| Abstract: | 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. |
