• Journal of the Korean Data and Information Science Society
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• 제28권2호
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• pp.251-260
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• 2017

Black와 Scholes (1973)와 Merton (1973)의 옵션 가격결정이론에 대한 논문이 발표 된 이후 다양한 실증 분석 결과에 의하여 시간의 흐름에 따라 변동성이 불변한다고 가정하는 Black-Scholes 모형이 시장의 옵션 가격을 적절히 설명하지 못하고 있다는 것이 밝혀지면서 많은 대안적인 연구들이 진행되어 왔다. 예를 들어, Duan (1995)은 위험중립측도 하에서의 몬테카를로 시뮬레이션을 통해 GARCH 모형을 따르는 기초 자산의 옵션가격을 도출하는 방법을 제시하였다. 그러나 실제 주식이나 환율 등의 금융자료에 수익률분포는 정규분포에 비해 꼬리가 두껍고, 급첨의 형태를 보이는 데 Duan (1995)의 옵션가격 결정 방법은 이를 적절히 반영하지 못하고 있다. 이를 해결하기 위해 본 논문에서는 정규혼합모형의 오차를 갖는 GARCH 모형을 이용한 옵션가격 결정 방법을 제안하고자 한다. KOSPI200 옵션가격 자료를 이용하여 본 논문에서 제시된 옵션가격과 정규분포를 가정한 GARCH 모형에 의해 결정된 옵션가격과 비교한 결과, 금융 자료의 급첨의 성질이 뚜렷한 불안정한 시기인 경우에 오차가 정규혼합모형이라고 가정한 GARCH 모형에 의한 옵션가격 결정의 성과가 월등히 좋아지는 것을 확인할 수 있었다.

• 경영과학
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• 제32권1호
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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.

• 한국산학기술학회논문지
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• 제12권2호
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• pp.712-717
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• 2011

동적 델타 헤징(Dynamic Delta Hedging)이란 옵션 발행자가 옵션의 만기정산금액(payoff)을 지급하기 위해 주기적으로 델타에 근거한 헤지 포지션을 조절함으로써 옵션의 payoff를 복제하고 옵션 가치변화에 따른 위험을 회피하는 방법이다. 본 연구에서는 헤지에 있어서 주요 변수인 블랙-숄즈의 모형에 의해 산출된 델타의 대체 값을 찾기 위해 기계학습의 일종인 인공신경망 학습을 적용하여 옵션의 만기 시 헤지 비용의 최소화 및 차익 실현을 위한 방법론을 제시하고자 한다. 기초자산의 현재가격, 변동성, 무위험이자율, 만기 등의 시장 상황 변화에 따른 다양한 시나리오에 대한 실험을 통해 본 연구에서 제시하는 방법론의 성능을 분석하고 그 우수성을 보인다.

• 청정기술
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• 제29권1호
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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.

• 대한수학회지
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• 제43권2호
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• pp.383-398
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• 2006

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

• Communications for Statistical Applications and Methods
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• 제23권1호
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• pp.21-32
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• 2016

We study asymptotic expansion formulae for numerical computation of Greeks (i.e. sensitivity) in finance. Our approach is based on the integration-by-parts formula of the Malliavin calculus. We propose asymptotic expansion of Greeks for a stochastic volatility model using the Greeks formula of the Black-Scholes model. A singular perturbation method is applied to derive asymptotic Greeks formulae. We also provide numerical simulation of our method and compare it to the Monte Carlo finite difference approach.

• 대한수학회논문집
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• 제23권1호
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• pp.141-151
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• 2008

In this paper, we derive the nonlinear equation for European option pricing containing liquidity risk which can be defined as the inverse of the partial derivative of the underlying asset price with respect to the amount of assets traded in the efficient market. Numerical solutions are obtained by using finite element method and compared with option prices of KOSPI200 Stock Index. These prices computed with liquidity risk are considered more realistic than the prices of Black-Scholes model without liquidity risk.

• East Asian mathematical journal
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• 제34권3호
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• pp.239-248
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• 2018

In this paper, we derive a closed-form formula of a second-order approximation for a European corrected option price under stochastic elasticity of variance model mentioned in Kim et al. (2014) [1] [J.-H. Kim, J Lee, S.-P. Zhu, S.-H. Yu, A multiscale correction to the Black-Scholes formula, Appl. Stoch. Model. Bus. 30 (2014)]. To find the explicit-form correction to the option price, we use Mellin transform approaches.

• East Asian mathematical journal
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• 제32권3호
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• pp.301-310
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• 2016

Lookback options, in the terminology of nance, are a type of exotic option with path dependency whose the payoff depends on the optimal (maximum or minimum) underlying asset's price occurring over the life of the option. In this paper, we exploit Mellin transform techniques to find a closed-form solution for European lookback options in Black-Scholes model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권2호
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• pp.77-84
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• 2000

Black-Scholes equation arising from option pricing in the presence of cost in trading the underlying asset is derived. The transaction cost is chosen precisely and generalized to reflect the trade in the real world. Furthermore the concept of the bandwidth is introduced to obtain the better rehedging. The model with bandwidth derived in this paper can be used to calculate the more accurate option price numerically even if it is nonlinear and more complicated than the models shown before.