Simulations of transaction costs and optimal rehedging

Abstract

This paper addresses the issue of hedging options under proportional transaction costs. The Black-Scholes environment assumes frictionless markets in which one can replicate the option payoff exactly by continuous rehedging. However, when transaction costs are involved, frequent rehedging results in the accumulation of transaction costs. Conversely, infrequent hedging results in replication errors. This document attempts to evaluate several rehedging strategies by Monte Carlo simulations. The simulations are constructed so that hedging errors and transaction costs are separated permitting the relative trade-offs to be inspected. Results show that an analytic approximation to a utility maximization approach is both effective and simple to implement. The strategy results in the requirement to hedge to within a dynamic band around the Black-Scholes delta. The band is a function of the option's gamma.

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