Estimating CDS RPV01 and Upfront Payments with the ISDA Model
Summary
The document asks how to calculate a credit default swap’s risky present value of a basis point (RPV01) and upfront payment for historical P&L. It presents a simplified formula based on coupon, par spread, remaining maturity, risk-free rate, and assumed recovery. The response says this approximation is very rough because it ignores convexity; spread changes do not have uniform valuation effects across spread levels.
For a more reliable conversion between standard quoted spreads and upfront value, the answer recommends the ISDA CDS Standard Model, using interest rate curves from the relevant historical date. An available converter can serve as a comparison when validating an implementation. The document does not provide a full calculation walkthrough or quantify the approximation’s error, so the simplified formula should not be treated as generally accurate for historical valuation.
Key ideas
- A simplified RPV01 formula uses spread, coupon, maturity, rates, and recovery assumptions.
- The provided answer characterizes the formula as rough because it omits convexity.
- Spread changes can have different valuation effects at different spread levels.
- The ISDA CDS Standard Model provides the recommended standard spread-to-upfront conversion.
- Historical P&L calculations should use interest rate curves from the corresponding dates.
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Full text
# Calculating RPV01 for the up-front payment of a CDS contract # Calculating RPV01 for the up-front payment of a CDS contract I'm trying to calculate the historical P&L of a CDS trading strategy, and am struggling to come up with the up-front payment of the contract. From what I can tell, the Mark-to-Market value of a contract is `MtM =(S(p) −C)×RPV01` where S(p) is the market spread and C is the coupon (either 1% p.a. or 5% p.a.). I'm having trouble following the calculation for the RPV01 following the ISDA pricing manual and instead found this gem of an answer: > A simple model for the value of a short protection CDS can be found if you write > V = (C-S) x RPV01, where > RPV01 = (1−exp(−gT))/g > and C is the coupon, S is the par CDS spread, T is the remaining life in years and > g=r+S/(1−R) where r is the risk-free (Libor) rate and R is the expected recovery rate, usually set to 40%. > If I set r=0.02 and T=5 for a notional of 10M USD then I get V equal to -144,317USD. So to enter into this contract I would receive an upfront payment of 144,317USD. My question is whether this is a rough estimation, or generally quite accurate? Is there another straightforward way to compute the RPV01 of a contract and thereon the MtM value/up-front payment? ## Answer by Dimitri Vulis (score 1) https://quant.stackexchange.com/a/63405 No, this is a very rough approximation, ignores convexity. Consider this: if some CDS spread changes from 30 bps to 31 bps, it's a much bigger deal than if it changes from 300 bps to 301 bps. You should bite the bullet and get the ISDA CDS standard model to run. (You can actually download an Excel add-in if you don't want to compile C++ code, but you really should do the latter). Then you you'll have the "official" conversion between the market standard quote spread and the upfront. Rememeber to use interest rate curves from the right historical date. IHS Maikit kindly provides a converter web page (thanks). You probably can't use it for your P&L for many days, but you can compare to verify that your own converter works correcly.
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