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In FX cash markets, market makers provide liquidity to clients for a wide variety of currency pairs. Because of flow uncertainty and market volatility, they face inventory risk. To mitigate this risk, they typically skew their prices to attract or divert the flow and trade with their peers on the dealer-to-dealer segment of the market for hedging purposes. This paper offers a mathematical framework to FX dealers will…
We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain around the continuous-time limit. Unlike in the risk-neutral case, the optimal inventories become mean-re…
In this paper we extend the market-making models with inventory constraints of Avellaneda and Stoikov ("High-frequency trading in a limit-order book", Quantitative Finance Vol.8 No.3 2008) and Gueant, Lehalle and Fernandez-Tapia ("Dealing with inventory risk", Preprint 2011) to the case of a rather general class of mid-price processes, under either exponential or linear PNL utility functions, and we add an inventory-…
This paper presents a model for analyzing inventory control policies for dealers that support the sales and service of manufactured goods. The environment faced by dealers is characterized by multiple stochastic demand classes (prioritized into emergency and regular), a principal source for boui emergency and regular requirements, multiple secondary sources for expedite requirements, and constraints on the lead time …
Abstract Two intermediary-based factors—a corporate bond dealer inventory measure and a broad intermediary distress measure—explain more than 40$\%$ of the puzzling common variation in credit spread changes beyond canonical structural factors. A simple intermediary-based model with partial market segmentation accounts for intermediary factors’ explanatory power and delivers three further implications with empirical s…
Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we consider a stochastic control problem similar to the one introduced by Ho…
Inventory matching is a standard mechanism/auction for trading financial stocks by which buyers and sellers can be paired. In the financial world, banks often undertake the task of finding such matches between their clients. The related stocks can be traded without adversely impacting the market price for either client. If matches between clients are found, the bank can offer the trade at advantageous rates. If no ma…
The VSTOXX index tracks the expected 30-day volatility of the EURO STOXX 50 equity index. Futures on the VSTOXX index can, therefore, be used to hedge against economic uncertainty. We investigate the effect of trader inventory on the price of VSTOXX futures through a combination of stochastic processes and machine learning methods. We formulate a simple and efficient pricing methodology for VSTOXX futures, which assu…
We propose a continuous-time stock-flow consistent model for inventory dynamics in an economy with firms, banks, and households. On the supply side, firms decide on production based on adaptive expectations for sales demand and a desired level of inventories. On the demand side, investment is determined as a function of utilization and profitability and can be financed by debt, whereas consumption is independently de…
A novel high-frequency market-making approach in discrete time is proposed that admits closed-form solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the variability of the partial filling of limit orders posted in a limit order book (LOB). As a result, we uncover new patterns as to how the demand's randomness affects the optimal pla…
We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an exogenous open market with finite liquidity. This endogenously leads to transient price impact in the dealer market. Smoot…
This paper studies how market informedness affects market makers' profitability in a computational market environment with heterogeneous learning agents. We develop an agent-based market model in which market makers differ in their information sets and inventory-risk aversion, prices form endogenously, fundamental values evolve exogenously, and market-taker order flow follows a state-dependent self-exciting process. …
We study strategic interactions in a broker-mediated market in which agents learn and exploit each other's private information. A broker provides liquidity to an informed trader and to noise traders while managing inventory in a lit market. The informed trader infers the broker's trading activity in the lit market, while the broker estimates the trader's private signal. Information leakage in the client's trading flo…
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option market making for options written on stocks in the presence of stochastic volatility. Mathematically, the problem is formulated as a stochastic optimal control problem and the con…
Classical market-making strategies based on stochastic control, such as the Avellaneda-Stoikov and the Guéant-Lehalle-Fernandez-Tapia (GLFT) extension, provide closed-form quoting rules, but rest on assumptions that break down at realistic microstructure timescales. One of them is that order flow is stationary, while empirical evidence points to the existence of regimes, possibly associated with algorithmic execution…
Automated market makers (AMMs) are a cornerstone of decentralised finance (DeFi). Constant product markets with concentrated liquidity, such as UniswapV3, are now a well-established design. In these markets, liquidity providers (LPs) face a sequential decision problem: they must decide when to rebalance their positions and which price ranges to allocate capital to as market conditions evolve. We formulate dynamic liq…
Hit ratio is a common service metric for electronic corporate bond market making, but raw hit-ratio targets can be economically misleading when client flow has heterogeneous adverse-selection content. This paper extends a stochastic-control framework for OTC bond RFQ market making with hit-ratio constraints by replacing raw hit ratio with a residual-quality-adjusted hit ratio. The key modelling distinction is that ad…
We study opportunistic optimal liquidation over fixed deadlines on BTC-USD limit-order books (LOB). We present RL-Exec, a PPO agent trained on historical replays augmented with endogenous transient impact (resilience), partial fills, maker/taker fees, and latency. The policy observes depth-20 LOB features plus microstructure indicators and acts under a sell-only inventory constraint to reach a residual target. Evalua…
Commodity Inventory Financing — Repo-like financing of physical stocks linking curve to rates.
Natural Gas Storage — Inventory levels driving seasonal price spikes and energy inflation.
Crypto Market Maker Inventory — Dealer inventory and hedge needs shaping crypto microstructure.
Positions that do not intend to sit overnight — session trends, opening-range breaks, or inventory mean reversion inside the day.
A price-based engine with a fundamental veto or tilt — inventories, COT, positioning, or nowcasts that can cut or flip a trend.
Stuffed means a dealer or salesperson was left long (or short) inventory they did not want, usually after a client or a syndicate left paper on the desk.
The quick ratio is cash, marketable securities, and receivables over current liabilities — current ratio without inventory.
Adverse selection is the expected loss a liquidity provider takes when the other side is informed — the Glosten–Milgrom reason spreads exist even with no inventory.
How price actually forms through order flow, spreads, inventory, and participant interaction.
Primary dealer holdings track how much inventory dealers are carrying, offering insight into balance-sheet absorption, market-making capacity, and Treasury market strain.
Short selling is selling a borrowed security, hoping to buy it back cheaper — a negative inventory financed by the borrow.
Adverse selection is the expected loss a liquidity provider takes when the other side is informed — the Glosten–Milgrom reason spreads exist even with no inventory.
Commodity Inventory Financing — Repo-like financing of physical stocks linking curve to rates.
Crypto Market Maker Inventory — Dealer inventory and hedge needs shaping crypto microstructure.
Positions that do not intend to sit overnight — session trends, opening-range breaks, or inventory mean reversion inside the day.
How price actually forms through order flow, spreads, inventory, and participant interaction.
The mechanics of price formation through order flow, spreads, inventory, and liquidity.
Natural Gas Storage — Inventory levels driving seasonal price spikes and energy inflation.
Primary dealer holdings track how much inventory dealers are carrying, offering insight into balance-sheet absorption, market-making capacity, and Treasury market strain.
The quick ratio is cash, marketable securities, and receivables over current liabilities — current ratio without inventory.
Short selling is selling a borrowed security, hoping to buy it back cheaper — a negative inventory financed by the borrow.
Stuffed means a dealer or salesperson was left long (or short) inventory they did not want, usually after a client or a syndicate left paper on the desk.