How Variation Margin PAI Affects Swap Convexity
Summary
The discussion explains how price alignment interest (PAI), paid on variation margin, changes the funding interpretation of cleared interest rate swaps. With perfect collateralization, where collateral tracks the derivative’s net present value, the collateral is treated as funding the exposure. The accepted answer says this implies valuing each party’s derivative using the collateral rate rather than its own unsecured funding rate.
It then frames convexity differences between collateralized and uncollateralized forwards in terms of the covariance between the derivative’s reference index and the spread between the relevant collateral rates. For cleared derivatives collateralized at OIS, the answer finds no such adjustment relative to an uncollateralized derivative assumed to have funding at OIS plus a constant spread. This is a theoretical result under stated assumptions, not a complete account of real-world swap pricing: the question itself sets aside volatility, positioning, and other sources of convexity, and the reply does not quantify those effects.
Key ideas
- PAI is interest paid on variation margin.
- Under perfect collateralization, collateral funds the derivative exposure.
- The answer uses the collateral rate as the discounting rate for each party.
- Convexity differences can arise from covariance between the reference index and collateral-rate spreads.
- The stated OIS comparison depends on assuming a constant unsecured funding spread.
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# Price Alignment Interest(PAI) Convexity Effect # Price Alignment Interest(PAI) Convexity Effect I've been looking at convexity adjustments in ED's for several years(more opportunities a few years ago then currently) and was wondering if my thinking on PAI impact on swaps convexity is correct. Prior to PAI being implemented by LCH and CME, if I was paying fixed on IRS and the market rallied(rates lower), my NPV would we negative and I'd have to post collateral. With PAI, I now earn interest on that collateral whereas the fixed receiver owes it. If the market sold off, as a payer of fixed, my NPV would be positive but I'd also owe interest on the collateral posted to me. I understand the bias of ED holders to be short vs swaps, i.e. the short can reinvest at higher rates when market sells off, etc. but the impact of PAI is a bit unclear to me. It seems as though the exchanges are trying to get cleared swaps to behave like bilateral ones again? For example if I am paying fixed on a swap prior to clearing, there was not a benefit as the trades were not margin'd on a daily basis which lead to a larger convexity adjustment(leaving vols and positioning out of the equation). With clearing, the trades are margin'd on a daily basis(I receive collateral that I can invest at higher rates) which would have theoretically collapsed the adjustment a bit but PAI seems to reduce or now eliminate any benefit of paying fixed in the swap as any earned interest at the higher rate is owed back to the cpty. I understand there are other factors as well that affect convexity adjustments such as the fixed 01 in ED vs non-fixed in fras/swaps so this is just one aspect that has been throwing me off a bit. Appreciate any thoughts on this. ## Answer by Antoine Conze (score 2, accepted) https://quant.stackexchange.com/a/46448 PAI is the interest paid on the VM. Assuming perfect collateralization (i.e. collateral always reset to the derivative NPV) it is shown (see Piterbarg "funding beyond discounting") that funding is entirely done trough the collateral and therefore the derivative should be valued by each party with discounting at the collateral rate rather than at its own funding rate. The theoretical convexity adjustment on forwards (in addition to different discounting) between derivatives collateralized at different collateral rates (or uncollateralized which for each party is equivalent to collateral rate set to its own unsecured funding rate) comes from the covariance between the derivative reference index and the spread between collateral rates. With cleared derivatives collateralized at OIS, there would be no convexity adjustment compared to the same uncollateralized derivative assumed to be funded at an unsecured rate OIS + constant spread.
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