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鄭都燮,李仁銓,李相夢,金三銀 한국잠사학회 1989 한국잠사곤충학회지 Vol.31 No.2
Principal component analysis and cluster analysis were performed on the nine quantitative characters of the one hundred and forty eight silkworm genetic stocks. The six major qauantitative characters such as cocoon yield, cocoon weight, cocoon shell weight,cocoon shell percentage, larval period of the 5th instar silkworm, and total larval period showed significantly positive correlation between them. The first three principal components extracted from the initial nine variables by principal component analysis accounted for about eighty percent of original information. The first and second prinicpal components were characterized as factors related to silk productivity, and cocoon productivity, respectively. On the basis of multivariate analysis using city block distance determined from the first three principal components to measure the phenotypic diversity, the one hundred and forty eight silkworm genetic stocks could be clustered into seven varietal groups, and the phenotypic diversity between the varietal groups was partly related to their geographical origins. Among 7 varietal group, group II and IV revealed higher silk and cocoon productivity.
정도섭,이상휘 한국기업경영학회 2013 기업경영연구 Vol.20 No.1
It is well known that the volatility of asset returns is not constant, which has put forth the development of many option models incorporating a stochastic or GARCH process of volatility. Although these option models successfully reduce pricing and hedging errors of the Black-Scholes model, the complexity of the models often discourages market participants to utilize these models in pricing and hedging options. An alternative approach to adjust Black-Scholes model misspecification is to extend Black-Scholes model’s strict distributional assumption by adjusting non-lognormal skewness and kurtosis. This paper examines pricing and hedging performances of a skewness and kurtosis adjusted option model proposed by Jarrow and Rudd when volatility follows a stochastic process. Consistent with the previous research, the results of this study show that the skewness and kurtosis adjusted Jarrow-Rudd model reduces Black-Scholes pricing errors substantially especially for long-term, deep-in-the-money options. For hedging, however, improvements for the Jarrow-Rudd model over the Black-Scholes model are not virtually found. Overall, the study shows Jarrow-Rudd model could be a better alternative for the Black-Scholes model for option pricing but not necessarily for hedging. But considering the fact that Monte Carlo simulations employed in this study may subject to a model risk, the results of this simulation should be taken with caution.
확률적 변동성하에서 변동성 스마일 기법의 옵션 가격 평가
정도섭 한국산업경제학회 2007 산업경제연구 Vol.20 No.3
변동성 스마일 기법(volatility smile technique)은 Black-Scholes 모형으로 시장옵션가격에 내재된 기초자산의 변동성을 구한 다음 옵션의 마니니스(moneyness)에 따라 추정한 변동성을 다시 Black-Scholes 모형에 투입하여 옵션의 가격을 평가하는 기법으로 Black-Scholes 모형의 가격괴리를 보완하기 위하여 옵션 딜러들이 개발한 방법이다. 이 논문에서는 시장참여자들이 선호하는 Black-Scholes 모형과 변동성 스마일 기법이 확률적 변동성하에서의 진실한 옵션가격을 얼마나 잘 평가하는지를 몬테카를로 시뮬레이션으로 살펴보았다. 시뮬레이션 결과, 확률적 변동성으로 비롯되는 Black-Scholes 모형의 가격괴리는 등가격 옵션의 경우 미미한 것으로 나타났다. 그러나 외가격 옵션이나 내가격 옵션의 경우 그리고 변동성 과정의 모수인 ρ와 σ가 0에서 크게 벗어나는 경우, Black-Scholes 모형의 가격괴리는 매우 심각하게 나타났다. 한편, 변동성 스마일 기법은 확률적 변동성으로 비롯되는 Black-Scholes 모형의 가격괴리를 외가격 옵션과 내가격 옵션에서 크게 개선하고 있었다. 시뮬레이션에서 검토된 옵션의 거의 모든 행사가격대와 만기에 있어서 변동성 스마일 기법은 진실한 옵션가격과 매우 근사한 가격을 산출하였고, 변동성 과정 모수인 ρ와 σ가 0에서 벗어나는 경우에도 가격오차율은 그다지 크지 않았다. 이러한 결과는 시장참여자들이 왜 정교한 확률적 변동성 모형의 존재에도 불구하고 보다 간편한 모형인 Black-Scholes 모형이나 변동성 스마일 기법을 압도적으로 선호하는지를 잘 설명하고 있다. The volatility smile method is not a true option pricing model. However, the method is widely used among options professionals in various forms. Essentially, the volatility method accepts market option prices as given and then involves calculating an implied volatility for each observed option price. Using Monte Carlo simulation experiments, this paper examines the pricing performance of the volatility smile technique when the underlying process driving security prices is characterized by a stochastic volatility process. The results of the simulation show that the stochastic volatility induces severe pricing errors of the Black-Scholes option pricing model for deep-in-the-money and deep out-of-the-money options. Such deviations, however, can be significantly reduced by using a relatively simple volatility smile method. This demonstrates why market participants still prefer simple option models to sophisticated option models.
Performances of Simple Option Models When Volatility Changes
정도섭 한국디지털정책학회 2009 디지털융복합연구 Vol.7 No.1
In this study, the pricing performances of alternative simple option models are examined by creating a simulated market environment in which asset prices evolve according to a stochastic volatility process. To do this, option prices fully consistent with Heston[9]'s model are generated. Assuming this prices as market prices, the trading positions utilizing the Black-Scholes[4] model, a semi-parametric Corrado-Su[7] model and an ad-hoc modified Black-Scholes model are evaluated with respect to the true option prices obtained from Heston's stochastic volatility model. The simulation results suggest that both the Corrado-Su model and the modified Black-Scholes model perform well in this simulated world substantially reducing the biases of the Black-Scholes model arising from stochastic volatility. Surprisingly, however, the improvements of the modified Black-Scholes model over the Black-Scholes model are much higher than those of the Corrado-Su model.