6.10.6 Advanced Extensions

Basic Prerequisites: 03 · The Search-and-Bargaining Model and 05 · Failure Modes.

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1. Intuition & Practical Objective

This page is the launchpad from the core OTC search model to its three most important extensions: central clearing (the post-2008 reform), dark markets & information (Duffie 2012), and the network/aggregation frontier. Each answers a question the base model leaves open.

• Central clearing. If bilateral dealer exposures cause contagion (§05), does a central counterparty (CCP) fix it? Answer: partly - multilateral netting slashes exposure, but the CCP becomes a concentrated single point of failure. This is the central post-2008 policy trade-off.
• Dark markets and information. DGP assumes symmetrically informed agents. In reality OTC traders have private information about who wants to trade and at what price - Dark Markets (Duffie 2012) is the book-length treatment of OTC pricing with information transmission.
• Beyond: network theory, dealer funding/liquidity regulation (the leverage ratio, SLR), and electronic RFQ/SEF venues reshaping OTC structure.

The one-sentence result. “Central clearing replaces a dense web of bilateral exposures with a single netted position against a CCP - cutting system exposure by up to $15\times$ in a dense network - but transfers the residual risk to one node, so the reform is a risk-transformation, not risk elimination.”

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2. Mathematical Ground Truth & Derivations

2.1 Multilateral netting: the CCP benefit

Let $W_{ij}$ be dealer $i$‘s gross exposure to dealer $j$. Total gross system exposure is ${\sum }_{i,j}{W}_{ij}$. A CCP interposes itself and each dealer faces only its net position:

$$n_i=\sum _j{W}_{ij}-\sum _j{W}_{ji},\text{net system exposure}=\frac{1}{2}\sum _i|n_i|.$$

The netting benefit is the ratio

$$\text{NB}=\frac{{\sum }_{i,j}{W}_{ij}}{\frac{1}{2}{\sum }_i|n_i|}.$$

In a complete network with balanced random exposures, cross-terms cancel and $n_i\to 0$: the benefit grows without bound as density $\to 1$. This is the formal statement of “the CCP becomes the single counterparty.”

2.2 The clearing trade-off (Duffie & Zhu 2011)

A CCP reduces bilateral contagion but concentrates risk. Model the CCP as a node with its own capital $C_{\text{ccp}}$ (a default fund) and compute expected system loss under two regimes:

$$L_{\text{bilat}}=\mathbb{E}\left[\text{cascade loss in the bilateral network}\right],L_{\text{ccp}}=\mathbb{E}\left[\text{loss to the CCP default fund}\right].$$

Clearing is beneficial when $L_{\text{bilat}}>L_{\text{ccp}}$, which holds when: (i) exposures are numerous and offsetting (high NB), (ii) dealers are heterogeneous in risk (netting removes most cross-risk), and (iii) the CCP’s own cover-2/cover-1 default-fund sizing is adequate. Clearing is harmful when exposures are concentrated in a few large dealers who would otherwise be monitored bilaterally, or when the CCP’s default fund is thin relative to member risk.

2.3 Information and dark markets

Extensions with private information (Duffie, Gârleanu & Pedersen 2005 §6; Duffie 2012): investors’ types are not observable. A dealer who cannot screen will quote wider spreads (adverse selection, bridged to Glosten–Milgrom). Two additional channels:

• Price dispersion: without a public tape, two meetings produce two prices. Dispersion is information about which side has private knowledge.
• Trade transparency: making trades public speeds price discovery (lower informational rent) but can harm large traders who want to hide their footprint - the transparency/execution trade-off encoded in Dodd–Frank → SEFs and trade reporting.

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3. Computational Implementation - netting benefit vs the clearing trade-off

We compute the netting benefit across network densities (the case for clearing), then compare contagion with bilateral links versus severed/cleared links (the trade-off). numpy. Ran and verified.

The reform, quantified. The netting benefit rises from $2.4\times$ to $15.5\times$ as the network gets denser - a CCP nets away almost all offsetting positions. And replacing bilateral links with CCP membership cuts the interdealer cascade sharply: at a $2\times$-capital shock the bilateral cascade destroys a mean of $49.7$ of $60$ dealers, while the cleared network loses only $7.0$; at $4\times$ it is $59.9$ vs $23.2$. But note the honest caveat: clearing reduces contagion, it does not eliminate it - the cleared case still loses dealers (the initial shock plus some residual), and the residual risk now sits at the CCP, which is why CCP default-fund sizing (cover-1/cover-2) is the live policy question. Clearing is a risk transformation, and its benefit is conditional on the CCP being adequately capitalised.

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4. Failure Modes & First-Principles Breakdowns

1. Netting benefit is only realised if trades are offsetting. A CCP on a network of one-directional exposures nets nothing; the benefit requires many participants with offsetting positions (dense interdealer markets).
2. The CCP becomes a single point of failure. Concentrated residual risk means a CCP default is a catastrophic systemic event; “too big to fail” migrates from dealers to CCPs.
3. Default-fund procyclicality. Margin and default-fund calls rise exactly when members are weakest - a CCP can amplify a shock it was meant to contain (the “margin spiral”).
4. Information frictions persist under clearing. Clearing removes counterparty risk, not adverse selection; a dealer quoting a customer still faces the winner’s curse (Glosten–Milgrom).
5. Dark markets resist transparency. Attempts to force transparency can push large trades off-venue or into less-regulated structures - the regulatory-arbitrage failure mode.
6. Model risk in the netting algebra. The netting benefit assumes exposures are correctly measured and simultaneously nettable; cross-product, cross-currency, and wrong-way-risk complications mean real netting is less clean than the formula suggests.

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5. References

• Duffie & Zhu (2011), Does a central clearing counterparty reduce counterparty risk?, Review of Asset Pricing Studies 1(1), 74–95
• Duffie (2012), Dark Markets: Asset Pricing and Information Transmission in Over-the-Counter Markets, Princeton UP
• Duffie, Gârleanu & Pedersen (2005), Over-the-counter markets, Econometrica 73(6)
• Duffie (2010), Asset price dynamics with slow-moving capital, JF 65(4)
• Allen & Gale (2000), Financial contagion, JPE 108(1)
• Bao, Pan & Wang (2011), The illiquidity of corporate bonds, Journal of Finance 66(3)

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6. Connected Graph Bridges

• Back: 05 · Failure Modes & Practice · Index Hub
• Forward topic-folder pages: Liquidity Risk & Asset Pricing · Systemic Risk & Aggregation · Counterparty Risk & XVA
• Base: Ergodicity & Statistical Mechanics (network/aggregation tools) · Probability & Measure Theory