# CVA for an inflation linked swap

I am trying to value an inflation linked swap and wish to calculate the associated CVA and DVA.

I think the best way to approach this would be via a simulation. Suppose I wish to calculate CVA over the period $[0,T]$ that is split into $[t_{i-1},t_{i}]$ for $i=0,1,2,...M$. We would then want to calculate an EPE (expected positive exposure) during each of the sub intervals and the set CVA = $\Sigma EPE*PD*LGD$ for each of the intervals.

My thinking on methodology to calculate the expected exposures would be as follows:

1) Forecast an expected CPI index level into the future to calibrate the simulations to.

2) For each $t_{i}$ simulate N CPI index levels (obviously dependent on the prior level and calibrated to the base forecast and appropriate volatility).

From here I am not entirely sure, but I realize that I essentially need a forward CPI index curve from this point until point $T$. How would I have to make use of my input CPI forecast to project a CPI forecast from each simulated point forward?

3) Then make use of the simulated CPI and associated forecast in each simulation, at each point in time, to value the swap and finally take an average over all the simulation, at each point in time to get the expected exposure at each $t_{i}$ and use this to calculate the CVA and DVA.

A side from my question in point 2 above, if anyone can suggest an improvement to this method or confirm that I am going about this in the correct way I would appreciate it.

Thanks.