미니 KOSPI 200 옵션 시장의 최적 옵션가격결정모형

국문 초록 (Abstract)

본 연구는 미니 KOSPI 200 옵션을 대상으로 최적 옵션가격결정모형을 찾는다. 옵션 가격결정모형으로는 Black and Scholes(1973) 모형, Ad-Hoc Black-Scholes 모 형, 확률 변동성(stochastic volatility)과 점프(jumps)를 고려한 모형을 비교한다. 연구 결과 미니 옵션 시장에서는 확률 변동성과 점프를 모두 고려한 모형이 내표본 및 외표본 가격결정에서 가장 우수한 성과를 보였고 헤징 성과에서는 2차항까지 포함 한 Ad-Hoc Black-Scholes 모형의 오차가 가장 작았다. 예측 기간을 1주일로 확장하 고, 월별로 성과를 검증한 경우에도 1일 예측과 일관된 결과를 보였고 각 모형들 간의 성과 차이는 통계적으로 유의하였다. 1차 항만을 고려한 Ad-Hoc Black-Scholes 모형의 가격결정 및 헤징 성과가 가장 우수했던 정규 옵션 시장을 대상으로 한 기존 연구들과 차별화된 결과를 확인하였다.

다국어 초록 (Multilingual Abstract)

Mini KOSPI 200 options are derivatives based on the KOSPI 200 index, just like the regular KOSPI 200 options. While the contract terms, such as expiration dates and trading hours, are identical, mini options are structured to allow smaller investments by reducing the contract size to one-fifth (from a multiplier of 250,000 KRW to 50,000 KRW). This makes them accessible to smaller investors, aiming to increase retail participation. However, the question remains: have mini options successfully attracted retail investors as originally intended? As market data reveals, the share of retail investors in the mini options market is significantly lower than in the regular options market, contrary to the product’s initial purpose. Institutional investors, particularly securities firms, dominate the mini options market, contributing to its low liquidity. As a result, the liquidity premium in mini options leads to higher pricing compared to regular options with the same strike prices and expiration dates. This creates a barrier for retail investors, who generally prefer long positions and are sensitive to price disparities. Therefore, mini options have not achieved their goal of increasing retail participation and are instead primarily traded by institutional investors. The difference in liquidity and the composition of market participants leads to differing price determination mechanisms between mini and regular options. The distinct characteristics of the mini options market suggest that the optimal option pricing models suitable for regular options may not be applicable to mini options. The Black-Scholes (BS) option pricing model, introduced in 1973, has long been a fundamental tool in the options market, but its limitations have led to the development of many alternatives. The BS model, while advantageous for its simplicity and closed-form solution, fails to accurately reflect real-world variables like volatility and risk-free interest rates. Implied volatility, which is calculated based on option prices, tends to vary with strike prices and expiration times, a phenomenon known as the volatility surface, indicating that the BS model does not fully capture market realities. To overcome these limitations, various alternative models have been proposed, including stochastic interest rate models, stochastic volatility models, jump diffusion models, variance gamma models, and regime-switching models that assume sudden changes in volatility. GARCH models that assume conditional heteroscedasticity in the underlying asset are also used. Additionally, the Ad-Hoc Black-Scholes (AHBS) model is popular among market participants for estimating implied volatility using simple regression analysis. Previous research has shown that stochastic volatility models offer the greatest improvement over the BS model. Studies focused on the regular options market found that the AHBS model outperforms more mathematically complex models, including stochastic volatility models, in both pricing accuracy and hedging performance. Given that mini options display characteristics distinct from regular options, it is necessary to question whether the optimal pricing models used for regular options can still be applied effectively. This study aims to identify the optimal option pricing model for the mini KOSPI 200 options market. By comparing in-sample and out-of-sample pricing accuracy and hedging performance, we aim to recommend the most suitable model for participants in the mini options market. The models under consideration include the BS model, the AHBS model, and models that account for stochastic volatility and jumps. Through this comparison, we examine how differences in liquidity and the composition of market participants affect option pricing and hedging. The study suggests that markets with a high proportion of retail investors may favor simpler models like the BS model, while markets dominated by institutional investors might see better performance with more mathematically complex models. Given that the mini options market has a lower proportion of retail investors compared to regular options, it is expected that more sophisticated models that account for stochastic volatility and jumps will outperform simpler models like the BS model. This study provides several contributions to existing research. First, it is the first to explore the optimal options pricing model specifically for the mini KOSPI 200 options market. While mini options share many characteristics with regular options, their smaller contract sizes and different participantcomposition create unique market dynamics. The study shows that institutional investors play a larger role in the mini options market than in the regular options market, and that mini options have lower liquidity. These factors must be considered when selecting the optimal pricing model. Second, this research utilizes long-term data spanning 90 months, from the market’s inception to the present, offering a comprehensive view of the market’s evolution. Most previous studies focused on the early stages of the mini options market, where liquidity was insufficient. By incorporating a longer time frame, this study is able to capture the effects of market maturity and changes in volatility and liquidity over time. The results are as follows. Models that account for both stochastic volatility and jumps show the best performance in both in-sample and out-of-sample pricing tests. In terms of hedging performance, the AHBS model that includes both first-order and second-order strike prices performs the best. However, the differences in hedging performance across models are relatively small. When the forecasting period is extended to one week, the results remain consistent with the one-day forecast. Monthly performance also shows consistency, with statistically significant differences between the models' performance over the entire sample period. Compared to previous studies on the regular options market, which found that simpler AHBS models provided the best pricing and hedging performance, this study reaches different conclusions. The differences in liquidity and participant composition between the mini and regular options markets play a significant role in the selection of the optimal pricing model.

목차 (Table of Contents)

• 요약
• Abstract
• Ⅰ. 서론
• Ⅱ. 옵션가격결정 모형
• 1. Ad-Hoc Black-Scholes 모형
• 2. 확률 변동성과 점프를 가정한 옵션가격결정모형
• Ⅲ. 자료
• Ⅳ. 실증분석
• 1. 내표본 가격결정 성과(In-sample Pricing Performance)
• 2. 외표본 가격결정 성과(Out-of-sample Pricing Performance)
• 3. 헤징 성과(Hedging Performance)
• 4. 강건성 검증(Robustness Check)
• Ⅴ. 결론
• References