A Formula for Interest Rate Swaps Valuation Under Counterparty Risk in Presence of Netting Agreements

31 Pages Posted: 9 May 2005

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Massimo Masetti

Royal Bank of Scotland (RBS); Universita di Bergamo

Date Written: May 4, 2005

Abstract

In this document we show how to handle counterparty risk for Interest Rate Swaps (IRS). First we establish a general formula, showing that counterparty risk adds one level of optionality to the contract. Then we introduce the default probabilities using a deterministic intensity model where the default time is modeled as the first jump of a time-inhomogeneous Poisson process. We consider Credit Default Swaps as liquid sources of market default probabilities.

We then apply the general formula to a single IRS. The IRS price under counterparty risk turns out to be the sum of swaption prices with different maturities, each weighted with the probability of defaulting around that maturity. Then we consider a portfolio of IRS's in presence of a netting agreement. The related option cannot be valued as a standard swaption, and we resort both to Monte Carlo simulation and to two analytical approximations, investigating them by Monte Carlo simulation under several configurations of market inputs. We find a good agreement between the formula and the simulations in most cases. The approximated formula is well suited to risk management, where the computational time under each risk factors scenario is crucial and an analytical approximation contains it.

Keywords: Interest Rate Swap, Counterparty Risk Pricing, Netting Agreements, Analytical Tractability, Simulation, Libor Model

JEL Classification: G13

Suggested Citation

Brigo, Damiano and Masetti, Massimo, A Formula for Interest Rate Swaps Valuation Under Counterparty Risk in Presence of Netting Agreements (May 4, 2005). Available at SSRN: https://ssrn.com/abstract=717344 or http://dx.doi.org/10.2139/ssrn.717344

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Massimo Masetti (Contact Author)

Royal Bank of Scotland (RBS) ( email )

135 Bishopsgate
London, EC2M 3UR
United Kingdom

Universita di Bergamo ( email )

Via Salvecchio, 19
Bergamo, 24129
Italy

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