Funding and Pricing Differences Between Listed and OTC Options

# European OTC options and their listed equivalent - CSA vs margin


# European OTC options and their listed equivalent - CSA vs margin












In the past I've only ever traded OTC options, and never really thought about the following:

If you trade a European OTC option you post/receive cash collateral and on this collateral you receive/pay interest. This is in line with no-arbitrage since one needs to borrow money to post collateral and the interest received on the collateral goes to paying the interest on the loan.

Now suppose you trade a listed (European) equivalent. As far as I know you post margin (initial + variation) but you don't receive/pay interest on this margin.

Am I right regarding the (no) interest on margin? But if so, isn't the listed equivalent different (different price/vol) from the OTC option? To post margin I'll borrow money on which I have to pay interest, but I am not receiving this interest back from the posted margin, which is different than the OTC case.

A basic question perhaps, just never really thought about this as never traded listed.

## Answer by SI7 (score 2, accepted)

https://quant.stackexchange.com/a/85268

When you trade a listed option on an exchange (e.g. Eurex) there will be different margin components: Premium Margin and additional margin (initial margin). In general, a CCP allows you to post cash or securities from an eligible pool of securities. Whichever you choose, there will be some fee. Cash collateral for example may be remunerated at ESTR - 20 bps and if you post bonds only there may be a flat fee of 15 bps p.a. on the securities you posted.

When trading this OTC it will depend on your CSA with your counterparty (form of eligible collateral, fees, remuneration etc)

In both cases, xVA desks at banks typically take care of doing pricing adjustments regarding the funding and remuneration of Margin.

## Answer by almost_surely_ (score 1)

https://quant.stackexchange.com/a/85815

Your instinct was right; it was aimed at the wrong leg. You already found in the comments that cash VM is remunerated at CCPs, so the specific worry dissolves. But there is a real funding difference between the listed and OTC versions of the same payoff, it's bigger than the one you were worried about, and building on SI7's answer it's worth separating into three distinct effects — because they have very different sizes and only one of them is symmetric.

### Effect 1: the VM remuneration spread

This is the one you asked about, and it's a pure discounting difference. For a fully VM-collateralised trade the discount rate is the collateral remuneration rate, not the risk-free rate (Piterbarg 2010). The forward of the underlying is unchanged — that's set by the underlying's own repo/funding — so only the discount factor moves:

$$\frac{V_{\text{CCP}}}{V_{\text{CSA}}} = e^{(r_c^{\text{CSA}} - r_c^{\text{CCP}})T}$$

Taking SI7's ESTR − 20bp against a CSA paying ESTR flat, on a 1-year ATM option (100 notional, 20% vol, premium 9.4134):

| collateral rate | price | vs CSA flat | in vol points |
| ESTR | 9.4134 | — | — |
| ESTR − 10bp | 9.4228 | +0.0094 | +0.02 |
| ESTR − 20bp | 9.4322 | +0.0188 | +0.05 |
| ESTR − 50bp | 9.4606 | +0.0472 | +0.12 |

So yes — the listed and OTC versions genuinely have different prices for the same payoff, and it is not an arbitrage. Two identical cash flows under two different collateral agreements are two different instruments from a funding standpoint. That's precisely why the CSA is part of the trade and not paperwork.

Note the direction, which catches people out: the trade collateralised at the lower rate is worth more. If you hold a positive-value position you hold collateral and owe interest on it at $r_c$; a lower $r_c$ means you owe less, so the position is worth more to you.

Five hundredths of a vol point, though. Real, bookable, not decision-changing.

### Effect 2: initial margin, which is where the money is

IM funding is roughly four times larger, and it behaves completely differently:

| IM (% notional) | funding spread | annual cost | % of premium |
| 10% | 25bp | 0.0250 | 0.3% |
| 15% | 50bp | 0.0750 | 0.8% |
| 20% | 100bp | 0.2000 | 2.1% |

Against 0.0188 for a 20bp VM spread, the 15%/50bp case is 4× the size.

The structural point is more important than the number: VM is a transfer, IM is a deadweight.

Variation margin flows between you and your counterparty. Your loss is their gain, so across the netting set it nets to zero and the only cost is the remuneration spread. Initial margin is posted by both parties to a third party — a CCP, or a segregated custodian under UMR — and neither side can use it. Nobody receives what you post. You fund it, you're remunerated below your funding cost, and the difference is gone.

That asymmetry is exactly why MVA exists as a separate adjustment rather than being folded into FVA. It isn't a rebadged funding cost, it's a cost with no offsetting benefit anywhere in the system.

One more asymmetry worth flagging, since it changes the answer depending on which side you're on: IM applies to short option positions, not long ones. A long listed option has bounded loss, so beyond the premium there's typically no additional margin. Short it and you're funding IM for the life of the trade. So "is listed more expensive than OTC?" has no single answer — it depends on your direction.

### Effect 3: settlement style, which dm63 is pointing at

dm63's comment is the deepest thing in the thread and worth developing.

Listed options come in two settlement styles, and they have completely different funding profiles:

- Equity-style (premium-paid). Premium settles at trade date, no VM on the option itself. Standard for listed equity options. Your funding question is then about the premium you paid away — not about collateral you hold.

- Futures-style (margined premium). Premium isn't paid up front; the position is marked to market daily. Standard for options on futures.

And in the futures-style case, the daily flows are not collateral at all — they are settlement. That cash is yours or it's gone; there is nothing posted to be remunerated. Which is exactly the futures-versus-forward distinction, and it carries the same consequence: when rates are stochastic and correlated with the underlying, daily settlement with no remuneration on the flows produces a convexity adjustment between the two (Cox–Ingersoll–Ross 1981). An OTC option collateralised under a CSA doesn't have that, because the VM sits as collateral earning $r_c$ rather than being settled away.

So "no interest on VM" was the right thought in the wrong place. It's true, but of futures-style settlement flows rather than of CCP cash collateral.

### And the OTC side isn't automatically the cleaner one

Two things worth keeping in view when comparing:

UMR closed most of the gap. Pre-2016 the "OTC has no IM" advantage was real. Since phase 6 completed in September 2022, in-scope bilateral counterparties post regulatory IM to segregated custodians — same deadweight, same MVA, now on both sides of the fence.

CSAs have their own frictions, and they're often worse than a CCP schedule precisely because they're negotiated: remuneration spreads, thresholds and minimum transfer amounts that leave you partially uncollateralised, one-way CSAs, and non-cash eligibility that hands the poster a cheapest-to-deliver option worth its own adjustment. A clean CCP schedule at ESTR − 20bp can easily be cheaper than a badly negotiated CSA at ESTR flat with a threshold.

### The short version

Three effects, in ascending order of how much they matter:

- VM remuneration spread — a discounting difference, about 0.05 vol points for 20bp on a 1-year option. Symmetric, small, real.

- IM funding (MVA) — roughly 4× larger, one-directional (shorts only), and a genuine deadweight because nobody receives what you post.

- Settlement style — equity-style versus futures-style changes the funding profile qualitatively, and futures-style brings a convexity adjustment that the collateralised OTC version doesn't have.

So the price and the implied vol should differ between the listed and OTC versions of the same payoff. Getting them to agree would be the anomaly.

### Code

```
import numpy as np
from scipy.stats import norm

S, K, T, sig, r = 100., 100., 1.0, 0.20, 0.030

def bs(S, K, T, r, v):
    d1 = (np.log(S/K) + (r + 0.5*v*v)*T)/(v*np.sqrt(T))
    return S*norm.cdf(d1) - K*np.exp(-r*T)*norm.cdf(d1 - v*np.sqrt(T))

base = bs(S, K, T, r, sig)

# Effect 1: collateral rate enters the DISCOUNTING only; the forward is unchanged
for bp in (10, 20, 50):
    px = base*np.exp(bp/1e4*T)
    print(f"ESTR-{bp}bp: {px:.4f}  ({px-base:+.4f})")

# Effect 2: IM funding, short positions
for im, spr in ((0.10, 25), (0.15, 50), (0.20, 100)):
    cost = 100*im*spr/1e4*T
    print(f"IM {im:.0%} @ +{spr}bp: {cost:.4f} per 100  ({100*cost/base:.1f}% of premium)")
```

### References

- V. Piterbarg, Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing, Risk, February 2010 — why the collateral rate is the discount rate, and the assumptions it needs.

- A. Green, XVA: Credit, Funding and Capital Valuation Adjustments, Wiley, 2015 — ColVA and collateral optionality under a negotiated CSA.

- A. Green, C. Kenyon, MVA: Initial Margin Valuation Adjustment by Replication and Regression, Risk, 2015 — the IM cost, done properly.

- J. Cox, J. Ingersoll, S. Ross, The Relation Between Forward Prices and Futures Prices, Journal of Financial Economics 9(4), 1981 — the settlement-style convexity.