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Market Making in Spot Precious Metals

Alexander Barzykin, Philippe Bergault, Olivier Guéant

Abstract

The primary challenge of market making in spot precious metals is navigating the liquidity that is mainly provided by futures contracts. The Exchange for Physical (EFP) spread, which is the price difference between futures and spot, plays a pivotal role and exhibits multiple modes of relaxation corresponding to the diverse trading horizons of market participants. In this paper, we model the EFP spread using a nested Ornstein-Uhlenbeck process, in the spirit of the two-factor Hull-White model for interest rates. We demonstrate the suitability of the framework for maximizing the expected P\&L of a market maker while minimizing inventory risk across both spot and futures. Using a computationally efficient technique to approximate the solution of the Hamilton-Jacobi-Bellman equation associated with the corresponding stochastic optimal control problem, our methodology facilitates strategy optimization on demand in near real-time, paving the way for advanced algorithmic market making that capitalizes on the co-integration properties intrinsic to the precious metals sector.

Market Making in Spot Precious Metals

Abstract

The primary challenge of market making in spot precious metals is navigating the liquidity that is mainly provided by futures contracts. The Exchange for Physical (EFP) spread, which is the price difference between futures and spot, plays a pivotal role and exhibits multiple modes of relaxation corresponding to the diverse trading horizons of market participants. In this paper, we model the EFP spread using a nested Ornstein-Uhlenbeck process, in the spirit of the two-factor Hull-White model for interest rates. We demonstrate the suitability of the framework for maximizing the expected P\&L of a market maker while minimizing inventory risk across both spot and futures. Using a computationally efficient technique to approximate the solution of the Hamilton-Jacobi-Bellman equation associated with the corresponding stochastic optimal control problem, our methodology facilitates strategy optimization on demand in near real-time, paving the way for advanced algorithmic market making that capitalizes on the co-integration properties intrinsic to the precious metals sector.
Paper Structure (9 sections, 35 equations, 10 figures)

This paper contains 9 sections, 35 equations, 10 figures.

Table of Contents

  1. Introduction
  2. The model
  3. Approximation technique
  4. Numerical results and discussion
  5. Concluding Remarks
  6. Statement and acknowledgement

Figures (10)

  • Figure 1: EFP spreads in basis points implied from four active futures contracts and spot mid prices of gold against USD in 2023 (green). Zoom in on 21 July also shows OTC forward rate -- OTC FWD -- (red) and demonstrates intraday mean reversion. Daily median difference in basis points between implied EFP and OTC forward rate (blue) illustrates mean reversion on a weekly scale.
  • Figure 2: Optimal gold spot pricing ladder (green), spot execution rate (blue) and futures execution rate (red) as functions of spot inventory for zero (left) and 1000 oz (right) futures inventory. EFP price deviation is zero, risk aversion $\gamma = 3\cdot 10^{-4}$, other parameters in the text. Different shades of green correspond to different sizes in the price ladder (lighter colors -- smaller size -- tighter spread).
  • Figure 3: Average gold spot (blue) and futures (red) inventory relaxation following a 1000 oz client spot trade with a termination condition in 1 hour obtained by numerically averaging $2\cdot 10^4$ Monte Carlo trajectories. The dashed line (yellow) shows the dynamics of $q^S + q^F$.
  • Figure 4: Inventory probability distribution of a spot gold market maker with access to futures hedging.
  • Figure 5: Gold spot and futures no-execution zones as functions of spot inventory and volatility-normalised EFP price deviation. Zero futures inventory, $\gamma=10^{-3}$ (left) and $10^{-4}$ (right). No execution in shaded areas, selling the corresponding instrument above the upper boundary and buying below the lower boundary.
  • ...and 5 more figures

Theorems & Definitions (1)

  • Remark 1