Simulating Inflation Swap Exposures for CVA and DVA

Summary

The document outlines a simulation-based approach to counterparty and own-credit valuation adjustments for an inflation-linked swap. It proposes dividing the valuation horizon into intervals, generating future CPI paths calibrated to a forecast and volatility, revaluing the swap along those paths, and averaging positive exposures at each time to estimate expected positive exposure. Those exposures would then be combined with default probability and loss given default by interval to estimate CVA; DVA follows a corresponding exposure treatment.

The central unresolved issue is how to construct the future CPI curve conditional on each simulated index level, so the proposed method is a question rather than a complete implementation. It gives no model specification, calibration evidence, numerical results, or detailed treatment of discounting, dependence between market risk and default, or exposure timing. The outline is useful for identifying the main simulation steps, but additional modeling and validation are needed before it can produce reliable adjustments.

Key ideas

• A simulation can estimate future exposures for an inflation-linked swap across a sequence of dates.
• CPI paths should reflect a forecast and an appropriate volatility model.
• At each simulated date, the swap must be revalued using a CPI curve conditional on that path.
• Expected positive exposure is combined with default probability and loss given default to estimate CVA.
• The document leaves the conditional forward CPI curve construction unresolved.

Tags

# CVA for an inflation linked swap


# 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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.