CVA vs DVA: What’s the Difference (and Why DVA Feels Wrong)

“What’s the difference between CVA and DVA?” is a standard interview question with a standard answer: CVA is the cost of your counterparty defaulting, DVA is the benefit of you defaulting. Recite that and you’ve answered the question.

But the good follow-up — the one that separates people who’ve thought about it from people who’ve memorised it — is this: why does DVA feel wrong? Because it does. DVA says your derivatives book gains value as your own credit gets worse, and that’s genuinely uncomfortable once you sit with it. This post covers both, and takes the discomfort seriously.

CVA: the part that makes sense

CVA — Credit Valuation Adjustment — is the market value of the risk that your counterparty defaults while they owe you money.

The logic is clean. You have a derivative that might, over its life, be worth something to you (they owe you). If they default while it’s in your favour, you lose that value, less recovery. CVA prices that possibility and subtracts it from the risk-free value of the trade:

The key feature is asymmetry: you only take a credit loss when the trade is in your favour. If they default while you owe them, you just pay what you owe and walk away unharmed. So CVA is built on your positive exposure — the expected amount they’d owe you at each future date.

Nobody argues with CVA. It’s a cost, it reduces the value of your position, and it matches intuition: risky counterparties are worth less to trade with.

DVA: the mirror image, and the discomfort

DVA — Debit Valuation Adjustment — is the same calculation from the other side of the table.

Your counterparty faces credit risk on you. From their perspective, they’re computing a CVA against you and marking down the trade accordingly. By symmetry, whatever is a credit cost to them is a credit benefit to you — because if you default while you owe them, you don’t pay in full. That expected saving is your DVA, and it adds value to your position:

DVA is built on your negative exposure — the expected amount you’d owe them — weighted by your own probability of default:

Look at that . The adjustment depends on your own default probability. And that’s where the trouble starts.

Why DVA feels wrong

Here’s the uncomfortable consequence, stated plainly: as your own credit deteriorates, your DVA goes up, and your derivatives book gains value.

Your credit spread widens, the market thinks you’re more likely to fail, and — on paper — you book a profit. Let’s see it:

import numpy as np
np.random.seed(7)

notional, T, n_steps, n_paths = 10_000_000.0, 5.0, 60, 40_000
dt = T/n_steps
r0, sigma_r, kappa = 0.03, 0.010, 0.20
fixed, r_disc, R = 0.03, 0.03, 0.40

# simulate rates, value a payer swap on every path
rates = np.full((n_paths, n_steps+1), r0)
for i in range(1, n_steps+1):
    Z = np.random.standard_normal(n_paths)
    rates[:,i] = rates[:,i-1] + kappa*(r0-rates[:,i-1])*dt + sigma_r*np.sqrt(dt)*Z
times = np.arange(n_steps+1)*dt
mtm = np.array([(rates[:,i]-fixed)*(T-times[i])*notional for i in range(n_steps+1)]).T

EE  = np.maximum(mtm, 0).mean(axis=0)   # they owe you  -> CVA
ENE = np.minimum(mtm, 0).mean(axis=0)   # you owe them  -> DVA

df = np.exp(-r_disc*times)
mid = lambda x: 0.5*(x[:-1]+x[1:])

def dva(h_self):
    surv = np.exp(-h_self*times)
    pd   = surv[:-1] - surv[1:]
    return (1-R)*np.sum(-mid(ENE)*mid(df)*pd)

print(f"DVA with our hazard at 1%: {dva(0.01):>8,.0f}")
print(f"DVA with our hazard at 4%: {dva(0.04):>8,.0f}")

DVA with our hazard at 1%:    2,740
DVA with our hazard at 4%:   10,336

Our credit got four times worse, and our DVA nearly quadrupled. Since value to us is risk-free minus CVA plus DVA, that rising DVA pushes our book’s value up. We’re deteriorating, and the accounting says we’re winning.

Is DVA nonsense, then?

No — and this is the nuance worth having ready. DVA is mathematically correct. It’s the symmetric truth of CVA: if you accept that a risky counterparty is worth less to trade with, you have to accept that you being risky makes you worth less to trade with too, which is a benefit to you and a cost to them. You can’t take CVA and reject DVA; they’re the same equation read from opposite ends.

The problem isn’t the maths. It’s monetising it. The DVA gain is only realised if you actually default — it’s the money you save by not paying your creditors in full. To turn that paper gain into cash, you’d have to buy back your own debt cheaply, or sell protection on yourself, and neither is clean. So DVA is a real value adjustment that you mostly can’t hedge and can’t spend. That combination — real on the balance sheet, unrealisable in practice — is exactly why it’s controversial, and why regulators treat it warily in capital calculations even though accountants recognise it.

Bilateral CVA: putting them together

When both sides have credit risk, the trade carries a bilateral adjustment:

def cva(h_cpty):
    surv = np.exp(-h_cpty*times); pd = surv[:-1]-surv[1:]
    return (1-R)*np.sum(mid(EE)*mid(df)*pd)

print(f"CVA:                {cva(0.02):>8,.0f}")
print(f"DVA:                {dva(0.01):>8,.0f}")
print(f"Bilateral (DVA-CVA):{dva(0.01)-cva(0.02):>8,.0f}")

CVA:                   5,366
DVA:                   2,740
Bilateral (DVA-CVA):  -2,625

Here the counterparty is riskier than we are (2% versus 1% hazard), so CVA outweighs DVA and the net adjustment is a cost. If our credit were the worse of the two, the sign would flip. Bilateral CVA is symmetric by construction — it has to be, or the two counterparties couldn’t agree on a price. My cost is your benefit; if we disagreed on the adjustment, there’d be a price gap and no trade.

The interview answer

If asked to distinguish them:

CVA is the cost of your counterparty’s default, built on your positive exposure and their default probability. DVA is the benefit of your own default, built on your negative exposure and your own default probability. Together they give the bilateral adjustment, which is symmetric so both sides agree on the price.

And if pushed on why DVA is controversial: because it means your book gains value as your credit worsens — the maths is the symmetric truth of CVA, but the gain is only realised if you actually default, so it’s real on paper and nearly impossible to monetise.

Give that second part and you’ve shown you understand DVA rather than just defined it.

Where they sit in the bigger picture

CVA and DVA were the first two valuation adjustments. Once the industry accepted that the risk-free price wasn’t the real price, the same logic spread: FVA for funding costs, MVA for margin, KVA for capital — collectively XVA. DVA was the one that forced everyone to confront how strange these adjustments can get, which is why it’s still the one that comes up in interviews.

If you want to see the machinery under all of this — exposure simulation, risk-neutral valuation, and the numerical methods that make XVA computable — that’s what we build in Risk-Neutral Valuation, where these adjustments stop being definitions and start having a P&L.

Get the Quant Reference Card — four pages covering stochastic calculus, measure change, the models you’ll actually meet, discretisation, rates, credit and XVA, with the practitioner notes that don’t make it into textbooks. Free.