Risk Premia in the Bitcoin Market

2024-10-19

AI Summary

This study investigates the distinctiveness and volatility-state dependence of Bitcoin’s first- (option-implied) and second-moment (realized return) risk premia, benchmarked against U.S. equity indices. Within the pricing kernel (PK) framework, we document—novelty—the Bitcoin PK exhibits a steeper W-shaped structure under low volatility, amplifying risk premia for both extreme gains and losses. Building on this, we propose a dual-volatility-regime classification method based on clustering of risk-neutral density functions. Employing PK projection, adaptive clustering, and volatility risk premium (VRP) modeling, we find that negative returns contribute 33% of Bitcoin’s total VRP; VRP is higher and downside concerns more pronounced in low-volatility regimes, whereas long–short VRPs converge under high volatility. The findings uncover a unique nonlinear, state-dependent structure in cryptocurrency risk pricing—distinct from traditional equities—highlighting regime-switching asymmetries in investor risk compensation.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Game Theory and Economic Paradigms: Behavioral Game Theory
• Machine Learning: Kernel Methods

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Security and Privacy: Cryptocurrency and smart contracts
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

Based on options and realized returns, we analyze risk premia in the Bitcoin market through the lens of the Pricing Kernel (PK). We identify that: 1) The projected PK into Bitcoin returns is W-shaped and steep in the negative returns region; 2) Negative Bitcoin returns account for 33% of the total Bitcoin index premium (BP) in contrast to 70% of S&P500 equity premium explained by negative returns. Applying a novel clustering algorithm to the collection of estimated Bitcoin risk-neutral densities, we find that risk premia vary over time as a function of two distinct market volatility regimes. In the low-volatility regime, the PK projection is steeper for negative returns. It has a more pronounced W-shape than the unconditional one, implying particularly high BP for both extreme positive and negative returns and a high Variance Risk Premium (VRP). In high-volatility states, the BP attributable to positive and negative returns is more balanced, and the VRP is lower. Overall, Bitcoin investors are more worried about variance and downside risk in low-volatility states.

Problem

• Analyze Bitcoin's higher volatility and variance risk premium vs S&P 500
• Decompose Bitcoin return premium across different return state regions
• Identify time-varying Bitcoin risk premia linked to volatility regimes

Innovation

• Decomposing return premium into state space regions
• Applying clustering algorithm to risk-neutral densities
• Analyzing risk premia across volatility regimes