Basic doubt on Potential Future Exposure

Hi,

I have recently started working on Potential Future Exposure (PFE) and stuck at the basic understanding of the concept. Before I state my doubt, let me summarize my understanding of the methodology. Lets say we are looking at a simple IRS here, for simplicity.

Have gone through the literature and am following this approach to find the PFE:

    1. 1. Assume current interest rates from the market are coming from a known short rate model (Lets assume its 1 factor, simple Vasicek model). So, we estimate(calibrate) the parameters of the model , by minimizing the distance between market bond prices and the expected model prices.


    1. 2. Simulate some large number of interest rate paths from fitted Vasicek though exact distribution approach(started with euler's scheme, later moved to exact approach)


  1. 3. Valuate my IRS at each time point of the simulated path. 95th percentile of the value at each time point gives the required PFE profile. Valuation at different time points is just the PV of the future cash flows discounted along the simulated path.


From step 1, we have calibrated in such a way, that the bond prices from the model are unbiased estimators of the market bond prices.
Since discount factors are nothing but bond prices with appropriate start and end times and unit notional, Step 3 would imply that PV at each date is a (non-linear) function of bond prices.

Since, E(f(X)) need not equal f(E(X)), Expectation of PV on Day 0 need to be equal to market determined PV of the IRS. In other words, the expected value of the simulated PVs does not equal to the market value of the IRS. What am I missing here?

Thnaks in advance for helping!
 
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