BSLP: Markovian Bivariate Spread-Loss Model for Portfolio Credit Derivatives

TL;DR

BSLP introduces a Markovian bivariate spread-loss model for portfolio credit derivatives, enabling fast pricing and accurate calibration, with applications in standard and non-standard tranche valuation.

Contribution

The paper develops a Markovian, short-rate intensity model for portfolio credit risk, allowing efficient lattice-based pricing and nearly perfect calibration to market data.

Findings

Enables fast lattice methods for derivative pricing.

Achieves nearly perfect calibration to liquid tranche quotes.

Provides an arbitrage-free interpolation model for non-standard tranches.

Abstract

BSLP is a two-dimensional dynamic model of interacting portfolio-level loss and spread (more exactly, loss intensity) processes. The model is similar to the top-down HJM-like frameworks developed by Schonbucher (2005) and Sidenius-Peterbarg-Andersen (SPA) (2005), however is constructed as a Markovian, short-rate intensity model. This property of the model enables fast lattice methods for pricing various portfolio credit derivatives such as tranche options, forward-starting tranches, leveraged super-senior tranches etc. A non-parametric model specification is used to achieve nearly perfect calibration to liquid tranche quotes across strikes and maturities. A non-dynamic version of the model obtained in the zero volatility limit of stochastic intensity is useful on its own as an arbitrage-free interpolation model to price non-standard index tranches off the standard ones.