베리어옵션의 헤지

Abstract

This study investigates the hedging effectiveness of and strategies for barrier options, which are widely used to design the payoff structure of exotic derivative products such as KIKO (knock-In, knock-Out) options and ELWs (equity-linked warrants). Although investors have traditionally focused on pricing and hedging exchange-traded derivatives, such as index futures and plain-vanilla options, recently, not only professional investors but also individual investors and small or venture firms have become increasingly interested in more complicated derivative assets in OTC (over-the-counter) markets. However, as the recent financial crisis and its effect on many small firms who have declared bankruptcy as a result of aggressively investing in KIKO options or other complicated derivative products indicate, there is a need for carefully evaluating such new derivative products and acquiring the necessary financial knowledge for adequately managing them. Further, there should be more serious research on and wider discussion of the ways in which various risks from such new financial products could be hedged and managed. Although a large number of studies examine the empirical performance of option pricing models and analyze the pricing ability and hedging effectiveness of such models for plain-vanilla options, few address the issue of hedging barrier options. In this regard, this study focuses on the issue of hedging barrier options by considering various economic situations which are generated by Monte Carlo simulation method. More specifically, this study examines the performance of the classical dynamic hedging (delta hedging) and analyzes the static hedging approaches proposed by Derman et al.(1994). To the best of the author’s knowledge, this paper is the first to consider the hedging effectiveness of barrier options. This study contributes to the previous literature as follows. The study 1) considers five cases for the analysis of the underlying stock process by varying simulation parameters, 2) examines the performance of delta hedging across these cases, and 3) compares the effectiveness of delta hedging with that of static hedging for each case. These five cases are as follows: 1) when the economic environment is normal, 2) when the underlying volatility is high, 3) when the underlying stock price approaches the barrier, 4) when there are no transaction costs, and 5) when the drift term for the underlying process has a negative value. For each case, this study evaluates the performance of delta hedging across portfolio rebalancing periods and examines the performance of static hedging across several types of hedging instruments (e.g., plain-vanilla options with different strike prices and maturity dates). The empirical results indicate that whereas static hedging is relatively stable and effective, dynamic hedging is unstable and ineffective, particularly when the volatility of the underlying stock price is high (Case 2) or when the price of the underlying stock approaches the barrier (Case 3). The results also imply that static hedging performs even better when (hypothetical) longer-term options are used together with currently traded KOSPI 200 options and suggest some ways in which barrier options could be priced through the static hedging approach.