Hello everyone,Currently I am building a framework in order to calculate the potential future exposure of an interest rate swap. I just wanted to check wheather I am doing the right steps and if any of you with more experience might have some suggestions:1)I calibrate a short rate model, e.g. Vasicek to the current yield curve (market observed), this will give me market implied estimates for volatility etcetera2)I simulate (so under risk neutral I guess) paths of the MtM, I use the expression on page 14 of 'Brigo & Mercurio Interest rate models theory and practice' for a RFS3) I take for example the 95% percentile, this will give me a measure for the PFEThe main question is whether I can use the risk neutral dynamics for the short rate model. There is a lot of discussion online about this, but I was hoping for some practicioners feedback All responses are welcome!James

Say you have to simulate the 10Y rate for a 1Y simulation horizon with a daily step. I think that what people do is: specify some dynamics for your rates process (like vasicek), calibrate the parameters over the daily fixings of the 10Y rates for the last N years (maximum likelihood, moment matching etc), simulate your process, re-price, take the percentile.You could have reasons for not calibrating some of the parameters and instead fix them using some extra assumptions. Also, the stuff you simulate could be garbage (not arbitrage free), and so you'll have to invent some trick to account for that.

In general we do not calibrate in the risk neutral measure for risk managment since we are concern about the real world probability of losses. However, risk-neutral calibration does give you the bounds of your real-world calibration, especially when parameters in many interest rate models are not observable market prices/quotes. Calibration in real-world measure often means using historical data. For PFE calculations, the time zero PFE should be calculated using risk-neutral measure (PFE=MTM taking into account collateral/netting agreements). Forward PFE will be dependent on your objective-world MC simulation.

@ tchew75 , thanks for your response. I thought that the MtM was basically the future price at time t>0 given the initial swap rate and the remaining payments from t on onwards and in that respect should be computed under the risk neutral measure (since is basically is a pricing-matter). In addition, isn't the initial swap rate such that the zero MtM and hence the PFE is zero? Regards,James

Indeed, the MtM of a swap is calculated under a risk-neutral measure (to be precise, under an equivalent martingale measure of your choice).The exact definition of PFE is up to your risk management; most people define the PFE as the maximum of the trade's exposure profile computed at 95% confidence.To calculate the exposure profile, you would, as DevonFangs says, simulate the underlying risk factors (interest rate curve for a swap) under the real-world measure, and for each scenario (i.e. each simulated curve) reprice the trade. Again, the pricing will be done under an equivalent martingale measure, just like when you calculate today's MtM. The 95th percentile of the MtMs at a certain furute date will give you one point of the trade's exposure profile.

Hi Cyril and all, a quick question:Mainstream banks calculate VaR using historical simulations (not Monte Carlo). Can we calculate PFE as well using the same approach? If I am not wrong, I heard Rebonato suggested such an approach (sorry I don?t have access to this paper).I guess, the reason no body doing historical simulation for PFE is because of the followings:- Firstly, the VaR is calculated for only 1 day horizon (and then scaled up for 10 days for regulatory purpose). On the other hand the time horizon for PFE is minimum 1 year. Such a long horizon cannot be captured in the historical VaR simulation methodology.Question 1: Suppose a bank possesses many years of historical data. In that case, can it use historical simulation for a 1 year horizon and take an appropriate percentile (like VaR) on the positive side of the distribution? - Secondly, due to short horizon, VaR simulations ignore the drift term. The drift term is very significant. I guess scaling of drift from 1 day to 250 days is linear ? i.e. much stronger impact of scaling up (i.e. not square root of time rule as we use in case of scaling up historical VaR from 1 day to 10 days).Question 2: How do we handle drift in historical simulations, if we ever want to opt for this approach?Precisely, why we cannot use historical simulation for PFE?Kind regards,