A Simple Covariance-Based VaR Estimate for Interest Rate Swaps

Summary

The document outlines a basic variance-covariance approach to estimating value at risk for an interest rate swap portfolio. First, choose benchmark swap tenors as market factors and calculate each portfolio’s profit or loss for a one-basis-point move in each tenor, holding other rates constant. These sensitivities form the portfolio’s exposure vector.

Next, estimate the covariance matrix of historical changes in those rates and combine it with the sensitivity vector to estimate portfolio risk at a chosen confidence level. The confidence level determines the normal-distribution quantile used to scale the estimate. The method is presented as a practical starting point for a simple portfolio, rather than a complete institutional risk framework. Its accuracy depends on the selected tenors, the historical sample, and the assumptions behind the covariance-based calculation; the document notes that larger swap-trading firms commonly use more elaborate VaR methods.

Key ideas

• Represent swap rate risk using sensitivities to selected benchmark tenors.
• Estimate rate-factor covariance from historical changes.
• Combine exposures and covariance, then scale by the quantile for the chosen confidence level.
• Treat the approach as a simple approximation whose assumptions and factor choices matter.

Tags

# VaR on Interest Rate Swaps


# VaR on Interest Rate Swaps












I am a newbie and was after a simple explanation on how VaR is calculated for a portfolio of IRS's.

## Answer by Dimitri Vulis (score 3)

https://quant.stackexchange.com/a/69469

Here is one very simple approach. However the devil is in the details.

Choose some benchmark tenors (market factors), e.g. 1Y, 2Y... 30Y swap rates.

For each tenor, calculate the P&L if the interest rate at this tenor moves 1 basis point, ceteris paribus. This gives you the vector of sensitivities to market factors.

Calculate the covariance matrix for your market factors, based on a few years of their historical changes.

Perform a matrix muliplication. Multiply the result of the matrix multiplication by the Z value for the desired probability.

(This is very similar to what you would do for a VaR of a portfolio consisting of spot positions in several foreign currencies. I wrote in detail about that here recalculate VaR from one currency to another )

This would be "good enough" for a simple portfolio. However most firms large enough to trade interest rate swaps usually do something more complicated for their VaR.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.