PUBLICATIONS OF MUZAFFER AKAT

Published papers

Pricing and Modeling Credit Derivatives

Abstract:
The market for credit derivatives has become increasingly popular and extremely liquid in the most recent years. The pricing of such instruments offers a myriad of new challenges to the research community as the dimension of credit risk should be explicitly taken into account by a quantitative model. In this paper, we describe a doubly stochastic model which also allows for stochastic volatility, with the purpose of pricing and hedging derivatives on securities subject to default risk. The stochastic volatility is modelled by a general ergodic process as proposed in Fouque et al. [2000a]. The default event is modelled by the first jump of a counting process Nt, doubly stochastic with respect to the Brownian Filtration which drives the uncertainty of the volatility process, and of the security price conditional on no-default event. Assuming absence of arbitrage, we provide all the possible equivalent martingale measures under this setting. In order to illustrate the method, two simple examples are presented: the pricing of defaultable stocks, and a framework to price multi-name credit derivatives "Doubly Stoch" pdf file.

A Unified Credit Risk Model

Abstract:
In recent years a lot of work has been done to try to bridge the gap between the two main approaches in credit risk modelling: structural and reduced form models. Many papers tries to obtain this using special assumptions about the problem. For instance, Duffie and Lando(1999) makes the connection using incomplete accounting information. Whereas we propose a unified approach that attains this in full generality. A model where the credit default event is defined as the minimum of the two default times, one from the structural default and the other from the exogenous intensity. In particular, we look at the effect of having stochastic volatility in the structural approach. We study the effects of time scales on the credit spread yield curves both for the stochastic volatility and the stochastic intensity. In this framework we use perturbation analysis to derive closed-form approximations for the credit spreads that would ease the work of calibration of parameters. The main quantities of interest are not only include fixed-income market data such as bond spreads but also the equity market data such as variance and leverage ratio. We test for the calibration of the model and stability of the model parameters for particular names of different credit ratings. We observe and analyze the differences of the behaviors of credit spreads between highly and lowly rated names. We analyze these differences. Results emphasize the importance of equtiy market data, such as variance and leverage ratio and also the stochastic default intensity. "Thesis" pdf file.