An examination of alternative option hedging strategies in the presence of transaction costs

Abstract

Substantial progress has been made in developing option hedging models that account for transaction costs. Previous analyses of option hedging strategies in the presence of transaction costs use a Monte Carlo simulation framework in conjunction with a mean variance rule to compare different strategies. These studies being based on simulated stock price data are essentially theoretical tests. It is not known, however, how various proposed hedging strategies compare in terms of hedging precision and transaction costs when tested using actual market data. In addition, the mean variance rule is subject to certain well-known restrictive assumptions.

This thesis aims to fill two gaps in the literature, by: (1) using actual market data to examine hedging performance, and (2) using a stochastic dominance rule as an alternative hedging performance measure. I undertake two studies. The first compares hedging strategies using Monte Carlo simulation together with mean variance and stochastic dominance criteria. Simulation allows us to study the consistency of the hedging outcomes determined by criteria rules in a controlled environment. The second study is a comprehensive empirical investigation of the merits of competing option hedging strategies with transaction costs, using S&P 500 index options. Both studies examine the hedging performance of the delta-neutral hedge. Given the widely documented volatility risk in empirical data, I further supplement the empirical study with a delta–vega-neutral hedge.

Consistent with the literature, the Monte Carlo simulation demonstrates that move-based strategies are superior to time-based strategies. In contrast, empirical testing shows time-based strategies, in particular the Black-Scholes discrete time hedging strategy, are the optimal hedging strategies. Empirically, I find that a delta-neutral hedge is sufficient for a hedger to attain the optimal tradeoff between hedging precision and transaction costs paid if the hedger is using time-based strategies. I further demonstrate that a hedger can save a substantial amount of transaction costs by simply switching from a move-based strategy to a time-based strategy. A hedger is able to save an average 46% of the transaction costs associated with a poorly performing hedging strategy by simply switching to the optimal hedging strategy. I also show that mean variance and stochastic dominance comparisons are not always mutually consistent with each other; however, the differences are usually small. The rank of each strategy under either rule is highly dependent on the characteristics of the empirical distribution of the net hedging error. I also show that a stochastic dominance test provides a precise ranking of hedging performance for each hedging strategy only when there are strong dominance relationships among the strategies, that is, when the empirical density functions of net hedging error for each of the strategies are sufficiently different. The comparisons presented in my study strengthen the confidence in the mean variance rule as a performance measure in assessing hedging outcomes in the presence of transaction costs. The findings of my thesis will assist financial institutions in making informed hedging decisions when transaction costs are taken into consideration.