Coins with benefits: On existence, pricing kernel and risk premium of cryptocurrencies

Cryptocurrencies come with benefits, such as anonymity of payments and positive network effects of user adoption, and transaction risks including unconfirmed transactions, hacks, and frauds. They compete with central-bank-regulated money but consumers may prefer one currency over the other. In our arbitrage-free world utility from consumption depends on benefits, which are governed by distinct stochastic processes, implying incomplete markets and distinct pricing kernels. We characterize the cryptocurrency kernels, evaluate the otherwise unobservable benefits, and show their contribution to pricing. The model explains both the co-existence of the two currencies and the high volatility of the cryptocurrency price.