC). The main features in ETCC are in three aspects. Firstly, the ETCC is nonparametric control chart which means it requires no pre-knowledge on the processes compared to many traditional parametric control chart, e.g. CUSUM and EWMA. Secondly, ETCC monitors multivariate processes, which are more often in the real life. Since multivariate processes bring more characteristics than the unique process, hence ETCC has strong potential in many application areas. Thirdly and the most important virtue of the ETCC is that it monitors the mean and covariance jointly, not separately, compared to many other control charts. Since its powerful detection capacity in covariance change, hence it has good performance for financial sequences during crisis period, where volatility is the main trigger of shift.In order to support the further research and practice of nonparametric multivariate statistical process control chart devised in this dissertation, an R package "EnergyOnlineCPM" is developed. At moment, this package has been accepted and published in the Comprehensive R Archive Network (CRAN), which is the first package that can online monitor the shift in mean and covariance jointly.

Systemic risk in market microstructure of crude oil and gasoline futures prices: A Hawkes flocking model approach

“…In addition, ones empirically observe systemic risk in a time-varying perspective through various data set. For example, Lucas et al (2014), Oh and Patton (2017) use CDS spread;Reboredo (2015) takes stock prices; Jammazi et al (2015) uses stock-bond returns; Choroś-Tomczyk et al (2014), Okhrin and Xu (2017) employ portfolio credit derivative prices.…”

Pricing and integration of credit default swap index tranches

“…Bhansali, Gingrich, and Longstaff (2008) exploit a simple linear version of a sophisticated model to estimate the systemic credit risk of the U.S. and European markets over an extended time period, while they do not examine whether the pricing of the CDX tranches is aligned with that of the other segments of the financial market. Okhrin and Xu (2017) and Wang, Rachev, and Fabozzi (2009) explore copula-based methods. Luo, Tang, and Wang (2018) examine the effect of a frailty factor on CDO pricing.…”