[Paper Review] Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlations

Damiano Brigo, Andrea Pallavicini+1 more|arXiv (Cornell University)|Nov 17, 2009

Credit Risk and Financial Regulations11 citations

TL;DR

This paper develops an arbitrage-free framework for bilateral counterparty risk valuation in interest-rate derivatives, incorporating stochastic credit spreads, default correlation, and interest rate volatility. It shows that the credit valuation adjustment (CVA) involves a long put and short call on the net present value, with adjustments highly sensitive to correlations and volatilities—particularly when credit spreads are stochastic and default timing is correlated with interest rates.

ABSTRACT

The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, as developed more in detail in Brigo and Capponi (2008), including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include Netting in our examples, although other agreements such as Margining and Collateral are left for future work.

Motivation & Objective

• To extend unilateral counterparty risk valuation to the bilateral case for interest-rate derivatives, including default risk for both the investor and counterparty.
• To rigorously model the impact of credit spread volatility, default correlation, and interest rate–credit spread correlation on CVA adjustments.
• To demonstrate that bilateral CVA is not simply a symmetric extension of unilateral CVA, but significantly altered by dynamic dependencies.
• To provide a practical valuation framework applicable to netted interest-rate swap (IRS) portfolios and exotic derivatives under realistic market dynamics.
• To highlight the importance of modeling stochastic credit spreads and default correlation, often neglected in standard industry models.

Proposed method

• Adopt an arbitrage-free valuation framework based on stochastic intensity models for default times, linked via a Gaussian copula to model dependence between counterparty and investor defaults.
• Use a two-factor Gaussian short-rate model (G2++) for interest rate dynamics and shifted square root processes with jumps (JCIR++) for credit spreads to capture stochastic volatility.
• Derive the bilateral CVA as a combination of a long position in a zero-strike put and a short position in a zero-strike call on the residual net present value at default times.
• Implement Monte Carlo simulations to value the adjustment under various scenarios, including netted portfolios and different yield curve shapes.
• Incorporate correlations between interest rates and credit spreads for both counterparties, as well as default–default correlation.
• Calibrate the model to market data using CDS term structures and implied volatilities, with separate parameter sets for high-risk and mid-risk counterparties.

Experimental results

Research questions

• RQ1 How does bilateral counterparty risk adjustment (CVA) for interest-rate derivatives change when both the investor and counterparty are subject to default risk?
• RQ2 What is the impact of credit spread volatility on bilateral CVA, and how does it affect the sign and magnitude of the adjustment?
• RQ3 How do correlations between default times of the investor and counterparty, and between default times and interest rates, influence the CVA?
• RQ4 How sensitive is the bilateral CVA to the shape of the initial yield curve (increasing, flat, decreasing)?
• RQ5 How do exotic features such as auto-callable triggers affect the bilateral CVA, and what role do correlations play in such structures?

Key findings

• The bilateral CVA is highly sensitive to the correlation between default times of the investor and counterparty, with adjustments changing sign under high negative correlation.
• For a decreasing yield curve, the bilateral CVA for a flat IRS portfolio (P3) reaches -1,193 basis points under high negative correlation, compared to +31 basis points for a flat curve.
• Credit spread volatility significantly impacts the CVA: increasing the volatility of the counterparty’s credit spread from 0% to 60% reduces the CVA from -1,193 to -328 bps for a decreasing curve.
• The adjustment for an auto-callable IRS portfolio with a 3% strike is -55 bps under high positive correlation (ρ=99%), compared to -71 bps under high negative correlation (ρ=-99%), showing non-linear sensitivity.
• The bilateral CVA for a long IRS portfolio (P1) can be as low as -1,193 bps under a decreasing yield curve and high negative correlation, indicating substantial risk to the long position.
• The adjustment is not additive or linear in correlation; even small changes in correlation parameters can reverse the sign of the CVA, invalidating simple scaling approaches.