A unified approach to pricing and risk management of equity and credit risk

We propose a unified framework for equity and credit risk modeling, where the default time is a doubly stochastic random time with intensity driven by an underlying affine factor process. This approach allows for flexible interactions between the defaultable stock price, its stochastic volatility and the default intensity, while maintaining full analytical tractability. We characterize all risk-neutral measures which preserve the affine structure of the model and show that risk management as well as pricing problems can be dealt with efficiently by shifting to suitable survival measures. As an example, we consider a jump- to-default extension of the Heston stochastic volatility model

Managing uncertainty:financial, actuarial and statistical modelling.

present value; Value; Actuarial;

On multicurve models for the term structure

In the context of multi-curve modeling we consider a two-curve setup, with one curve for discounting (OIS swap curve) and one for generating future cash flows (LIBOR for a give tenor). Within this context we present an approach for the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives) with one of the main goals being also that of exhibiting an "adjustment factor" when passing from the one-curve to the two-curve setting. The model itself corresponds to short rate modeling where the short rate and a short rate spread are driven by affine factors; this allows for correlation between short rate and short rate spread as well as to exploit the convenient affine structure methodology. We briefly comment also on the calibration of the model parameters, including the correlation factor.Comment: 16 page

Term structure models: a perspective from the long rate

Term structure models resulted from dynamic asset pricing theory are discussed by taking a perspective from the long rate. This paper attempts to answer two questions about the long rate: in frictionless markets having no arbitrage, what should the behavior of the long rate be; and, in existing dynamic term structure models, what can the behavior of the long rate be. In frictionless markets having no arbitrage, the yields of all maturities should be positive and the long rate should be finite and non-decreasing. The yield curve should level out as term to maturity increases and slopes with large absolute values occur only in the early maturities. In a continuous-time framework, the longer the maturity of the yield is, the less volatile it shall be. Furthermore, the long rate in continuous-time factor models with a non-singular volatility matrix should be a non-decreasing deterministic function of time. In the Black-Derman-Toy model and factor models with the short rate having the mean reversion property, the long rate is finite. The long rate in Duffie-Kan models with the mean reversion property is a constant. The long rate in a Heath-Jarrow-Morton model can be infinite or a non-decreasing process. Examples with the long rate being increasing are given in this paper. A model with the long rate and short rate as two state variables is then obtained.

A Heat Kernel Approach to Interest Rate Models

We construct default-free interest rate models in the spirit of the well-known Markov funcional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and construct models by means of the so called propagation property. The propagation property can be found implicitly in all of the popular state price density approaches, in particular heat kernels share the propagation property (wherefrom we deduced the name of the approach). As a related matter, an interesting property of heat kernels is presented, too

Calibrating risk-neutral default correlation.

The implementation of credit risk models has largely relied on the use of historical default dependence, as proxied by the correlation of equity returns. However, as is well known, credit derivative pricing requires risk-neutral dependence. Using the copula methodology, we infer risk neutral dependence from CDS data. We also provide a market application and explore its impact on the fees of some credit derivatives.

A linear algebraic method for pricing temporary life annuities and insurance policies

We recast the valuation of annuities and life insurance contracts under mortality and interest rates, both of which are stochastic, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations is developed which allows for fast and accurate computation of expected values. Our reformulation of the valuation problem provides a general framework which can be employed to find insurance premiums and annuity values covering a wide class of stochastic models for mortality and interest rate processes. The proposed approach provides a computationally efficient alternative to Monte Carlo based valuation in pricing mortality-linked contingent claims