Handling Floating-Rate Fixings and Accrued Interest in CVA/DVA Simulation
Summary
The document discusses accrued interest and floating-rate fixings in Monte Carlo CVA/DVA calculations for interest rate derivatives under a one-factor Hull–White short-rate model. One response addresses a fixing date that falls between adjacent simulation dates: it suggests interpolating the simulated short rate between those dates, then using that interpolated value to derive the floating-rate fixing. Other responses distinguish contractual coupon accrual and payment terms from collateral interest, noting that an interest rate swap specifies who pays what and when, while collateral arrangements can determine separate accrual conventions.
A further response describes future floating-leg fixings as path-dependent forward rates in the simulation, with discounting along each path using a chosen numeraire. The answers offer several perspectives rather than a unified implementation specification. They do not provide a complete algorithm, interpolation error analysis, or treatment of all contract conventions, so the suggested handling should be checked against the instrument terms and simulation design.
Key ideas
- A floating-rate fixing date may fall between two simulation dates in a Monte Carlo setup.
- One response suggests interpolating the simulated short rate to estimate the rate at that intervening fixing date.
- Swap coupon accrual and collateral interest follow contract and collateral agreement terms, respectively.
- Future floating-leg fixings can depend on each simulated path and its chosen discounting framework.
- The responses do not provide a complete implementation or assess interpolation accuracy.
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# Accrued Interest in Monte Carlo simulation for CVA/DVA computation
# 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?
## Answer by byouness (score 1)
https://quant.stackexchange.com/a/39812
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.
## Answer by Phil H (score 0)
https://quant.stackexchange.com/a/9533
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.
## Answer by experquisite (score -1)
https://quant.stackexchange.com/a/9541
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.