How DVA and FVA Can Overlap in Funding a Derivative Liability
Summary
The discussion compares two ways for a bank to fund a one-year liability: issuing a zero-coupon bond or creating an uncollateralized derivative that provides an upfront premium and requires a later payment. The bond’s economic value reflects the issuer’s credit risk, while risk-free discounting alone values the derivative without XVA adjustments.
It describes how debit valuation adjustment (DVA) can bring the derivative liability’s value in line with the bond by reflecting the bank’s own default risk and recovery. Funding valuation adjustment (FVA), applied to the same negative exposure using a funding spread, may produce a different value and an apparent additional funding benefit. The post raises this as evidence of possible overlap between DVA and FVA, but does not resolve how they should be modeled or combined. It is an intuitive question and comparison, not a complete derivation or consensus on treatment.
Key ideas
- A bank can compare bond issuance with an uncollateralized derivative as alternative ways to create a future payment obligation.
- A bond’s market price incorporates the issuer’s credit risk, while risk-free discounting alone does not.
- DVA adjusts a liability for the bank’s own default risk and can align its value with the bond comparison.
- Adding FVA to DVA may create an apparent extra funding benefit and raise a potential overlap issue.
- The discussion identifies the valuation question but does not settle the appropriate modeling approach.
Tags
Full text
# FVA and DVA overlap (intuitive explanation) # FVA and DVA overlap (intuitive explanation) Can anybody, in the most intuitive way possible explain why there is an FVA DVA overlap, specifically why DVA and FBA are similar? Note my mathematical ability is only to bachelor degree level, so go easy on me. ## Answer by yoggi-yalla (score 1) https://quant.stackexchange.com/a/73487 The most intuitive explanation I have found is to consider two different options for a bank in need of funds, they could either: - Emit a bond, let's say a zero-coupon bond with nominal 1 which expires in one year, or - Create a synthetic bond using an uncollateralized derivative where we receive some up-front premium and pay 1 in one year. Once the initial transaction is complete we're left with a single payment in one years time, regardless of the option we chose. Now, what is our perceived value of this liability? In option 1 we would look at the prevailing bond price, this is the price at which we could buy back our debt and hence it represents the economic value. This bond price can traditionally be seen as the risk-free discounted price, minus some adjustment to account for the credit risk. In option 2, without the use of XVA's, we would simply value it using risk-free discounting. If we introduce DVA as $(1-R)\int_0^Td(t)ene(t)pd(t)dt$ where $d$ is the discount factor, $R$ is the recovery rate, $T$ is the payment date, $ene$ is the expected negative exposure and $pd$ is the probability of us defaulting, then we should arrive at the same value as option 1. If we further introduce FVA as $\int_0^Td(t)ee(t)fs(t)dt$ where $ee$ is the expected exposure (which in this case is always negative) and $fs$ as the funding spread, then we will arrive at a different value than option 1, which I find very hard to explain. In particular, we would seemingly prefer this over option 1 as we experience an additional funding benefit, but I can't see how or why the bank is better off in this scenario. I don't have a firm view on how one should model it, but if they are simply added together I believe that there is certainly an overlap. Anyways, I hope that this gives you an idea of the problem!
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.