Computation of arbitrage in frictional bond markets

  • Authors:

  • Mao-cheng Cai;Xiaotie Deng;Zhongfei Li

  • Affiliations:

  • Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong;Department of Finance, Lingnan (University) College, Sun Yat-Sen University, Guangzhou, China

  • Venue:
  • Theoretical Computer Science - Algorithmic applications in management
  • Year:
  • 2006

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Abstract

In this paper we study the computational problem of arbitrage in a frictional market with a finite number of bonds and finite and discrete times to maturity. Types of frictions under consideration include fixed and proportional transaction costs, bid-ask spreads, taxes, and upper bounds on the number of units for transaction. We develop a necessary and sufficient condition for the existence of arbitrage. In addition, we obtain some negative result on computational difficulty in general for arbitrage under those frictions: it is NP-complete to identify whether there exists a cash-and-carry arbitrage transaction and it is NP-hard to find an optimal cash-and-carry arbitrage transaction.