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

Question

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 1

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.