6.10 Dealer Banks & OTC Markets

Basic Prerequisites: Adverse Selection & Glosten–Milgrom (why informed flow widens a spread) and Inventory Management & Quote Skewing (the single-dealer inventory view). (these are the folder-level prerequisites for pages 02–06; page 01 states its own, smaller, entry requirements)

1. Intuition & Practical Objective

Not every market is an exchange. The most important markets in the world by notional volume - corporate bonds, interest-rate swaps, credit default swaps, FX, mortgage-backed securities, repo, emerging-market debt, bank loans - do not have a central order book. They are over-the-counter: a buyer phones (or messages) a dealer, negotiates a price for a customized trade, and the dealer - a bank - takes the other side onto its own balance sheet. There is no ticker, no tape, no continuous auction. There is a dealer and a negotiation.

This folder is the dealer-banks and OTC markets topic-folder for Pillar 6. It is a hub: it (a) gives you the fast formula-and-model lookup below for the search-and-bargaining equilibrium, and (b) routes you to six sub-pages that walk from zero intuition through the search model, dealer capacity, the failure modes, and the post-2008 clearing architecture. Primary verified sources: Duffie, Gârleanu & Pedersen (2005), Over-the-Counter Markets, Econometrica 73(6) - the anchor model, read from the primary PDF and re-derived here; Duffie (2010), Presidential Address: Asset Price Dynamics with Slow-Moving Capital, JF 65(4) - the dealer-capacity/beltway view; and Duffie (2012), Dark Markets - the book-length capstone. Cross-checked against Hasbrouck Empirical Market Microstructure (Ch 1–2, dealer and search markets).

The one-sentence essence. “An OTC market is a search market: an investor who wants to trade must find a counterparty, and when two meet they bargain - so the price depends not only on fundamentals but on each side’s outside option (how easily each can find someone else), and the bid-ask spread is the price of immediacy a dealer sells.”

2. Mathematical Ground Truth & Derivations

Quick-Reference Lookup (job #1). Formulas are transcribed from Duffie–Gârleanu–Pedersen (2005), Theorem 2 (eqs 14–16) and eq (19), and re-derived in the folder. Every number in the check column was re-executed and reproduced exactly (§3 and the sub-pages).

Notation: $r$ discount rate; $δ$ the dividend loss of a low intrinsic type; $λ$ the investor-to-investor meeting intensity (search ability); $ρ$ the investor-to-dealer meeting intensity (dealer accessibility); $λ_{u}, λ_{d}$ the intensities of switching from low to high / high to low intrinsic type; $s$ asset supply per capita; $q$ the seller’s bargaining power vs another investor; $z$ the dealer’s bargaining power vs an investor; $V_{σ}$ the value function of type $σ \in {lo, hn, ho, ln}$ ; $L = V_{l o} - V_{l n}$ the seller’s gain from trading, $H = V_{h o} - V_{hn}$ the buyer’s.

Quantity	Formula	Verified check
Steady-state high-type mass	$\frac{λ _{u}}{λ _{u} + λ _{d}}$	$1/1.1 = 0.909091$
Condition 1 (which side is rationed)	$s < \frac{λ _{u}}{λ _{u} + λ _{d}}$	$0.8 < 0.909091$ ✓
Ask (investors buy from dealer)	$A = \frac{1}{r} - \frac{δ}{r} \frac{λ _{d} + 2 λ μ _{l o} ( 1 - q )}{D}$	$A = 18.315906$
Bid (investors sell to dealer)	$B = \frac{1}{r} - \frac{δ}{r} \frac{zr + λ _{d} + 2 λ μ _{l o} ( 1 - q )}{D}$	$B = 18.140204$
Interinvestor price	$P = \frac{1}{r} - \frac{δ}{r} \frac{( 1 - q ) r + λ _{d} + 2 λ μ _{l o} ( 1 - q )}{D}$	$P = 18.206093$
Common denominator	$D = r + λ_{d} + 2 λ μ_{l o} (1 - q) + λ_{u} + 2 λ μ_{hn} q + ρ (1 - z)$	-
Bid-ask spread	$A - B = \frac{δz}{D}$ (the frictionless fundamental surplus is $zδ / r$ ; search discounts it to $zδ / D$ )	$0.175702$ ; $δz / D = 0.175702$ ✓
Monopolist spread ( $z = 1$ )	$A - B = \frac{δ}{D} = \frac{δ}{r + λ _{d} + 2 λ μ _{l o} ( 1 - q ) + λ _{u} + 2 λ μ _{hn} q}$ (the full $D$ above; the $2 λ μ$ search terms do not drop out)	$= 0.219628$ at $ρ = 0, λ = 26$
Nash price between investors	$P = (V_{l o} - V_{l n}) (1 - q) + (V_{h o} - V_{hn}) q$	eq (11)
Dealer quotes from bargaining	$A = zH + (1 - z) M, B = z L + (1 - z) M$	eqs (12)–(13); $M$ = interdealer price
Walrasian limit	$P^{*} = \frac{1}{r}$	$20.0000$
Heterogeneous-investor spread	$A - B = \frac{zδ}{D}$ (same $D$ ; eq 19 is the $z$ -weighted case of the general spread)	eq (19)

Critical caveat (the result that surprises everyone). With competing dealers ( $z < 1$ ), faster contact between investors and dealers ( $ρ ↑$ ) tightens the spread to zero and prices converge to Walrasian. With a monopolistic dealer ( $z = 1$ ), faster contact widens the spread - the investor’s threat to find another investor is worth less once the dealer has already absorbed everyone. The whole comparative statics hinges on $z$ , the bargaining power, not on the level of the friction.

3. Computational Implementation - the DGP equilibrium engine

Standard library only. This reproduces the headline numbers above: the Theorem-2 prices, the convergence to Walrasian under fast search, and the competing-vs-monopolist divergence. Ran and verified (§3 of 03 · The Search-and-Bargaining Model).

The spread vanishes as search gets fast (competition) but widens under a monopolist - the paper’s central, counterintuitive comparative static, reproduced.

4. Failure Modes & First-Principles Breakdowns

Hub signposts - the full analysis lives in 05 · Failure Modes & Practice. In one line each:

Search frictions are a tax on liquidity. When $λ, ρ \to 0$ the spread is bounded only by the discount rate - an investor with a liquidity need pays a huge concession (the OTC “illiquidity discount” $1/ r - P$ ).
Dealer capacity is finite and procyclical. A dealer absorbs a supply shock only up to its balance-sheet capacity; shock size relative to capital sets the price impact, which reverses as capital arrives (04 · Dealer Capacity).
Contagion runs through the dealer network. Bilateral OTC exposures chain defaults: a shock to one dealer can cascade through the interdealer web (Duffie 2010; the 2008 crisis) - the reason central clearing was mandated.
Bargaining power, not fundamentals, can dominate the price. In a search market the “price” is a bilateral split; two identical assets can trade at different prices in the same instant.
Opacity compounds everything. No public tape means no mark-to-market, so balance-sheet losses are discovered late and fire sales feed back into prices.

5. References

Duffie, Gârleanu & Pedersen (2005), Over-the-counter markets, Econometrica 73(6), 1815–1847
Duffie (2010), Presidential address: Asset price dynamics with slow-moving capital, Journal of Finance 65(4), 1237–1267
Duffie (2012), Dark Markets: Asset Pricing and Information Transmission in Over-the-Counter Markets, Princeton University Press
Duffie (2012), Over-the-counter markets, in Handbook of Financial Econometrics
Hasbrouck (2007), Empirical Market Microstructure, OUP
Bao, Pan & Wang (2011), The illiquidity of corporate bonds, Journal of Finance 66(3), 911–946

6. Connected Graph Bridges

Foundational base: Probability & Measure Theory · Stochastic Calculus & Itô · Econometrics & Time Series
Sibling topic (in-pillar): Inventory Management & Quote Skewing · Market-Maker Economics & Rebates · Liquidity Risk & Asset Pricing
Risk-pillar bridge: Counterparty Risk & XVA · Systemic Risk & Aggregation
Derivative-pillar bridge: Counterparty Risk & XVA (the OTC derivative valuation-adjustment side)
Sub-pages (in-folder): 01 From Zero · 02 OTC Market Structure · 03 The Search-and-Bargaining Model · 04 Dealer Capacity & Balance Sheets · 05 Failure Modes & Practice · 06 Advanced Extensions

Beginner: start at 01 · Practitioner: start at 05

Kwant Atlas

Explorer

6.10 Dealer Banks & OTC Markets

1. Intuition & Practical Objective

2. Mathematical Ground Truth & Derivations

3. Computational Implementation - the DGP equilibrium engine

4. Failure Modes & First-Principles Breakdowns

5. References

6. Connected Graph Bridges

6.10.1 Dealer Banks & OTC Markets from Zero

6.10.2 OTC Market Structure

6.10.3 The Duffie–Gârleanu–Pedersen Search-and-Bargaining Model

6.10.4 Dealer Capacity & Balance Sheets

6.10.5 Failure Modes & Practice

6.10.6 Advanced Extensions