# CVA as a running spread - risk annuity calculation in the Monte Carlo framework

I have simulated future term structures in the one-factor Hull-White model and calculated the CVA of a particular trade (let's say, now I have it in absolute value, in dollars). However, I want to represent this CVA value as a running spread. As far as I understood from the Gregory's book (2011) "Counterparty credit risk - The new challenge for global financial markets", to get the annual spread value I have to divide my absolute CVA value by the CDS risky annuity (and then also by the par value to get the value in %). This is something where I am stuck.

The formula of the risk annuity given in the book is (1-exp(-(r+h)(T-t)))/(r+h) where r is the constant continiously compounded interest rate and h is the hazard rate. For my case T-t = 12 years, and the yearly CDS spread is 300 bps. However, in my example r is not constant (I have the upward-sloping initial interest rate term structure).

Can anyone advice me how to estimate CVA as a running spread in this case? If u also can offer a good paper as a reference, I would also be very grateful.