# Accrued Interest in Monte Carlo simulation for CVA/DVA computation

I'm implementing the CVA/DVA for some interest rates derivatives, with the short rate following a Hull-White model (one factor). Once I have calibrated the model and I get the results with the simulation, a quite interesting question arose.

For instance, say an IRS: Which is the known interest rate used to compute the accrued interest?

Does anyone know how to compute it?

If I understood your question correctly, what you are saying is that you are in trouble when, at a simulation date $t_i$, you need the fixing of the floating rate at a fixing date $t_f$ that is between $t_i$ and the previous simulation date $t_{i-1}$: $t_f \in ]t_{i-1}, t_i[$

If that is your question, then since at $t_i$, the values of the short rate at $t_i$ and $t_{i-1}$ are already known, you can get its value at $t_f$ by interpolation between these two simulation dates. You can then use this interpolated value of the short rate to compute your floating rate fixing.

An IRS contract will state in detail what interest is payable to whom and when.

The typical vanilla Xibor IRS at present has a CSA for daily-rebalanced cash accruing at OIS rates. So the coupons are fixed on Xibor, and between coupon payments the PV is collateralised with cash, rebalanced every day using OIS interest accrual.

However, some old CSAs permit posting other kinds of collateral, and even a choice of currency.

• Yes, but computing the CVA DVA implies to simulate the future interest rate model (HW1F), and then to price the IRS among the IRS's time of life. Once we calculate the Zero Coupon Yield for all our scenarios for different dates of valuation – SciPhy Nov 22 '13 at 9:40
• Are you saying you want to do this with a single curve? My answer regards dual-curve pricing. – Phil H Nov 22 '13 at 9:45
• Sorry.My comment was not shown completely Yes,but computing the CVA DVA implies to simulate the future interest rate model (HW1F),and then to price the IRS among the IRS's time of life.Once we calculate the ZCY at the future dates of valuation we need to price the IRS at the future.And my question is, how could I estimate the known interest rate so that I am able to compute the accrual interest when we price the IRS at a future time? – SciPhy Nov 22 '13 at 10:45
• I could set up the dates of simulation when the coupons start...but it does not work since I am interested into pricing thousand of IRS simultaneously. – SciPhy Nov 22 '13 at 10:58
• @ Carlos : whatever method you will finally choose you will have to use a calculation that "approximates" the fixings date simulation of your IRS portfolio. Best regards – TheBridge Nov 22 '13 at 18:21

Accrued interest is based on a fixed floating rate, there's nothing stochastic about those rates unless the IRS is calculated in arrears, which is not the standard.

If you are talking about the future float leg fixings, those are the forward libor rates on each path of your simulation, discounted by the zero coupon or other numeraire of your choosing, along each path of your simulation.