July 30th, 2015, 12:02 pm
As I have already written in another thread:-If the credit risk is taken care of by some CVA calculation, then the appropriate discount rate for any payment is the funding rate. The reason is that this is the rate that a trader can invest or borrow in. For me is it completely intuitive that two banks with different funding costs disagree on e.g. the price of a collateralized. For the bank with the higher funding costs it is simply more expensive to set up the hedge. I don't understand why Hull&White seem to disagree ...- Assume two zero-bonds with same maturity but different (credit) risk. Even though both are collateralized at the funding-rate their value will be different as the trade with the higher (credit) risk will have a higher CVA. If you wanted to merge everything in 1 equation then you would need to discount with a rate equal to the funding-rate plus some credit-spread (which will always be >= 0)-A collateralized trade consist of it's inherent payoff plus a stochastic collateral flow (i.e. some stochastic dividend). Both parts need to be discounted with the funding rate. Thes result is the same as if the inherent payoff (without stochastic collateral flow) was discounted at the OIS rate. OIS discounting is just only a theoretical shortcut.-I would agree Hull&White that the OIS curve is probably the closes proxy of a risk-free curve nowadays. Therefore I find it intuitive to use the OIS curve to get the "no-default value" in a CVA calculation (though my CVA knowledge is limited)Hope this heldped a bit. And if anybody disagrees with any of the points, pls let me know. I'm always happy to be proven wrong
.Cheers,Bernd
Last edited by
BerndSchmitz on July 29th, 2015, 10:00 pm, edited 1 time in total.