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#6189
rkapl
Participant

Dear Niall!

Sorry to be insisting on that, but after reading the chapter from “Modern Derivatives Pricing and Credit Exposure Analysis” by Lichters, Stamm and Gallagher and quoting them (hope this is allowed…):
“If the uncollateralized derivative has a positive value for the bank, the offsetting trade will require collateral; if the value is negative, collateral
will be received. Posted collateral only accrues interest at the collateral rate, while it is usually funded via unsecured borrowing in the money market, and so will create a cost of the funding spread.
The opposite is true for any received collateral: if it is rehypothecable, it saves the bank the funding spread or can be invested, generating a funding benefit of the lending spread.”

“Based on this argument, a simple definition of FVA can be given in a very similar fashion as the sum of unilateral CVA and DVA which we defined by (8.2), namely as an expectation of exposure times funding spreads, see for example Chapter 14 in Gregory [74]”

“The interpretation of this formula is that if the current exposure of the uncollateralized derivative at some future point in time is positive, the bank will pay collateral on the offsetting trade, which costs an equal amount of funding at the bank’s borrowing rate.
Likewise, a negative current exposure creates a funding benefit which can be invested at the lending rate.”

Following these arguments, it seems to me that both the formula in “Modern Derivatives Pricing and Credit Exposure Analysis” and the formula in the userguide (and the implementation following both) seems to be mixed up. I can also see a potential source of confusion, as the offsetting (hedge) trade’s ENE (causing a collateral requirement on the bank) is actually the original trade’s EPE (as the cashflows need to be completely offsetting) and vice versa with the EPE.

I have created an example case for your argument above (FBA and FCA is applied to an already collateralised trade, in that case an increase in EPE would mean that the exposure to your counterparty has increased, thus they must post more margin to you and thus you get a benefit, so an EPE increase leads to an FBA increase), in this the FBA/FCA is actually correct, however this seems to be not the point of FVA, which focuses on the uncollateralised parts (trades, imperfect CSA, etc.) of the business.

Anyway, I’d rather make this a configurable calculation, as it is quite fundamental and only easily revertable in case of borrowing_spread = lending_spread.

-regards,
Roland