Nikkei225 옵션시장의 가격결정커널에 관한 연구

류두진 ( Doo Jin Ryu ) 한국경영공학회 2012 한국경영공학회지 Vol.17 No.2

This study examines the pricing kernels implied by the Nikkei225 index and option prices. Following Rosenberg and Engle(2002), based on the two specifications of the pricing kernels (one is the power pricing kernel and another is the polynomial pricing kernel), we estimate the empirical pricing kernels that successfully explain the price dynamics of the Nikkei225 options. We find some interesting results in the Japanese financial market. First, the power pricing kernel generally decreases with the underlying Nikkei225 index returns, which shows stark contrasts with the results in the S&P500 (U.S.) options market. Second, the time-varying pricing kernels generally outperform the time-invariant pricing kernels in explaining the dynamics of the Nikkei225 option prices, but this does not hold when pricing ITM options which are not actively traded. Third, the (time-varying) polynomial pricing kernel, which has more complicate and flexible functional structure than the (time-varying) power pricing kernel, shows better pricing performance. Considering that there is little research on the Nikkei225 options and there is not a single published article that investigates the pricing kernels in the Japanese options market, this study can be a stepping stone for the future research.

Pricing Kernel-Based Option Valuation Approach : A New Perspective

Doojin Ryu 한국재무학회 2011 한국재무학회 학술대회 Vol.2011 No.09

This study examines the empirical performance of three model-based option valuation approaches in the KOSPI200 options market. We evaluate the in-sample pricing, out-of-sample pricing and hedging performance of the approaches based on the specification of option pricing models directly (a pricing model-based approach), on the pricing kernels implied by the option pricing models (an implied pricing kernel-based approach), and on parametric pricing kernels which are independently structured to have their own explicit functional forms (a parametric pricing kernel-based approach). Two option pricing models, a GARCH option pricing model and a Black-Scholes (BS) option pricing model, and their implied pricing kernels are analyzed and two parametric pricing kernel specifications suggested by Rosenberg and Engle (2002) are compared in a unified framework which extends the GARCH process of Duan (1995) to reflect the dynamics of asymmetric volatility. We find that the empirical performance of the approaches related to the GARCH and Black-Scholes option pricing models is moderately improved when we estimate the structural parameters using options data (options-based estimation) compared to the model performances when estimating the parameters using only a time-series of underlying returns data (underlying returns-based estimation). With the estimates under the underlying returns-based estimation, the pricing modelbased option valuation approach outperforms the implied pricing kernel-based option valuation approach for both the GARCH and BS option pricing models. However, with the estimates under the options-based estimation, this relationship is reversed in pricing OTM options in the case of the GARCH option pricing model. Although the BS option pricing model is generally the worst performer with the estimates under the underlying returns-based estimation, it yields better performance for pricing ITM options and similar performance for hedging compared to the GARCH option pricing model with the estimates under the options-based estimation. The option valuation approach based on the parametric pricing kernel of which functional form is a Chebyshev polynomial performs best out of all approaches and methods considered in this study

Pricing Kernel-Based Option Valuation Approach: A New Perspective

류두진 ( Doo Jin Ryu ) 한국금융공학회 2012 한국금융공학회 학술발표회 Vol.2012 No.-

This study examines the empirical performance of three model-based option valuation approaches in the KOSPI200 options market. We evaluate the in-sample pricing, out-of-sample pricing and hedging performance of the approaches based on the specification of option pricing models directly (a pricing model-based approach), on the pricing kernels implied by the option pricing models (an implied pricing kernel-based approach), and on parametric pricing kernels which are independently structured to have their own explicit functional forms (a parametric pricing kernel-based approach). Two option pricing models, a GARCH option pricing model and a Black-Scholes (BS) option pricing model, and their implied pricing kernels are analyzed and two parametric pricing kernel specifications suggested by Rosenberg and Engle (2002) are compared in a unified framework which extends the GARCH process of Duan (1995) to reflect the dynamics of asymmetric volatility. We find that the empirical performance of the approaches related to the GARCH and Black-Scholes option pricing models is moderately improved when we estimate the structural parameters using options data (options-based estimation) compared to the model performances when estimating the parameters using only a time-series of underlying returns data (underlying returns-based estimation). With the estimates under the underlying returns-based estimation, the pricing modelbased option valuation approach outperforms the implied pricing kernel-based option valuation approach for both the GARCH and BS option pricing models. However, with the estimates under the options-based estimation, this relationship is reversed in pricing OTM options in the case of the GARCH option pricing model. Although the BS option pricing model is generally the worst performer with the estimates under the underlying returns-based estimation, it yields better performance for pricing ITM options and similar performance for hedging compared to the GARCH option pricing model with the estimates under the options-based estimation. The option valuation approach based on the parametric pricing kernel of which functional form is a Chebyshev polynomial performs best out of all approaches and methods considered in this study.

An Empirical Comparison of Option Valuation Approaches: The Case of KOSPI 200 Options

류두진 ( Doo Jin Ryu ) 한국금융공학회 2010 한국금융공학회 학술발표회 Vol.2010 No.2

This paper examines the empirical performance of two option valuation approaches: the pricing model-based option valuation approach, which is based on the direct specification of the option pricing models, and the implied pricing kernel-based option valuation approach, which is based on pricing kernels implied by option pricing models under the unified GARCH framework. In terms of parameter estimates obtained from the underlying returns-based estimation, the pricing model-based approach always outperforms the implied pricing kernel-based approach. However, in terms of parameter estimates obtained from the option-based estimation, the implied pricing kernel-based approach outperforms the pricing modelbased approach in pricing OTM options in the case of the GARCH option pricing model, and both of the option valuation approaches supported by the Black-Scholes option pricing model, which are generally poor performers, perform better than those option valuation approaches supported by the GARCH option pricing model in pricing ITM options and show similar performance in hedging.

가격결정핵에 기초한 기초자산의 로그노말분포와 정규분표에 의한 B-S의 OPM유도

구본열 한국기업경영학회 2008 기업경영연구 Vol.15 No.3

본 연구는 유럽식 콜옵션 가격결정의 유도과정에 대하여 기존의 연구와는 달리 재무론의 가격결정이론에 핵심적인 역할을 하는 가격결정핵을 옵션이론에 적용시켜 새롭게 B-S의 OPM을 유도하는 방법에 대하여 살펴보고자 하였다. 이를 위하여 가격결정핵으로부터 선도가격결정핵과 자산고유-가격결정핵의 개념을 도입하였다. Poon-Stapleton(2005)은 전통적인 유도방법에 따라 주어진 가정하에 B-S OPM을 두 가지의 방법으로 유도한 Brennan(1979)의 연구에 기반을 두고 있다. 그들은 Brennan의 가정을 완화함과 동시에 가격결정핵의 개념을 도입하여 두 가지 방법의 B-S OPM을 유도하는 방법을 제시하였다. 첫 번째는 기초자산이 로그노말분포를 하고 자산고유-가격결정핵이 멱함수를 가지는 경우이고, 두 번째는 기초자산이 정규분포를 하고 선도가격결정핵이 로그노말분포를 가정하는 경우이다. 본 연구는 이와 같이 Brennan에 의해 제시된 두 가지 방법의 B-S OPM의 유도과정에 대하여 가격결정핵에 근거하여 유도한 Poon-Stapleton의 연구에 기초를 두고 있다. 따라서 본 연구는 가격결정핵에 근거하여 B-S의 OPM을 유도하기 때문에 비교적 최근의 이론을 적용한 새로운 유도방법을 시도한 점과 국내에 처음으로 가격결정핵이론에 근거하여 B-S OPM을 유도할 수 있음을 소개하는 점에서 의의가 크다고 하겠다. 그리고 Poon-Stapleton의 유도과정과 달리 선도가격결정핵에 대한 독자의 이해도를 높이기 위하여 재무론에 충실하도록 체계적이고 분석적으로 모형을 유도하였다. 더구나 두 번째 방법의 B-S의 OPM 유도과정에서 Poon-Stapleton의 연구에 오류가 있음이 발견되어 독자적으로 이들의 오류부분을 수정하여 B-S의 OPM을 유도한 결과, Brennan(1979)과 Krouse(1986)의 연구와 일치함으로써 본 연구의 유도과정이 옳음을 확인하였다 We use the one-period complete markets model to derive the B-S OPM. We show two derivation methodologies depend on the underlying asset’s distributions and in particular, on the shapes of the pricing kernel which sub-classifies the spot pricing kernel, the forward pricing kernel and the asset-specific kernel. Fisrt, we derived a model of contingent claims prices, where the underlying asset has a lognormal distribution, and the asset-specific pricing kernel has power function which has constant elasticity. These assumptions are sufficient to establish the B-S OPM for the prices of European-style options. Second, then we extended the analysis to contingent claims on the underlying asset with normal distribution and the forward pricing kernel is lognormal. These assumptions are also able to derive the B-S OPM for the prices of European-style options.

ELW 발행이 주가와 거래량에 미치는 효과

고봉찬 ( Bong Chan Kho ),김진우 ( Jin Woo Kim ) 한국파생상품학회(구 한국선물학회) 2016 선물연구 Vol.24 No.1

옵션가격결정에 관한 Black and Scholes(1973)모형에 의하면 완전시장 하에서 옵션은 기초자산과 무위험자산으로 완전 복제가 가능한 중복자산이므로 옵션의 거래가 기초자산 가격에 영향을 미치지 못하게 된다. 그러나 현실의 불완전시장 하에서 옵션의 거래가 기초자산 가격에 영향을 미치게 된다는 결과는 기존 연구들에 의해 잘 알려져 있다. 따라서 본 연구는 옵션과 경제적 기능이 동일한 국내 ELW의 발행이 실제 기초자산의 가격과 거래량에 어떠한 영향을 미치는지 분석하고, 이러한 영향이 증권시장전체의 완전성에 기여하는 방향으로 나타나는지를 검증하고자 한다. 이를 위하여 2005년 12월부터 2011년 8월까지 기초자산이 개별주식인 ELW의 일별거래자료를 대상으로 분석을 수행하였으며, 분석결과는 다음과 같다. 먼저 ELW 상장일 전후 ±15일의 사건기간 동안 기초자산 주식의 가격과 거래량은 모두 유의하게 증가하는 것으로 나타났으며, 해당 주식수익률의 변동성(총위험)은 감소하나 베타(체계적 위험)는 불변인 것으로 나타남으로써 기존의 옵션에 대한 연구결과와 일치하고 있다. 이처럼 ELW 발행이 기초자산 주식의 가격과 거래량 및 변동성에 유의한 효과를 미친다는 결과는 현재 증권시장이 불완전하다는 것을 시사하는 것이며, 이러한 효과를 통해 증권시장이 더 완전해지는 것인지를 검증할 필요성이 제기된다. 이에 대한 검증결과, 자산가격결정에 필요한 가격커널을 복제하는데 있어서 기초자산과 무위험자산만으로 충분치 않으며 ELW의 존재가 유의하게 필요한 것으로 나타나서 ELW가 국내증권시장의 완전성을 증대시키는데 기여하는 유용한 금융자산임을 확인하였다. The option pricing model of Black and Scholes (1973) shows that an option contract is redundant in a complete market as it can be completely replicated by its underlying assets and risk free assets. However, in a real world of incomplete markets, many studies have shown that option contracts are not redundant and can affect prices and trade volume of underlying assets as they contribute to the market completeness. Thus, this paper examines whether this holds for ELWs (Equity-Linked Warrants) in Korean stock market, which are well known to have the same function as option contracts. To do this, we analyze the effects of ELW listings on underlying stocks’ prices, trade volume, and volatilities, and test whether ELWs contribute to market completeness. Using the daily trading data of 5,799 ELWs on individual stocks from December 2005 to September 2011, we find that underlying stocks show significantly positive cumulative abnormal returns (CAARs) and abnormal trade volume after ELW listing dates, implying that the ELW listing affects significantly positive effects on prices and trade volume of underlying stocks. The volatility of underlying stocks is significantly decreasing after the ELW listing. The systematic risk measured as beta, however, does not change over the event window. This result indicates that the decrease in volatility of underlying stocks comes from the decrease of unsystematic risks, and the correlations between returns of market index and underlying stocks are increasing after the ELW listing. The result that ELW listing can have significant effects on the underlying market implies that current stock market is incomplete, and thus, it is natural to ask whether ELWs can contribute to market completeness. Using the method suggested by Buraschi and Jackwerth (2001), we examine whether ELWs are necessary to replicate the pricing kernel used in asset pricing. We select risk-free asset, underlying stock and ELW as reference assets to replicate the pricing kernel, and find that the pricing kernel cannot be replicated completely without ELWs. This result implies that ELWs are not redundant financial assets and are necessary to increase the market completeness in Korean stock market.

글로벌 금융위기 이후 한국 주식유통시장의 위험가격에 관한 연구

손경우,유원석 한국유통과학회 2015 유통과학연구 Vol.13 No.5

Purpose – The purpose of this study is to investigate risk price implied from the pricing kernel of Korean stock distribution market. Recently, it is considered that the quantitative easing programs of major developed countries are contributing to a reduction in global uncertainty caused by the 2007~2009 financial crisis. If true, the risk premium as compensation for global systemic risk or economic uncertainty should show a decrease. We examine whether the risk price in the Korean stock distribution market has declined in recent years, and attempt to provide practical implications for investors to manage their portfolios more efficiently, as well as academic implications. Research design, data and methodology – To estimate the risk price, we adopt a non-parametric method; the minimum norm pricing kernel method under the LOP (Law of One Price) constraint. For the estimation, we use 17 industry sorted portfolios provided by the KRX (Korea Exchange). Additionally, the monthly returns of the 17 industry sorted portfolios, from July 2000 to June 2014, are utilized as data samples. We set 120 months (10 years) as the estimation window, and estimate the risk prices from July 2010 to June 2014 by month. Moreover, we analyze correlation between any of the two industry portfolios within the 17 industry portfolios to suggest further economic implications of the risk price we estimate. Results – According to our results, the risk price in the Korean stock distribution market shows a decline over the period of July 2010 to June 2014 with statistical significance. During the period of the declining risk price, the average correlation level between any of the two industry portfolios also shows a decrease, whereas the standard deviation of the aver-age correlation shows an increase. The results imply that the amount of systematic risk in the Korea stock distribution market has decreased, whereas the amount of industry-specific risk has increased. It is one of the well known empirical results that correlation and uncertainty are positively correlated, therefore, the declining correlation may be the result of decreased global economic uncertainty. Meanwhile, less asset correlation enables investors to build portfolios with less systematic risk, therefore the investors require lower risk premiums for the efficient portfolio, resulting in the declining risk price. Conclusions – Our results may provide evidence of reduction in global systemic risk or economic uncertainty in the Korean stock distribution market. However, to defend the argument, further analysis should be done. For instance, the change of global uncertainty could be measured with funding costs in the global money market; subsequently, the relation between global uncertainty and the price of risk might be directly observable. In addition, as time goes by, observations of the risk price could be extended, enabling us to confirm the relation between the global uncertainty and the effect of quantitative easing. These topics are beyond our scope here, therefore we reserve them for future research.

The Role of the Variance Premium in GARCH Option Pricing Models

Suk Joon Byun,Byoung-Hyun Jeon,Byungsun Min,Sun-Joong Yoon 한국재무학회 2014 한국재무학회 학술대회 Vol.2014 No.05

We develop a discrete-time option pricing model using a variance-dependent pricing kernel of Christoffersen, Heston and Jacobs (2013) under an economic framework allowing for dynamic volatility and dynamic jump intensity. Using this model, we examine the role of the variance premium and jump risk premium in explaining S&P 500 index option returns. Our results stress the importance of the variance premium in explaining the stylized characteristics of index option returns, including short-term option returns, which are insufficiently explained by extant option pricing models. In particular, the variance premium can explain both 1-month holding period returns of 2-month maturity straddles, which are significantly negative, and call returns, which decrease according to moneyness. Even though the jump risk premium emphasized in the previous literature is able to well fit the option prices, it does not improve the explanatory power for the above two stylized option returns. The outperformance of the variance premium stems from its ability to capture the wedge between physical and risk-neutral volatilities.

가우시안 커널 네트워크를 이용한 원유가격예측

김동민(Dongmin Kim),신성국(Sung Kuk Shyn) 한국정보기술학회 2020 Proceedings of KIIT Conference Vol.2020 No.10

원유가격은 그 중요성에도 불구하고 높은 변동성으로 인하여 가격 예측의 어려움이 많다. 이에 우리는 원유시장의 변동성에 알맞은 가우시안 커널 네트워크를 이용한 원유가격예측을 진행하고자 한다. 가우시안 커널네트워크는 커널의 개수, 데이터 간격 등 연구자의 직관에 의존한 다양한 실험변수들을 체계적으로 설정하고, 가우시안 함수를 바탕으로 학습을 최적화 시키는 장점을 가지고 있다. 위 논문에서는 일 분석, 주 분석, 월 분석의 세 가지 큰 틀로 연구를 진행하였다. 각 데이터별로 가우시안 커널 네트워크를 구성하고 데이터 부족으로 인한 과적합 및 정확도 저하의 현상은 일 데이터의 재가공을 통해 정확도를 향상시킨다. Although the importance of crude oil price is getting higher, its prediction is a very difficult task due to the highly volatile nature in oil market. Therefore our research conducted crude oil price prediction task based on Gaussian Kernel Network. Gaussian Kernel Network can systematically set its hyperparameters that were previously set based on researchers’ intuition such as kernel numbers, intervals of dataset, etc. Furthermore, it maximizes its learning capacity by setting models’ kernel based on Gaussian function. Our work analyzes daily, weekly, and monthly fluctuations of crude oil price respectively. Gaussian Kernel Network is established for each dataset and the problems of overfitting and low-precision are resolved using data augmentation techniques.

Valuation of Exotic Options under Lévy Processes : A Pricing Kernel Approach

조승모 한양대학교 경제연구소 2011 경제연구 Vol.32 No.1

In this paper, we show that Gerber and Shiu (1994)’s method of option pricing under Lévy processes using the Esscher transform can be extended to pricing exotic options such as compound options, chooser options, extendible options, and reset strike options. Here, rather than following the original approach by Gerber and Shiu (1994), we slightly modify the pricing method from the risk-neutral valuation to the pricing kernel approach for better intuition and easier mathematical derivation.