JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Cambridge University Press and University of Washington School of Business Administration are collaborating with JSTOR to digitize, preserve and extend access to The Journal of Financial and Quantitative Analysis. AbstractThis paper analyzes the strategy that minimizes the initial cost of replicating a contingent claim in a market with transactions costs and trading constraints. The linear programming and two-stage backward recursive models developed are applicable to the replication of convex as well as nonconvex payoffs and to a portfolio of options with different maturities. The paper's formulation conveniently accounts for fixed and variable transactions costs, lot size constraints, and position limits on trading. The article shows that in the presence of trading frictions, it is no longer optimal to revise one's portfolio in each period. At the optimum, cash flows in excess of the desired ones may be generated. The optimal policy trades off the curvature of the payoff that is generated against the terminal slack. I. IntroductionThis article investigates the problem of an investor who wishes to replicate a given payoff in an imperfect market. The standard models of option replication and valuation rely on continuous trading but assume the absence of any trading constraints. The market imperfections on which the study focuses are transactions costs1 and restrictions on trading in the form of lot size constraints2 and position limits. These frictions become more significant if one includes the market impact of large orders and the delay in executing trades, especially when trading illiquid securities.3As Figlewski (1989, p. 301) states, "...transactions costs make a substantial difference in the outcome of an options arbitrage, even when done by a market maker."The problem of hedging call and put options in the presence of proportional transactions costs has been eonsidered by Leland (1985), and at the Derivative Securities Symposium at Queen's University for their comments and suggestions. The authors are responsible for any errors. The authors also thank JFQA Referee Phelim Boyle for helpful comments.^oeb (1983) documents that the costs of trading in securities can be significant. 2See Robertson (1990) for information on lot size constraints. 3For a discussion of these issues, see Hasbrouck and Schwartz (1988) and Amihud and Mendelson (1988). 117This content downloaded from 84.

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