Pricing Exotic Derivatives for Cryptocurrency Assets—A Monte Carlo Perspective

In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discreetly monitored window average lookback option, whose monitoring frequencies are randomly selected within the time to maturity, and whose monitoring price is the average asset price in a specified window surrounding the instant. We price these options whose underlying asset is the CCI30 index of various Cryptocurrencies, as opposed to a single cryptocurrency, with the intention of reducing volatility, and thus, the option price. We employ the Normal Inverse Gaussian (NIG) and Rough Fractional Stochastic Volatility (RFSV) models to the cryptocurrency market, and using the Black-Scholes as the benchmark model. In doing so, we intend to capture the extreme characteristics such as jumps and volatility roughness for cryptocurrency price fluctuations. Since there is no availability of a closed-form solution for lookback option prices under these models, we utilize the Monte Carlo simulation for pricing, and augment it using the antithetic method for variance reduction. Finally, we present the simulation results for the lookback options, and compare the prices resulting from using the NIG model, RFSV model with those from the Black-Scholes model. We find that the option price is indeed lower for our proposed window average lookback option, than for a traditional lookback option. We found the Hurst parameter to be H=0.09 which confirms that the cryptocurrency market is indeed rough.