베리어옵션의 헤지 (Hedging Barrier Options)

서지정보

· 발행기관 : 한국기업경영학회
· 수록지 정보 : 기업경영연구 / 18권 / 1호 / 39 ~ 63페이지
· 저자명 : 류두진

초록

본 연구는 최근 들어 기업이 투자 및 위험관리의 목적으로 관심을 갖게 된 KIKO와 같은 장외파생상품의 수익구조설계에 널리 활용되는 베리어옵션의 헤지전략에 대하여 살펴본다. 구체적으로, Knock- In 혹은 Knock-Out형태의 수익구조를 갖는 이색옵션인 베리어옵션에 대하여, 동적헤지의 대표적인 헤지방법인 델타헤지와 Derman, Ergener, and Kani(1994)가 제시한 정적헤지의 성과를 모의실험방법을 사용하여 조사해본다. 구체적으로, 극단적인 경우를 포함한 다양한 경제상황을 묘사할 수 있도록 기초자산의 확률과정의 모수를 변화시키면서 기초자산의 가격경로를 생성하고, 베리어옵션의 이론적인 폐쇄해와 델타값을 유도하여, 재조정주기에 따른 동적헤지의 성과를 비교하였다. 또한, 다양한 기초자산의 확률과정마다, 헤지에 사용되는 표준옵션의 종류와 수를 바꾸어 가면서 정적헤지의 성과를 살펴보았다. 기초자산가격의 변동성이 크거나, 기초자산의 가격이 베리어옵션의 설정된 경계값 근처에서 움직일 때 매우 불안정한 헤지성과를 보인 동적헤지의 경우와는 달리, 정적헤지의 성과는 대체로 안정적이고 유효했으며, 현재 한국거래소에서 거래되는 표준옵션들보다 만기가 긴 옵션들이 활용된다면, 정적헤지의 성과는 더욱 우월해질 것으로 판단된다. 또한 정적헤지의 방법론을 적용하면 베리어옵션과 같은 이색옵션의 적절한 가격결정을 할 수 있을 것으로 기대된다.

영어초록

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.

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