CDS volatility: daily return calculated by simple substraction (Pt - Pt-1)?

Question

I am working on validating the CDS volatility generated by a third party risk engine. It appears that returns are calculated with simple substractions and adjusted for the CS01:

(Price of the CDS today - Price of the CDS yesterday) * CS01

The argument is that log returns or log returns approximation [(Pt - Pt-1)/Pt-1] cannot apply to fixed income instruments in general as prices are distorted by duration, therefore returns cannot be normal.

Have you ever seen these returns calculated like this? What do you make of this this statistically speaking?

Answer 1

If I understand correctly, you are looking for the volatility of the daily change in the mark to market of a credit default swap. You are given a daily series of CDS spreads (market standard quotes, not upfronts) for your swap's maturity (you don't need to think about using 1 5Y quote to price a swap with 4Y left to maturity). Rather than re-price the swap every day by feeding the market data into your pricing model, you calculate the CS01 at inception (the change in mark to market caused by 1 basis point change in the CDS spread, which you calculate by bumping the CDS spread at inception 1bp and re-running your pricing model). Then you estimate the daily P&L by multiplying the daily change in CDS spread by the CS01. You assume that other contributions to the change in mark to market are tiny (e.g. PL from the change in interest rates) or predictable and don't affect the volatility (e.g. your running spread accrues daily).

This assumes that you never change the recovery assumption (because that too would affect the mark to market), but people seldom change it. This assumes that you have no CDS spread gamma. You only use the first order term of Taylor expansion (CDS spread delta). On days when the CDS spread change is comparable to the spread itself (e.g. form 100 to 130 bps), this will be inaccurate.

This assumes (I think) that you calculate the CS01 (the delta) at inception and it does not change during the life of the swap. But it does change - if the CDS spread changes a lot (because of the gamma) or as your swap gets closer to maturity.

Answer 2

Okay, here my only opinion and it's not the academic answer that you should rely on, just "on-desk experience", but anyway. Answering your question about:

Have you ever seen these returns calculated like this?

According to CDS. - definitely not. If we are talking about single-name CDS derivative instrument. (not about index one). I double @Dimitri's answer about modelling gamma and that's why:

Let's be honest, prices on CDS instrument, shows us a probability of default. For example if default of Thomas Cook is inevitable, you don't need to be a genius, to mark the price up. So, we could describe volatility as a change of probability of a probability of default. (but remember, when we talk about index CDS derivatives, you could multiply it, because it has dozens of names), so it's closely relative to second order greeks Gamma/Vomma pricing in options. Guess, you probably find Vomma calculation a bit useful in your case.