Using PCA to Analyze a Two-Maturity Swap-Spread Box Trade

Summary

The document considers how to represent the risk of a four-leg relative-value trade involving 10-year and 30-year swap spreads. Each spread combines a swap and a benchmark bond; the example takes opposing positions in the two maturities to express a view that one spread is cheap relative to the other. Although the package has four instruments, the proposed analysis reduces it to the two time series of swap spreads.

With those two series, the position can be studied as a spread between spreads using a PCA-style framework. The response expects the maturities to be highly correlated, which would make their difference less variable than either series alone. This is a framing suggestion, not a detailed risk calculation: it gives no PCA loadings, hedge ratios, sample period, or empirical results. In practice, the leg sensitivities and the construction of each swap spread still need to be aligned with the time series used for the analysis.

Key ideas

• A four-leg swap-and-bond package can be represented through its two underlying maturity-specific swap spreads.
• The relative-value position is analyzed as a spread between the 10-year and 30-year swap spreads.
• PCA can be applied to the two spread time series to examine their shared and differential variation.
• High correlation between the spread series would imply lower variability in their difference, but the document provides no measured PCA results.

Tags

# Using PCA model to capture Risk on a box trade on Swap spread


# Using PCA model to capture Risk on a box trade on Swap spread












I have PCA models to capture Risk for Swaps trading

I have a question regarding a multi-leg package which has 4 legs (box spread).

Typically, a box spread is a switch between two Swap Spread, where a Swap Spread is trading the spread between the Swap and the Bond yield. So the 4 leg package has 2 Swaps leg and 2 Bond leg.

For example, the following structure:- Leg 1: Buy the 10Y Swap Leg 2: Sell the 10Y Bencmark Bond Leg 3: Sell the 30Y Swap Leg 4: Buy the 30Y Benchmark Bond

The trade is done as a relative value trade since the trader thinks the 10Y swap spread is cheaper relative to the 30Y Swap spread. What's the best way I can capture the risk of this package, using a PCA model?

Thanks

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/36552

Since the 10 year and 30 year swap spreads are frequently traded and have time series available, think of this as a 2 variable problem. You then have a simple "spread of spreads" trade which is easily analysed using PCA type methodology. You should find a high correlation between these two spreads, so the variability of the spread of spreads is quite low.

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