Mathematics Meets Crypto Markets

A permissionless blockchain is a distributed protocol that must remain stable without a central enforcer. Its security and liveness depend not only on cryptography and networking, but also on strategic behavior. This research frames a blockchain as a hierarchy of games, from consensus participation to transaction propagation and token holding decisions. It formalizes the main player types and equilibrium concepts used in blockchain analysis, discusses how strategic deviations arise as equilibrium responses, and connects protocol security to aggregate equilibrium quantities such as total hashrate.

Perpetual futures are futures without expiry whose prices are kept close to a reference index through periodic funding transfers between longs and shorts. This paper systematizes the main pricing approaches used across centralized exchanges (CeFi) and decentralized exchanges (DeFi), connects them to the cost-of-carry framework, and analyzes how market microstructure (order book vs. AMM vs. oracle-quoted pools) shapes equilibrium pricing, risk, and solvency.

This research examines the fundamental differences between options and perpetual futures in managing liquidation risk during volatile market conditions. Through quantitative analysis of the October 2025 deleveraging event, the paper demonstrates how options' convex payoff structure provides superior risk control compared to linear perpetual futures exposure. Additionally, the study presents six option-market warning signs that serve as predictive indicators for systemic deleveraging in perpetual futures markets, including IV-RV spreads, put skew, term-structure inversion, and dealer gamma positioning. The paper includes market mechanics, margin dynamics, and actionable hedging overlays that combine both instruments for optimal risk management.

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.

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.

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.