Super-replication of European Options with Convex Payoff under Proportional Transaction Costs

Abstract

The paper examines the super-replication of contingent claims in a discrete time financial market with proportional transaction costs. The sole assumption on stock price dynamics is that the returns are bounded. The class of path-dependent European options with nonnegative convex payoff functions is considered. It is proved that the pricing of this type of options can be studied through the pricing of a suitable binomial model. As a consequence, it is shown that the pricing algorithm, which is essentially a dynamic programming procedure on a tree, can be used when the set of possible scenarios is not finite.

Keywords

• super-replication
• transaction costs
• model uncertainty
• European options