Pricing Exotic Derivatives for Cryptocurrency Assets - A Monte Carlo Perspective

23 Pages Posted: 10 Jun 2021

See all articles by Mesias Alfeus

Mesias Alfeus

Department of Statistics and Actuarial Science - Stellenbosch University

Shiam Kannan

Cornell University

Date Written: June 8, 2021

Abstract

In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discretely 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 found 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 cryptocurrencies market is indeed rough.

Suggested Citation

Alfeus, Mesias and Kannan, Shiam, Pricing Exotic Derivatives for Cryptocurrency Assets - A Monte Carlo Perspective (June 8, 2021). Available at SSRN: https://ssrn.com/abstract=3862655 or http://dx.doi.org/10.2139/ssrn.3862655

Mesias Alfeus (Contact Author)

Department of Statistics and Actuarial Science - Stellenbosch University ( email )

Matieland
m
Stellenbosch, 7602
South Africa
0633236629 (Phone)
7405 (Fax)

Shiam Kannan

Cornell University ( email )

Ithaca, NY
United States
9083342916 (Phone)

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