6.10.1 Dealer Banks & OTC Markets from Zero

Basic Prerequisites: Inventory Management & Quote Skewing.

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1. Intuition & Practical Objective

This page explains why over-the-counter (OTC) markets exist at all - with no prior knowledge of dealer banks needed. The objective is one idea: when a trade is customized and infrequent, an exchange cannot match it, so a dealer must stand in the middle - and the dealer’s price is set by negotiation, not by an auction.

Start with the dumbest question: why isn’t everything traded on a stock exchange? A stock exchange is a beautiful machine: everyone trades the same standardized share, thousands of buyers and sellers arrive every second, and a continuous auction sets one price. But most of finance is not standardized:

• A pension fund wants a 27-year interest-rate swap with a specific notional schedule to hedge a pension liability. No one else wants that exact contract.
• A bank wants to sell a $40m tranche of a specific corporate bond. The bond rarely trades; there is no crowd.
• An airline wants to hedge jet-fuel exposure with a bespoke collar.

For these, there is no continuous market, only a search for a counterparty, and someone must be willing to be the counterparty now. That someone is a dealer - typically a dealer bank - who quotes a price, takes the position onto its balance sheet, and earns the bid-ask spread for providing immediacy.

Three steps:

1. Standardization is what makes an exchange possible. Exchanges need fungibility (every unit identical) and volume. Customized contracts have neither, so they cannot be centrally matched. They trade bilaterally: one buyer, one seller, one negotiated price.

2. Immediacy is a product you must pay for. If you want to trade now, you either (a) wait and search for the other side, or (b) pay a dealer to take the other side instantly. The bid-ask spread is the price of option (b). This is exactly the “supply of dealer services” view (Stoll 1978) - the dealer sells a service, and the spread is its fee.

3. The price is a bargain, not an auction. Because the two sides meet bilaterally, the price depends on each side’s outside option - how easily each could find someone else. A single trade price in an OTC market encodes both the asset’s value and the relative bargaining power of the two parties. This is the insight that becomes the search-and-bargaining model (Duffie–Gârleanu–Pedersen 2005).

The one-sentence essence. “An OTC market is not an auction with many participants but a search market with two: a dealer who sells immediacy and a customer who needs it, haggling over a price that reflects how fast each can find an alternative.”

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2. Mathematical Ground Truth & Derivations

The first, simplest model: a dealer’s bid-ask as the price of immediacy.

Suppose an asset will be worth $V$ to the current holder at some horizon, but the holder has a liquidity need - a pure discount-rate/impatience cost $\delta$ per unit time of holding when they would rather not (Duffie–Gârleanu–Pedersen call low intrinsic type $lo$). If an investor must hold forever, the asset’s value to them is the present value of a stream that is penalized by $\delta$:

$$V^{lo}={\int }_0^{\infty }{e}^{-rt}(1-\delta )dt=\frac{1-\delta }{r},V^{hn}={\int }_0^{\infty }{e}^{-rt}dt=\frac{1}{r}.$$

The gain from trade between a low-type owner (wants to sell) and a high-type non-owner (wants to buy) is therefore

$$H-L=\frac{1}{r}-\frac{1-\delta }{r}=\frac{\delta }{r}.$$

That gap - the frictionless fundamental surplus - is the maximum total spread the two sides could ever split; the equilibrium spread $z\delta /D$ is strictly smaller because search frictions discount it (see the hub’s $D$). In a frictionless Walrasian world they would jump straight to $P^{\ast }=1/r$ and split the surplus costlessly. In a search world they cannot: each side can only trade when a counterparty is found.

Search turns the split into a spread. Let $\lambda$ be the intensity at which an investor meets another investor, and $\rho$ the intensity at which an investor meets a dealer. When two investors meet they Nash-bargain and split the surplus with the seller getting $(1-q)$ and buyer $q$:

$$P=(V_{lo}-V_{ln})(1-q)+(V_{ho}-V_{hn})q.$$

When an investor meets a dealer, the dealer has an outside option - unloading in the frictionless interdealer market at price $M$ - and bargaining power $z$, so:

$$A=zH+(1-z)M,B=zL+(1-z)M,⟹A-B=z(H-L).$$

This is the whole intuition in one line: the OTC bid-ask spread is a fraction $z$ of the fundamental surplus $\delta /r$, where $z$ is how much of the bargaining power the dealer holds. A dealer with all the power ($z=1$) takes the entire surplus; perfect competition ($z\to 0$) closes the spread to zero.

Why doesn’t competition always close it? Because a search market is inherently uncompetitive - you trade with the one counterparty you happened to meet, not with “the market.” Prices converge to Walrasian only as search gets fast enough that a better outside option is credible. That is the deep result of the folder’s model page.

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3. Computational Implementation - why dealers matter for allocation

We simulate an OTC market of investors who may trade only directly with each other (no dealer, $\rho =0$), at meeting intensity $\lambda$. Each asset is worth more to a high intrinsic type, so efficient allocation means every asset ends up held by a high type. Search frictions leave the market misallocated; faster search (or a dealer) fixes it. Stdlib + numpy; ran and verified.

Allocation efficiency rises monotonically with search intensity and approaches the Walrasian limit of $1$ (every asset held by a high type). The gap between the curve and $1$ is the search-friction cost - exactly the illiquidity the dealer is paid to remove. Note the dimension: at $\lambda =2$ (an investor finds another investor about once every half-period), $6.3\%$ of assets sit in the “wrong” hands.

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4. Failure Modes & First-Principles Breakdowns

1. “OTC” is not “unregulated chaos” - it is a different mechanism. Beginners assume no exchange means no market structure. In fact OTC markets have rich structure: designated dealers, interdealer brokers, RFQ (request-for-quote) platforms, trade-reporting regimes. Confusing “no central book” with “no rules” is the first error.
2. Customization is the cause, not the bug. The reason a corporate bond or a bespoke swap trades OTC is that each contract is unique, so there is no fungible crowd to match. Blaming OTC for “illiquidity” misses that the illiquidity is intrinsic to the customization.
3. The spread is not the dealer’s “greed.” It is the price of immediacy and inventory risk-bearing. Stoll’s dealer-services view (1978) - and every model in this folder - derives the spread from a service rendered, not spite.
4. Two identical assets can trade at two prices at the same instant. In a bilateral market, price depends on who you found and how much they needed to trade. Price dispersion (not a single price) is a defining OTC feature (bridged to Liquidity Risk & Asset Pricing).

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5. References

• Duffie, Gârleanu & Pedersen (2005), Over-the-counter markets, Econometrica 73(6)
• Duffie (2012), Dark Markets, Princeton UP
• Stoll (1978), The supply of dealer services in securities markets, Journal of Finance 33(4)
• Hasbrouck (2007), Empirical Market Microstructure

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6. Connected Graph Bridges

• Base: Inventory Management & Quote Skewing · Market-Maker Economics & Rebates
• Continue: 02 · OTC Market Structure · Index Hub