<main>
BlogResearchServices
Back to home

Mathematics Meets Crypto Markets

Research & Publications

Quantitative research papers covering topics in mathematical finance, risk management, statistical modeling, and computational methods.

Derivatives Pricing
Oct 2025
5
Pricing Models for Perpetual Futures in Crypto
A unified model that explains centralized and decentralized implementations of perpetual futures. This research compares four design archetypes including dYdX v4, GMX v2, Hyperliquid, and Drift, showing how production choices map into the same state variables. It provides lessons for market design and a research outlook focused on adaptive funding, on-chain money market integration, and formally verified liquidation rules.
Market Microstructure
Nov 2025
6
Market Making in TradFi, CeFi, and DEXs
A quantitative analysis comparing market making mechanisms across traditional finance, centralized crypto exchanges, and decentralized exchanges. This research examines the Avellaneda-Stoikov framework, stochastic volatility extensions, and CFMM dynamics. It explores how inventory risk, impermanent loss, MEV, and JIT liquidity transform the market making problem across venues while preserving the core utility maximization framework.
Quantitative Finance
Nov 2025
7
Assumptions in Quantitative Finance
A comprehensive analysis of the assumptions underlying quantitative finance models, from Black-Scholes to modern market microstructure frameworks. This research note examines distributional assumptions, dynamical models, correlation structures, and crypto-specific failures. It reveals how model failures stem from using frameworks outside their valid domains, particularly in decentralized markets where block times, oracle latency, and MEV introduce structural discontinuities.
Risk Management
Sep 2022
43
Value-at-Risk on Decentralised Finance: Methodologies and Use Cases
This research evaluates Value-at-Risk (VaR) methodologies for cryptocurrency portfolios, comparing Historical Simulation, GARCH models, and Variance-Covariance methods. Through rigorous backtesting, the study reveals that traditional VaR approaches struggle with crypto market volatility and regime changes. A proprietary Kaiko methodology demonstrates superior accuracy in capturing market dynamics. The paper includes practical applications for portfolio optimization, showing how VaR can minimize risk while maintaining returns across major cryptocurrencies including BTC and ETH.

Sorbonne University & Ecole Polytechnique

Collaborate on Research

Interested in discussing research ideas or exploring collaborative opportunities?

© 2025 amykhaldoun.com All rights reserved.

BlogResearchServices