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Despite being described as a medium of exchange, cryptocurrencies do not havethe typical attributes of a medium of exchange. Consequently, cryptocurrenciesare more appropriately described as crypto assets. A common investmentattribute shared by the more than 2,500 crypto assets is that they are highlyvolatile. An investor interested in reducing price volatility of a portfolio ofcrypto assets can do so by constructing an optimal portfolio through standardoptimization techniques that minimize tail risk. Because crypto assets are notbacked by any real assets, forming a hedge to reduce the risk contribution of asingle crypto asset can only be done with another set of similar assets (i.e.,a set of other crypto assets). A major finding of this paper is that cryptoportfolios constructed via optimizations that minimize variance and ConditionalValue at Risk outperform a major stock market index (the S$\&$P 500). As ofthis writing, options in which the underlying is a crypto asset index are nottraded, one of the reasons being that the academic literature has notformulated an acceptable fair pricing model. We offer a fair valuation modelfor crypto asset options based on a dynamic pricing model for the underlyingcrypto assets. The model was carefully backtested and therefore offers areliable model for the underlying crypto assets in the natural world. We thenobtain the valuation of crypto options by passing the natural world to theequivalent martingale measure via the Esscher transform. Because of the absenceof traded crypto options we could not compare the prices obtained from ourvaluation model to market prices. Yet, we can claim that if such options oncrypto assets are introduced, they should follow closely our theoretical pricesafter adjusting for market frictions and design feature nuances.

Modelling Crypto Asset Price Dynamics, Optimal Crypto Portfolio, and Crypto Option Valuation