# Funding Valuation Adjustment (FVA) - understanding issues

Having trouble with understanding the logic of FVA. Let's assume that as a trader I trade with a client an uncollateralised fx forward. Then, I hedge my position with "risk-free" bank with which I have a signed CSA.

1. Having EE profile for the trade I calculate FVA and get some value. What is the meaning for this value? The future value of the trade may be much more or less than FVA. How does this value hedge funding risk?

2. Why should I calculate FVA for the client's portfolio (e.g. incremental FVA)? It seems more logical to calculate FVA for the "risk-free" bank as funding risk comes from CSA agreement.

Any help is highly appreciated. Thanks.

• So sadly a bit busy to write out a full answer here but essentially - if your CSA-d hedge perfectly replicated the market risk on your uncollateralised FX forward, then all that is left is the funding spread you are paying (if the uncollateralised deriv is ITM) on the hedge. So that but for sign, the relevant exposure is the same. The spread is driven by the CSA contract, however the exposure you are hedging is driven by the uncollat trade, so it's all the same thing. Here is an excellent reference btw: defaultrisk.com/pa_crdrv_08.htm (Burgard and Kjaer 2010) for a general framework – Mehness Jan 20 '17 at 14:06
• The mathematics is quite nice actually, and you find that the doubly survival - contingent FVA term + the bank first to default term collapse to a symmetric bank defaults first term. Again, if get some time later will write out the relevant time integrals as an answer. – Mehness Jan 20 '17 at 14:09
• Thank you for the comment. The thing is that the funding spread is given in %, but the resulting funding cost is Exposure(t) * funding spread. Since Exposure varies over time funding cost can be much more or less than expected value. Does this mean that funding risk is managed via expected values? – dmitry Jan 20 '17 at 14:44
• so this is why if I get some time I'll try and write out the proper time integral - you cannot just multiply an exposure by a spread, that's a gross oversimplification but it is sadly the sort of thing you see a lot (especially in regulatory approaches). Effectively you integrate the +ve MTM over time with the doubly survival contingent funding spread for the FVA part (this amounts to a bank FTD term) or funding cost.That giuve you a true picture. After all you will almost jcertainly have funding spread interest rate correlation in many cases for example.. – Mehness Jan 20 '17 at 14:51
• but do check out that reference it's a nice treatment, and really all you need to understand is what's contained in equation (2.3) or Main Result 3 that pretty much covers it (albeit in a simplified stylised form) – Mehness Jan 20 '17 at 14:54