# How to convert the CDS Upfront Fee into the Traded Spread?

If I know all the economics of a CDS trade included the Upfront Settlement Fee from the ISDA CDS Model, how can I convert that amount back to Traded Spead? Can some help explain the process?

• This is all explained on the official website: cdsmodel.com/cdsmodel/documentation.html?# under "Standard CDS contract converter specification" Feb 9, 2017 at 8:34
• Your question is not clear. What is the Traded Spread? Do you want to convert the upfront fee into a par spread that leads to a zero CDS value, or a spread so that the CDS value is equal to the upfront fee? Feb 9, 2017 at 14:31
• Here is real example of what I am looking to achieve. Lets say I only know the following information: Trade Date: 2/9/17 Maturity Date: 12/20/21 Notional: 10mm Fixed Coupon:500bps Upfront Fee: \$270,324 and assuming 40% recovery, how could I determine the Traded Spread from this information? I believe we are saying Traded Spread and Par Spread are the same. Feb 9, 2017 at 15:29
• Are you trying to find out the traded (par) spread on 2/9/17 or today? If the answer is today, you need to access CDS market data to construct a spread curve. Markit is the standard here. Dec 14, 2019 at 22:20

You should check this answer: How to interpret the 'price' of a CDS?

It explains the relation between spread and upfront. In your particular case you might consider using a simple model mentioned at the end of that 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)g=r+S/(1−R)

where r is the risk-free (Libor) rate and R is the expected recovery rate, usually set to 40%.

• Thank you this information. The issue that I am finding with this equation is that I am trying to solve for S (CDS Spread) and when finding the value for RPV01 the CDS Spread is embedded in the calculation ( by solving for "g"). What is the Libor value here or how would I solve for Libor? Feb 11, 2017 at 4:35
• @ChrisN In your example maturity is in 5 years, so as a risk free rate you might use US treasury bond with 5y maturity. That's right, the equation i ls not directly solvable for S, so you might consider using a numerical method to find a solution for that equation Feb 11, 2017 at 6:33

Or, if you need a quick estimate, you could use $$T$$ as a rough approximation for the RPV01.

$$s \approx c - V/T$$