MicroHedger

A computational replication of "Gamma Positioning and Market Quality" by Buis et al. (2024), exploring the impact of dynamic hedgers' gamma positioning on market quality, with a particular focus on liquidity and probability dry-outs, through agent-based simulations.

Paper Overview

This project replicates the research presented in:

"Gamma Positioning and Market Quality"
Boyd Buis, Mary Pieterse-Bloem, Willem F.C. Verschoor, Remco C.J. Zwinkels
Journal of Economic Dynamics and Control, Volume 164, 2024
DOI: 10.1016/j.jedc.2024.104880

Abstract

The original paper studies the effect of gamma positioning of dynamic hedgers on market quality through simulations. Key findings include:

• Positive gamma positioning reduces volatility and increases market stability, while negative gamma positioning increases volatility and makes markets more prone to failures
• Price discovery typically worsens when dynamic hedgers become more prevalent, regardless of positioning sign
• Policy implications: Altering net gamma position of dynamic hedgers can serve as a policy instrument to improve market quality, especially for low-liquidity instruments

Project Objectives

MicroHedger aims to:

1. Replicate the zero-intelligence agent-based model from Buis et al. (2024)
2. Reproduce key findings regarding gamma positioning effects on market failure rates, in particular the phase diagrams w.r.t. different parameters that are provided as in table 1.
3. Analytise trajectories of volumes of the limit-order book all paths, failed and unfailed, under various time horizons to confirm stationarity.

Table 1: Failure rate of simulated markets, presented in Buils et al. (2024)

	-80	-60	-40	-20	0	20	40	60	80
Panel A: immediacy i
i = 0.3	0%	0%	0%	0%	0%	0%	0%	0%	0%
i = 0.325	5%	10%	0%	0%	0%	0%	0%	0%	0%
i = 0.35	50%	45%	5%	0%	0%	0%	0%	0%	0%
i = 0.375	95%	90%	45%	0%	20%	0%	0%	0%	0%
i = 0.4	100%	95%	100%	90%	85%	0%	0%	0%	0%
i = 0.45	100%	100%	100%	100%	100%	95%	65%	10%	10%
i = 0.5	100%	100%	100%	100%	100%	100%	100%	100%	95%
Panel B: news volatility σₙ
σₙ = 0.01	0%	0%	0%	0%	0%	0%	0%	0%	0%
σₙ = 0.025	10%	0%	0%	0%	0%	0%	0%	0%	0%
σₙ = 0.05	35%	15%	10%	5%	0%	0%	5%	10%	0%
σₙ = 0.075	75%	70%	55%	35%	20%	20%	20%	20%	40%
σₙ = 0.1	100%	100%	90%	75%	65%	55%	55%	70%	65%
σₙ = 0.125	100%	100%	90%	85%	80%	100%	95%	80%	65%
Panel C: order decay ζ
ζ = 0.05	0%	0%	0%	0%	0%	0%	0%	0%	0%
ζ = 0.075	50%	15%	0%	0%	0%	0%	0%	0%	0%
ζ = 0.1	70%	40%	5%	0%	0%	0%	0%	0%	0%
ζ = 0.125	80%	80%	25%	5%	0%	0%	0%	0%	0%
ζ = 0.15	100%	100%	50%	15%	0%	0%	0%	0%	5%
ζ = 0.175	100%	100%	85%	35%	10%	5%	0%	0%	0%
Panel D: market maker spread μₚ
μₚ = -0.1	0%	0%	0%	0%	0%	0%	0%	0%	0%
μₚ = -0.15	0%	5%	0%	0%	0%	0%	0%	0%	0%
μₚ = -0.2	25%	20%	0%	0%	0%	0%	0%	0%	0%
μₚ = -0.25	90%	75%	20%	0%	0%	0%	0%	0%	0%
μₚ = -0.3	100%	100%	95%	20%	0%	10%	40%	30%	30%
μₚ = -0.35	100%	100%	100%	90%	5%	75%	85%	75%	75%

Methodology

The simulation framework implements:

• Zero-intelligence agents as baseline market participants
• Dynamic hedgers with configurable gamma positioning
• Market quality metrics including volatility, liquidity, and price discovery measures
• Stress testing scenarios to evaluate market resilience

Key Model Components

• Agent Types: note that for the first 4 types, we model 4 different order arrival processes (rather than agents' behaviour).
  • informed investors (liquitidy takers);
  • uninformed investors;
  • informed market makers (liquidity providers);
  • uninformed market makers;
  • dynamic hedgers.
• Gamma Positioning: Positive, negative, and neutral gamma scenarios
• Market Structure: Continuous double auction with realistic market microstructure
• Quality Metrics: Market failure rate (and probably bid-ask spreads, price impact, volatility measures, and market depth)

🚀 Getting Started

Prerequisites

# Boost required
brew install boost # for MacOS using Homebrew
sudo port install boost # MacOS using Mac Ports

Installing the project

git clone https://github.com/yilvas09/MicroHedger.git
cd MicroHedger

Building the project

# create a build subfolder for built executables
mkdir build
cd build
# build with cmake and make
cmake ..
make

Experiments and results

Comparative statics

We first set a list of benchmark parameters as in table 2. We then vary the option position and each of the following parameters, in order to obtain a two-dimension surface of market failure rate.

Table 2: Benchmark parameters

Parameter	Value	Meaning
Ticksize	0.01	tick size
N	100	number of paths
T	20	number of trading sessions ('days')
H	10	number of trading intervals ('hours')
Q	4	number of trading sub-intervals ('quarters')
λ	40	order arrival intensity
u	0.3	probability of market orders
i	0.3	probability of informed orders
$\sigma_p $	0.1	std.dev. of spreads of incoming limit orders
$\mu_p$	-0.1	mean of spreads of incoming limit orders
$\sigma$	0.089	implied volatility for delta calculation
$\nu_{\text{min}}$	0	minimum volume of incoming orders
$\nu_{\text{max}}$	1	maximum volume of incoming orders
$p_0$	5	initial value of the fundamental price
$\mu_0$	0	mean of the fundamental news shock
$\sigma_0$	0	std.dev. of the fundamental news shock
$\xi$	0.05	order decay parameters

Results

	-80	-60	-40	-20	0	20	40	60	80
Panel A: immediacy i
i = 0.3	16%	5%	2%	0%	0%	0%	0%	0%	0%
i = 0.325	62%	52%	19%	1%	0%	0%	0%	0%	0%
i = 0.35	82%	83%	76%	13%	0%	0%	0%	0%	0%
i = 0.375	95%	100%	100%	85%	26%	10%	3%	2%	1%
i = 0.4	100%	100%	100%	100%	99%	73%	47%	36%	17%
i = 0.45	100%	100%	100%	100%	100%	100%	100%	100%	100%
i = 0.5	100%	100%	100%	100%	100%	100%	100%	100%	100%
Panel B: news volatility σₙ
σₙ = 0.01	19%	8%	2%	0%	0%	0%	0%	0%	0%
σₙ = 0.025	24%	14%	2%	0%	0%	0%	0%	0%	0%
σₙ = 0.05	31%	19%	6%	0%	0%	0%	0%	0%	1%
σₙ = 0.075	35%	29%	21%	0%	0%	1%	3%	2%	3%
σₙ = 0.1	52%	39%	24%	3%	0%	3%	4%	11%	10%
σₙ = 0.125	56%	53%	39%	14%	1%	11%	21%	28%	26%

Stationarity

In particular, when we vary the number of trader sessions/intervals/sub-intervals, we also plot the trajectories bid/ask volumes of the LOB, to confirm all other comparative statics tests are performed under a time horizon long enough to guarantee stationarity.

📁 Project Structure

MicroHedger
├── CMakeLists.txt
├── README.md
├── main.cpp
├── libs
│   ├── Bar.cpp
│   ├── Bar.hpp
│   ├── CMakeLists.txt
│   ├── DeltaHedger.cpp
│   ├── DeltaHedger.hpp
│   ├── LOB.cpp
│   ├── LOB.hpp
│   ├── Random.cpp
│   ├── Random.hpp
│   ├── Utils.cpp
│   └── Utils.hpp
└── tests
    ├── CMakeLists.txt
    ├── test_bar.cpp
    ├── test_lob.cpp
    ├── test_paired_vector_sort.cpp
    └── test_random.cpp

Documentation

📝 Citation

If you use MicroHedger in your research, please cite both this repository and the original paper:

@article{buis2024gamma,
  title={Gamma positioning and market quality},
  author={Buis, Boyd and Pieterse-Bloem, Mary and Verschoor, Willem FC and Zwinkels, Remco CJ},
  journal={Journal of Economic Dynamics and Control},
  volume={164},
  pages={104880},
  year={2024},
  publisher={Elsevier}
}

@misc{microhedger2024,
  title={MicroHedger: A Replication of Gamma Positioning and Market Quality},
  author={[Your Name]},
  year={2024},
  url={https://github.com/yilvas09/MicroHedger}
}

Contact

For questions, suggestions, or collaboration opportunities, please:

• Open an issue on GitHub
• Contact the maintainer via email yutongzhao2000@gmail.com.

Acknowledgments

• Original authors Buis, Pieterse-Bloem, Verschoor, and Zwinkels for their foundational research
• Open source community for tools and libraries (e.g. Boost) used in this project

---

This project is part of ongoing research in market microstructure and algorithmic trading. The simulation framework is designed for academic and research purposes.