On fair designs of cross‐chain exchange for cryptocurrencies via Monte Carlo simulation

Cryptocurrency is one of the earliest and the most successful applications of blockchain, and it utilizes the distributed ledger, which is a commonly used technique in blockchain, to make a decentralized transaction within the blockchain of a cryptocurrency. However, how to make a decentralized transaction of cryptocurrencies between parties on different blockchains, that is, the cross‐chain exchange, is not well‐studied. In this paper, we develop a new method to make cross‐chain exchanges based on the classical atomic swap. We first study the optionality embedded into the atomic swap and propose to add a premium into the atomic swap, and then design a new procedure with the premium to guarantee the fairness of the cross‐chain exchange. We also provide an algorithm based on the least‐squares Monte Carlo method to estimate the premium and analyze the convergence of the algorithm. Moreover, we study the cross‐chain exchange with margin trading. We propose an adapted exchange procedure to make a fair cross‐chain exchange and an algorithm to estimate the fair premium under the margin trading. Numerical experiments are provided to show the effectiveness of the algorithms.