Siti Norafidah Mohd Ramli
First Name: Siti
Department Dept of Applied Finance and Actuarial Studies
Supervisor(s): Dr Jiwook Jang ,
A Stochastic Maximum Principle for Mean-Field Models with Jumps and its Application to Finance
To provide a bond pricing framework that allows for dependency between the interest rate and default intensity processes which are assumed to follow mean-reverting jump diffusion processes.
Key literature/theoretical perspective
(1)Copula-dependent collateral default intensity and its application to CDS rate (Jang, 2007)
(2)Pricing the credit default swap rate for jump diffusion default intensity processes (Ma & Kim, 2010)
(3) Pricing basket default swaps in a tractable shot-noise model (Herbertsson, Jang & Schmidt, 2011)
The time to default is modelled according to a Cox process whose intensity follows a mean reverting jump diffusion process. We also assume that a bond issuer’s default intensity is correlated to the short rate process where a copula function is utilized to address the issue of correlated jumps to capture the dependence structure between two processes. The copula families considered are a Farlie-Gumbel-Mogenstern copula, a normal copula and a t-copula. The bond price formula derived under this model has affine term structure. We then used the model to price corporate bonds and compare the pricing performance of each copula. Upon calibration of the model using the corporate bonds data in year 2011, we found that t-copula provides the best fit with the lowest error.
Jump diffusion processes, Default intensity, Cox process, Copulas, Corporate bond pricing