Discrete tenor models for credit risky portfolios driven by time-inhomogeneous Lévy processes

A Consistent Stochastic Model of the Term Structure of Interest Rates for Multiple Tenors

Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor ("roll-over risk"), we construct a stochastic model framework for the term structure of interest rates in which a frequency basis (i.e. a spread applied to one leg of a swap to exchange one floating interest rate for another of a different tenor in the same currency) arises endogenously. This rollover risk consists of two components, a credit risk component due to the possibility of being downgraded and thus facing a higher credit spread when attempting to roll over short-term bo…

违约过程建模与信用估值调整

Default Process Modeling and Credit Valuation Adjustment

本文提出了一个便捷的框架用于违约过程建模与含信用风险衍生品定价，通过整合违约距离、违约概率等指标提供信用估值调整的综合视角，证明风险估值为Martingale，简化技术问题且数值结果与历史一致。

Security Pricing with Information-Sensitive Discounting

In this paper incomplete-information models are developed for the pricing of securities in a stochastic interest rate setting. In particular we consider credit-risky assets that may include random recovery upon default. The market filtration is generated by a collection of information processes associated with economic factors, on which interest rates depend, and information processes associated with market factors used to model the cash flows of the securities. We use information-sensitive pricing kernels to give rise to stochastic interest rates. Semi-analytical expressions for the price of …

Defining, Estimating and Using Credit Term Structures. Part 1: Consistent Valuation Measures

In this three-part series of papers, we argue that the conventional spread measures are not well defined for credit-risky bonds and introduce a set of credit term structures which correct for the biases associated with the strippable cash flow valuation assumption. We demonstrate that the resulting estimates are significantly more robust and remain meaningful even when applied to deeply distressed bonds. We also suggest a new definition of credit bond duration and convexity which remains consistent for distressed bonds and introduce new relative value measures for individual bonds in the conte…

Robust XVA

We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the return rate of her counterparty's bond, but is confident that it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to impor…

Stochastic evolution equations in portfolio credit modelling with applications to exotic credit products

We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the asset values. This density evolves according to a stochastic partial differential equation and we establish existence and uniqueness for the solution taking values in a suitable function space. The loss function of the portfolio is then a function of the evolution of this density at the default boundary. We develop numerical methods for pricing and calibratio…