Abstract
Transaction costs of derivative hedging appear in financial markets. This paper considers the problem of delta hedging and the reduction of expected proportional transaction costs. In the literature the expected approximate proportional transaction costs are customarily estimated by the gamma term, usually the largest term of the associated series expansion. However, when options are to expire in a month or few weeks, other terms may become even larger so that more precise estimates are needed. In this paper, different higher-order estimates of proportional transaction costs are analyzed. The problem of the reduction of expected transaction costs is considered. As a result, a suitably adjusted delta is given, for which the expected approximate proportional transaction costs can be reduced. The order of the mean and the variance of the hedging error can be preserved. Several examples are provided.