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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…
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…
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…
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…
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 liquidity on decentralized exchanges (DEXs), identifying factors at the platform, blockchain, token pair, and liquidity pool levels with predictive power for market depth metrics. We introduce the v2 counterfactual spread metric, a novel criterion which assesses the degree of liquidity concentration in pools using the ``concentrated liquidity'' mechanism, allowing us to decompose the effect of a factor on ma…
We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon $T$. A trader uses both limit and market orders, and a large market order faces an adverse price movement caused by the liquidity risk. First, we study a single period model where the trader places a limit order and/or a market order a…
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. …
This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker's quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, lea…
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…
We empirically study the trading activity in the electronic on-book segment and in the dealership off-book segment of the London Stock Exchange, investigating separately the trading of active market members and of other market participants which are non-members. We find that (i) the volume distribution of off-book transactions has a significantly fatter tail than the one of on-book transactions, (ii) groups of member…
Prediction markets are attracting growing attention as trading volumes rise and their practical relevance increases. To ensure efficient price discovery, liquidity provision becomes ever more important. Due to the binary settlement structure in prediction markets, optimal market making leads to an optimization problem that is fundamentally different from the ones studied in classical settings. In this paper, we devel…
High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which generalize the self-financing relationships of frictionless markets to electronic markets with limit order books. We use NASDAQ ITCH data to identify significant empirical features s…
Primary dealer holdings track how much inventory dealers are carrying, offering insight into balance-sheet absorption, market-making capacity, and Treasury market strain.
How price actually forms through order flow, spreads, inventory, and participant interaction.
Natural Gas Storage — Inventory levels driving seasonal price spikes and energy inflation.
Inventory Risk MM (Quant).
Inventory Cycle (Economy).
Bullwhip Effect (Economy).
Just in Time Inventory (Economy).
Just in Case Inventory (Economy).
Crypto Market Maker Inventory — Dealer inventory and hedge needs shaping crypto microstructure.
Oil Inventory Draw (Commodities).
Commodity Inventory Financing — Repo-like financing of physical stocks linking curve to rates.
Crude Curve WTI — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve Brent — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve RBOB — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve ULSD — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve HH — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve TTF — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve JKM — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve copper — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve aluminum — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve nickel — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve zinc — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve iron ore — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve gold — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve silver — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve corn — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve wheat — Commodity curve, inventory, or geopolitics-linked supply concept.
Crude Curve soy — Commodity curve, inventory, or geopolitics-linked supply concept.
Product Crack WTI — Commodity curve, inventory, or geopolitics-linked supply concept.
Product Crack Brent — Commodity curve, inventory, or geopolitics-linked supply concept.
Product Crack RBOB — Commodity curve, inventory, or geopolitics-linked supply concept.
Product Crack ULSD — Commodity curve, inventory, or geopolitics-linked supply concept.
Product Crack HH — Commodity curve, inventory, or geopolitics-linked supply concept.
Product Crack TTF — Commodity curve, inventory, or geopolitics-linked supply concept.
Product Crack JKM — Commodity curve, inventory, or geopolitics-linked supply concept.
Product Crack copper — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk aluminum — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk Brent — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk copper — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk corn — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk gold — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk HH — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk iron ore — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk JKM — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk nickel — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk RBOB — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk silver — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk soy — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk TTF — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk ULSD — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk wheat — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk WTI — Commodity curve, inventory, or geopolitics-linked supply concept.
Ag Weather Risk zinc — Commodity curve, inventory, or geopolitics-linked supply concept.
Commodity Inventory Financing — Repo-like financing of physical stocks linking curve to rates.
Copper Balance aluminum — Commodity curve, inventory, or geopolitics-linked supply concept.
Copper Balance Brent — Commodity curve, inventory, or geopolitics-linked supply concept.
Copper Balance copper — Commodity curve, inventory, or geopolitics-linked supply concept.
Copper Balance corn — Commodity curve, inventory, or geopolitics-linked supply concept.
Copper Balance gold — Commodity curve, inventory, or geopolitics-linked supply concept.
Copper Balance HH — Commodity curve, inventory, or geopolitics-linked supply concept.