Modelling Dynamic Portfolio Credit Risk

In this paper we present a model to price and hedge basket credit derivatives and collateralised loan obligation. Based upon the copula-approach by Schönbucher and Schubert (2001) the model allows a specification of the joint dynamics of credit spreads and default intensities, including a speci¯cation of the infection dynamics which cause credit spreads to widen at defaults of other obligors. Because of a high degree of analytical tractability, joint default and survival probabilities and also sensitivities can be given in closed-form which facilitates the development of hedging strategies based upon the model. The model uses a generalisation of the class of Archimedean copula functions which gives rise to more realistic credit spread dynamics than the Gaussian copula or the Student-t-copula which are usually chosen in practice. An example speci¯cation using Gamma-distributed factors is provided.FdR – Publicaties zonder aanstelling Universiteit Leide

Evolutionary estimation of a Coupled Markov Chain credit risk model

There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions and thereby default probabilities of companies. As the likelihood of the model turns out to be a non-convex function of the parameters to be estimated, we apply heuristics to find the ML estimators. To this extent, we outline the model and its likelihood function, and present both a Particle Swarm Optimization algorithm, as well as an Evolutionary Optimization algorithm to maximize the likelihood function. Numerical results are shown which suggest a further application of evolutionary optimization techniques for credit risk management

Option market making under inventory risk

Delta, European options, Gamma, Inventory management, Liquidity, Market microstructure, Vega, G13, G11, C61,

Option hedging for small investors under liquidity costs

Following the framework of Cetin et al. (finance stoch. 8:311-341, 2004), we study the problem of super-replication in the presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized black-scholes economy. We find that the minimal super-replication price is different from the one suggested by the black-scholes formula and is the unique viscosity solution of the associated dynamic programming equation. This is in contrast with the results of Cetin et al. (Finance Stoch. 8:311-341, 2004), who find that the arbitrage-free price of a contingent claim coincides with the Black-Scholes price. However, in Cetin et al. (Finance Stoch. 8:311-341, 2004) a larger class of admissible portfolio processes is used, and the replication is achieved in the L (2) approximating sense. JEL (C61 - G13 - D52)

A Discrete-Time Approach to Arbitrage-Free Pricing of Credit Derivatives

This paper develops a framework for modelling risky debt and valuing credit derivatives that is flexible and simple to implement, and that is, to the maximum extent possible, based on observables. Our approach is based on expanding the Heath-Jarrow-Morton term-structure model to allow for defaultable debt. Rather than follow the procedure of implying out the behavior of spreads from assumptions concerning the default process, we work directly with the evolution of spreads. The risk-neutral drifts in the resulting model possess a recursive representation that facilitates implementation and makes it possible to handle path-dependence and early exercise features without difficulty. The framework permits embedding a variety of specifications for default; we present an empirical example of a default structure which provides promising calibration results.Credit Risk, Derivatives, No-Arbitrage

Can the implied volatility surface move by parallel shifts?

Implied volatility, Smile asymptotics, Long rates, 60G44, 91B70, G13,