• Journal for History of Mathematics
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• v.15 no.3
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• pp.59-64
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• 2002

This paper investigates a history of Fourier Series for the heat equation and how deeply it is related to modern famous three equations, Navier-Stokes equations in fluid dynamics, drift-diffusion equations in semiconductor, and Black-Scholes equation in finance. We also propose improved models for the heat equation with finite propagation speeds.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.185-202
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• 2006

In this paper, using the Black-Scholes analysis, we will derive the partial differential equation of convertible bonds with both non-stochastic and stochastic interest rate. We also find numerical solutions of convertible bonds equation with known interest rate using the finite element method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.175-187
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• 2010

This paper presents the numerical valuation of the two-asset step-down equitylinked securities (ELS) option by using the operator-splitting method (OSM). The ELS is one of the most popular financial options. The value of ELS option can be modeled by a modified Black-Scholes partial differential equation. However, regardless of whether there is a closedform solution, it is difficult and not efficient to evaluate the solution because such a solution would be represented by multiple integrations. Thus, a fast and accurate numerical algorithm is needed to value the price of the ELS option. This paper uses a finite difference method to discretize the governing equation and applies the OSM to solve the resulting discrete equations. The OSM is very robust and accurate in evaluating finite difference discretizations. We provide a detailed numerical algorithm and computational results showing the performance of the method for two underlying asset option pricing problems such as cash-or-nothing and stepdown ELS. Final option value of two-asset step-down ELS is obtained by a weighted average value using probability which is estimated by performing a MC simulation.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.756-763
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• 2005

본 논문에서는 KOSPI200 지수선물의 분 단위 가격 데이터를 이용하여 거래비용을 고려한 옵션 복제 전략들의 성과를 비교하였다. 비교를 위해 사용한 옵션 복제 전략들은 (1)Black-Scholes 델타(delta) 전략, (2)Black-Scholes 델타 한도 전략, (3)Leland 전략, (4)Whalley-Wilmott 전략이다. 각 전략들은 옵션 복제를 위한 기초자산 거래와 관련된 두 가지 질문에 대한 답을 준다. 첫 번째 질문은 거래 시점에 관한 것으로, '언제 거래할 것인가'이고, 두 번째 질문은 거래량에 관한 것으로, '얼마만큼 거래할 것인가'이다. 본 논문에서는 현실적인 KOSPI200 지수선물 거래수수료(거래금액 대비 0.01%) 환경에서 잔존만기 1년인 유럽형 등가격 콜 옵션을 복제하는 경우를 실험하였다. 실험 결과 Leland 전략을 제외한 나머지 세 전략들의 복제 성과가 상대적으로 뛰어난 것으로 나타났다. 그러나 이들 세 전략들 간에는 복제 성과에 대해 뚜렷한 차이를 발견하기 어려웠다. 한편, 복제 종료 시점에서의 복제 손익에 큰 영향을 미치는 요인은 복제 오차(복제 포트폴리오의 만기 가치와 복제 대상 옵션의 만기 현금흐름의 차이)인 것으로 나타난 반면, 복제를 위한 기초자산 거래비용이 복제 종료 시점에서의 복제 손익에 미치는 영향은 적은 것으로 나타났다.

• Korean Management Science Review
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• v.32 no.1
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• pp.1-13
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• 2015

We estimate the option value embedded in reverse mortgages using the framework of European put option. The reverse mortgage is a very useful financial product for senior citizens who own homes but do not have a cash income while it is a high risk one from lender's perspective. One of benefits of the reverse mortgages is that the debt limit is restricted to the scope of the disposition price of the collateralized house, which is considered a put option to borrowers. The put option is evaluated using Black-Scholes model and a sensitive analysis is performed on variables such as discount rate, volatility, and time period. We confirm that the option value of reverse mortgages increases rapidly as the borrowers live longer than their life expectancy. The results of this study can be used to promote the reverse mortgage program more effectively in order to solve the problem of income shortage of the elderly homeowners.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.2
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• pp.712-717
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• 2011

Option issuers generally utilize Dynamic Delta Hedging(DDH) technique to avoid the risk resulting from continuously changing option value. DDH duplicates payoff of option position by adjusting hedge position according to the delta value from Black-Scholes(BS) model in order to maintain risk neutral state. DDH, however, is not able to guarantee optimal hedging performance because of the weaknesses caused by impractical assumptions inherent in BS model. Therefore, this study presents a methodology for dynamic option hedge using artificial neural network(ANN) to enhance hedging performance and show the superiority of the proposed method using various computational experiments.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.1
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• pp.1-8
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• 2021

As a nation experiencing rapid economic growth, South Korea and its government have made a continuous effort toward efficient research investments to achieve transformation of the Korean industry for the fourth industrial revolution. To achieve the maximum effectiveness of the research investments, it is necessary to evaluate its funding's worth and default risk. Thus, incorporating the concepts of the Black-Scholes-Merton model and the Greeks, this study develops a default-risk evaluation model in the foundation of a system dynamics methodology. By utilizing the proposed model, this study estimates the monetary worth and the default risks of research funding in the public and private sectors of Information and Communication technologies, along with the sensitivity of the R&D economic worth of research funding to changes in a given parameter. This study finds that the public sector has more potential than the private sector in terms of monetary worth and that the default risks of three types of research funding are relatively high. Through a sensitivity analysis, the results indicate that uncertainty in volatility, operation period, and a risk-free interest rate has trivial impacts on the monetary worth of research funding, while volatility has large impacts on the default risk among the uncertain factors.

• Clean Technology
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• v.29 no.1
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• pp.59-70
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• 2023

This study aims to introduce a biowaste processing system that uses spent coffee grounds and implement a real options method to evaluate the proposed process. Energy systems based on eco-friendly fuels lack sufficient data, and thus along with conventional approaches, they lack the techno-economic assessment required for great input qualities. On the other hand, real options analysis can estimate the different costs of options, such as continuing or abandoning a project, by considering uncertainties, which can lead to better decision-making. This study investigated the feasibility of a biowaste processing method using spent coffee grounds to produce biofuel and considered three different valuation models, which were the net present value using discounted cash flow, the Black-Scholes and binomial models. The suggested biowaste processing system consumes 200 kg/h of spent coffee grounds. The system utilizes a tilted-slide pyrolysis reactor integrated with a heat exchanger to warm the air, a combustor to generate a primary heat source, and a series of condensers to harness the biofuel. The result of the net present value is South Korean Won (KRW) -225 million, the result of the binomial model is KRW 172 million, and the result of the Black-Scholes model is KRW 1,301 million. These results reveal that a spent coffee ground-related biowaste processing system is worthy of investment from a real options valuation perspective.

• The Korean Journal of Financial Management
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• v.9 no.1
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• pp.35-55
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• 1992

Black과 Scholes가 옵션가격모형(價格模型)을 개발한 후 그 모형에서의 가정들을 완화시킴으로써 옵션모형들이 발전되어 왔다. Black-Scholes의 옵션가격모형(價格模型)의 문제점중의 하나는 주가의 분산이 만기일까지 일정(一定)하다는 가정이다. 본 연구에서는 장기옵션이 Scorer 이용하여 주가분산(株價分散)의 중요성을 고찰하였다. 즉 Cox, Ingersoll과 Ross의 일반균형이론(一般均衡理論)에 근거한 random variance 옵션모형을 도출하였고 이것을 Black-Scholes 옵션모형과 비교하였다. 장기유럽식 옵션에 대하여 주가변동성(株價變動性)의 위험(危險)프레미엄이 중요한 요소이고 위험(危險)프레미엄을 고려한 random variance 옵션모형이 위험(危險)을 고려치 않는 random variance옵션모형(模型)보다 예측력이 높게 나타났다.