• 응용통계연구
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• 제25권1호
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• pp.55-66
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• 2012

블랙-숄즈 모형이 실제 기초자산의 움직임을 반영하지 못한다는 사실이 실증연구에 의하여 밝혀진 이후 기초자산의 움직임을 레비확률과정을 이용하여 모형화한 옵션가격결정 모형들이 그 대안 중 하나로 연구되어 왔다. 본 논문에서는 블랙-숄즈 모형의 대안으로 제시된 레비모형 중 Variance Gamma 모형이 국내 주식시장에서의 기초자산의 움직임을 블랙-숄즈 모형보다 충실히 재현해내는지 알아보고자 한다. 이를 위하여 Madan 등 (1998)의 연구에서와 같이 로그수익률의 확률밀도함수와 옵션 가격 결정식을 바탕으로 KOSPI 200자료를 이용하여 모수를 추정하고 우도비 검정을 실시하였다. 또한, 옵션 가격을 추정한 후 모형 간의 비교를 위하여 다양한 통계량을 계산하고, 회귀분석을 통하여 변동성 스마일 현상이 교정되는지를 살펴보았다. 연구결과로부터 Variance Gamma 모형 하에서 추정된 옵션 가격이 블랙-숄즈 모형 하에서 추정된 그것보다 더 시장가격과 가까우나, 이 모형도 변동성 스마일 현상을 해결해주지는 못함을 확인할 수 있었다.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.769-784
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• 2013

We consider the modulus-based successive overrelaxation method for the linear complementarity problems from the discretization of Black-Scholes American options model. The $H_+$-matrix property of the system matrix discretized from American option pricing which guarantees the convergence of the proposed method for the linear complementarity problem is analyzed. Numerical experiments confirm the theoretical analysis, and further show that the modulus-based successive overrelaxation method is superior to the classical projected successive overrelaxation method with optimal parameter.

• 산업경영시스템학회지
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• 제45권4호
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• pp.21-30
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• 2022

To mitigate the environmental impacts of the energy sector, the government of South Korea has made a continuous effort to facilitate the development and commercialization of renewable energy. As a result, the efficiency of renewable energy plants is not a consideration in the potential site selection process. To contribute to the overall sustainability of this increasingly important sector, this study utilizes the Black-Scholes model to evaluate the economic value of potential sites for off-site wind farms, while analyzing the environmental mitigation of these potential sites in terms of carbon emission reduction. In order to incorporate the importance of flexibility and uncertainty factors in the evaluation process, this study has developed a site evaluation model focused on system dynamics and real option approaches that compares the expected revenue and expected cost during the life cycle of off-site wind farm sites. Using sensitivity analysis, this study further investigates two uncertainty factors (namely, investment cost and wind energy production) on the economic value and carbon emission reduction of potential wind farm locations.

• 대한수학회보
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• 제51권4호
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• pp.1087-1100
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• 2014

We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권1호
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• pp.43-50
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• 2020

We investigate the domain of influence of the local volatility function on the solutions of the general Black-Scholes model. First, we generate the sample paths of underlying asset using the Monte Carlo simulation. Next, we define the inner and outer domains to find the effective volatility region. To confirm the effect of the inner domain, we use the root mean square error for the European call option prices, and then change the values of volatility in the proposed domain. The computational experiments confirm that there is an effective region which dominates the option pricing.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권2호
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• pp.121-137
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• 2022

In this paper, we investigate an efficient hybrid method for solving two-asset time fractional Black-Scholes partial differential equations. The proposed method is based on the Crank-Nicolson the radial basis functions methods. We show that, this method is convergent and we obtain good approximations for solution of our problems. The numerical results show high accuracy of the proposed method without needing high computational cost.

• Communications for Statistical Applications and Methods
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• 제14권2호
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• pp.459-479
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• 2007

Theories related to financial market has received big attention from the statistics community. However, not many courses on the topic are provided in statistics departments. Because the financial theories are entangled with many complicated mathematical and physical theories as well as ambiguously stated financial terminologies. Based on our experience on the topic, we try to explain the rather complicated terminologies and theories with easy-to-understand words. This paper will briefly cover the topics of basic terminologies of derivatives, Black-Scholes pricing idea, and related basic mathematical terminologies.

• Journal of applied mathematics & informatics
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• 제2권2호
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• pp.47-52
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• 1995

in this paper we reduce the trading strategy of discounted security model to trading strategy of original model

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권4호
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• pp.249-273
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• 2010

Often in practice, the implied volatility of an option is calculated to find the option price tomorrow or the prices of, nearby' options. To show that one does not need to adhere to the Black- Scholes formula in this scheme, Figlewski has provided a new pricing formula and has shown that his, alternating passive model' performs as well as the Black-Scholes formula [8]. The Figlewski model was modified by Henderson et al. so that the formula would have no static arbitrage [10]. In this paper, we show how to construct a huge class of such static no arbitrage pricing functions, making use of distortions, coherent risk measures and the pricing theory in incomplete markets by Carr et al. [4]. Through this construction, we provide a more elaborate static no arbitrage pricing formula than Black-Sholes in the above scheme. Moreover, using our pricing formula, we find a volatility curve which fits with striking accuracy the synthetic data used by Henderson et al. [10].

• 재무관리논총
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• 제3권1호
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• pp.213-231
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• 1996

In this study we conduct a specification test of at-the-money option volatility. Results show that the implied volatility estimate recovered from the Black-Scholes European option pricing model is nearly indistinguishable from the implied volatility estimate obtained from the Barone-Adesi and Whaley's American option pricing model. This study also investigates whether the use of Black-Scholes implied volatility estimates in American put pricing model significantly affect the prediction the prediction of American put option prices. Results show that, at long as the possibility of early exercise is carefully controlled in calculation of implied volatilities prediction of American put prices is not significantly distorted. This suggests that at-the-money option implied volatility estimates are robust across option pricing model.