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"Modelling Crypto Asset Price Dynamics, Optimal Crypto Portfolio, and Crypto Option Valuation"
This study explores crypto asset price dynamics, optimal portfolio construction, and valuation methods for crypto options, providing a comprehensive framework for crypto investment and risk management.

1. Research Objectives

• Identify a multivariate model that best explains crypto return distributions.

• Construct an optimal crypto portfolio by minimizing risk using VaR (Value at Risk) and CVaR (Conditional Value at Risk).

• Develop a pricing model for crypto options based on crypto assets as underlying securities.

2. Research Methodology

Data Source: Collected daily closing prices (July 25, 2017 – July 2, 2019) for seven major cryptocurrencies:

• Bitcoin, Ethereum, XRP, Litecoin, Bitcoin Cash, EOS, Binance Coin.

Price Modeling:

• Applied the ARMA(1,1)-GARCH(1,1) model to capture crypto return volatility.

• Tested various multivariate distributions for joint modeling.

Portfolio Optimization:

• Used Monte Carlo simulations and backtesting to validate strategies.

• Measured portfolio risk using VaR and CVaR.

Crypto Option Valuation:

• Applied Esscher transformation to derive risk-neutral pricing.

• Used Generalized Hyperbolic Distributions for fair value estimation.

3. Key Findings

1) Crypto Portfolio Diversification Can Reduce Risk

• While individual cryptos are highly volatile, a well-diversified portfolio can stabilize returns, sometimes even outperforming traditional stock markets.

• This is similar to mixing volatile chemicals to create stable rocket fuel—proper asset allocation enhances stability.

2) Portfolio Construction: Identifying Risk Contributors and Stabilizers

• Understanding which cryptos reduce risk and which ones increase it is crucial for portfolio construction:

  • Bitcoin (Risk Stabilizer) → Reduces overall portfolio volatility, acting like a buffering agent.

  • EOS (Risk Contributor) → Increases portfolio volatility, akin to adding extra spice to a dish.

• Portfolio Strategy:

  • Allocating more Bitcoin while adjusting EOS exposure can enhance stability without sacrificing returns.

3) CVaR-Based Portfolio Optimization is Most Effective

• Minimizing CVaR (Conditional Value at Risk) results in the most stable long-term performance.

• CVaR considers extreme losses, making it ideal for crypto risk management.

• Investors should focus on how much they might lose in worst-case scenarios, not just average performance.

4) New Valuation Framework for Crypto Options

• Proposed a novel approach to pricing crypto options, crucial for the nascent crypto derivatives market.

• As crypto option markets mature, this framework can guide fair pricing and hedging strategies.

• However, market realities (e.g., liquidity constraints, transaction fees) must also be considered.

Conclusion

This study demonstrates that crypto investing can be stabilized through diversification and risk management, despite its inherent volatility.
It also highlights the potential of crypto options as an emerging asset class, offering hedging opportunities and structured investment products.

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