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Market Making and Transient Impact in Spot FX

Alexander Barzykin

Abstract

Dealers in foreign exchange markets provide bid and ask prices to their clients at which they are happy to buy and sell, respectively. To manage risk, dealers can skew their quotes and hedge in the interbank market. Hedging offers certainty but comes with transaction costs and market impact. Optimal market making with execution has previously been addressed within the Almgren-Chriss market impact model, which includes instantaneous and permanent components. However, there is overwhelming empirical evidence of the transient nature of market impact, with instantaneous and permanent impacts arising as the two limiting cases. In this note, we consider an intermediate scenario and study the interplay between risk management and impact resilience.

Market Making and Transient Impact in Spot FX

Abstract

Dealers in foreign exchange markets provide bid and ask prices to their clients at which they are happy to buy and sell, respectively. To manage risk, dealers can skew their quotes and hedge in the interbank market. Hedging offers certainty but comes with transaction costs and market impact. Optimal market making with execution has previously been addressed within the Almgren-Chriss market impact model, which includes instantaneous and permanent components. However, there is overwhelming empirical evidence of the transient nature of market impact, with instantaneous and permanent impacts arising as the two limiting cases. In this note, we consider an intermediate scenario and study the interplay between risk management and impact resilience.
Paper Structure (4 sections, 18 equations, 3 figures)

This paper contains 4 sections, 18 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Transient Impact of Client Trades with the Dealer
  3. Hedging with Transient Impact
  4. Numerical Examples

Figures (3)

  • Figure 1: Optimal top of book (TOB) ask quote $\delta^{1,a}_*$ and execution speed $v_*$ as functions of inventory $q$ and impact state $x$ for a set of parameters defined in the text. The dashed line corresponds to the approximate solution for $x=0$.
  • Figure 2: 2d plot of optimal execution speed $v_*$ as a function of inventory $q$ and impact state $x$ for a set of parameters defined in the text.
  • Figure 3: P&L, position, execution speed and impact state dynamics following an inventory shock of $q_0 = 50$ M for a parameter set defined in the text. The results were obtained via Monte Carlo simulation with $10^4$ trajectories. Dashed lines correspond to the model optimized with Almgren-Chriss impact.