• 대한수학회논문집
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• 제13권2호
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• pp.367-375
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• 1998

In this paper, we present the close solution for minimal hedging portofolis $II^*$ when payment f for American option admits the integral option.

• 충청수학회지
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• 제29권3호
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• pp.503-508
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• 2016

We propose a number of finite difference methods for the prices of a European option under the CGMY model. These numerical methods to solve a partial integro-differential equation (PIDE) are based on three time levels in order to avoid fixed point iterations arising from an integral operator. Numerical simulations are carried out to compare these methods with each other for pricing the European option under the CGMY model.

• 대한수학회보
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• 제58권2호
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• pp.349-364
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• 2021

This paper studies the optimal surrender policies for a variable annuity (VA) contract with a surrender option and a fixed insurance fee for guaranteed minimum maturity benefits (GMMB). In our proposed model, a policyholder pays the fixed insurance fee. Based on the integral transform techniques, we derive the analytic integral equations for the optimal surrender boundary and the value function of the VA contract that can be solved numerically by recursive integration method. We provide numerical values for the value function, the optimal surrender boundary, and the expected optimal surrender time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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• pp.31-41
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• 2011

I introduce a derivative called "Snowball Currency Option" or "USDKRWSnowball Extendible At Expiry KO" which was traded once in the over-the-counter market in Korea. A snowball currency option consists of a series of maturities the payoffs at which are like those of a long position in a put option and two short position in an otherwise identical call. The strike price at each maturity depends on the exchange rate and the previous strike price so that the strike prices are random and path-dependent, which makes it difficult to find a closed form solution of the value of a snowball currency option. I analyze the payoff structure of a snowball currency option and derive an upper and a lower boundaries of the value of it in a simplified model. Furthermore, I derive a pricing formula using integral in the simplified model.

• 대한수학회보
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• 제53권5호
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• pp.1411-1425
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• 2016

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

• 한국과학교육학회지
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• 제35권1호
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• pp.121-130
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• 2015

국가 수준의 표준화된 학업 성취도 평가 결과를 분석하여 학생들의 성취 수준을 파악하고 이를 교육정책 수립이나 교수활동 개선에 반영하는 과정은 교육의 책무성으로 중요한 부분이다. 본 연구에서는 과학과 국가 수준 학업 성취도 평가 결과를 분석하고, 답지 반응률 분포 곡선을 활용하여 평가 문항의 특성을 분석하고자 하였다. 이를 위해 2010년부터 2013년까지 시행된 과학과 성취도 평가 결과를 성취 수준에 따라 분석하였으며, 성취도 점수에 따른 특정 문항의 정오답 반응률을 토대로 최적 곡선을 추정한 그래프인 답지 반응률 분포 곡선을 활용하여 선다형 평가 문항 112개의 정답지와 오답지 반응률 곡선의 유형을 분류하고, 유형별 문항 특성을 분석하였다. 분석 결과, 정답지는 5가지 유형(S자형, J자형, 직선형, F자형, 계단형)으로 분류하였고, 오답지는 4가지 유형(보통형, 평지형, 산지형, 상승형)으로 분류하였다. S자형의 정답지 반응 곡선과 보통형의 오답지 반응 곡선이 조합인 문항이 가장 많았으며, 성취 수준에 따라 학생들을 변별하는데 적절한 문항인 것으로 분석되었다. 또한, 정답 반응률 분포와 오답 반응률 분포가 서로 연관되는 것으로 나타났다. 연구 결과를 토대로 교수 학습, 교실 평가 등에서 함의를 논의하였다.

• 대한산업공학회지
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• 제38권4호
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• pp.244-248
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• 2012

We present a simple numerical method for pricing American put options under a constant elasticity of variance (CEV) model. Our analysis is done in a general framework where only the risk-neutral transition density of the underlying asset price is given. We obtain an integral equation of early exercise premium. By exploiting a modification of the integral equation, we propose a novel and simple numerical iterative valuation method for American put options.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.79-84
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• 2003

Likelihood estimation in random-effect models is often complicated because the marginal likelihood involves an analytically intractable integral. Numerical integration such as Gauss-Hermite quadrature is an option, but is generally not recommended when the dimensionality of the integral is high. An alternative is the use of hierarchical likelihood, which avoids such burdensome numerical integration. These two approaches for fitting binary data are compared and the advantages of using the hierarchical likelihood are discussed. Random-effect models for binary outcomes and for bivariate binary-continuous outcomes are considered.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권2호
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• pp.159-168
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• 2015

Abstract. We propose a fast and robust finite difference method for Merton's jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권4호
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• pp.231-249
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• 2020

We present an efficient and robust finite difference method for a two-asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.