• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.181-192
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• 2016

We consider several methods to approximate option prices with correction terms to the Black-Scholes option price. These methods are able to compute option prices from various risk-neutral distributions using relatively small data and simple computation. In this paper, we compare the performance of Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method of using Normal inverse gaussian distribution, and an asymptotic method of using nonlinear regression through simulation experiments and real KOSPI200 option data. We assume the variance gamma model in the simulation experiment, which has a closed-form solution for the option price among the pure jump $L{\acute{e}}vy$ processes. As a result, we found that methods to approximate an option price directly from the approximate price formula are better than methods to approximate option prices through the approximate risk-neutral density function. The method to approximate option prices by nonlinear regression showed relatively better performance among those compared.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.939-942
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• 2009

본 연구는 경북지역의 11개 관측소와 인근 9개의 관측소의 강우자료를 이용하여 경북지역에 한정된 확률강우량도를 작성하였다. 최근 행정구역별 치수계획의 수립이 빈번해지고 소규모 유역의 개발로 인한 홍수량 산정 등이 빈번해지고 있다. 그러나 대부분이 강우관측소가 유역내에 위치해 있지 않고 인접한 기상관측소의 자료를 이용하고 있는 실정이고, 공공기관이나 실무를 수행함에 있어 유역의 강우량 적용에 있어 소규모 유역의 강우량이 지점강우량에 의해 결정되므로 어느 정도의 편차를 보이는지 추정이 사실상 곤란하였다. 따라서 본 연구에서는 경북지역에 한정하여 지점강우량을 빈도해석하여 확률강우량도를 작성하여 강우관측소가 인접하지 않아도 소규모 유역의 확률강우량의 근사치를 추정하여 지점빈도해석과 비교할 수 있도록 확률강우량도를 작성하였다. 경북지역인근 강우관측소의 자료를 강우 분석하여 확률분포형을 선정한 결과 거창, 구미, 대구, 문경, 밀양, 봉화, 안동, 영덕, 영주, 울산, 의성, 제천 충주, 추풍령, 합천은 Gumbel 분포가 적합한 것으로 나타났으며, 보은은 2변수 Log-Gumbel 분포가 적합한 것으로 나타났으며, 영천, 울진, 태백은 Gamma 분포가 적합한 것으로 나타나고 포항은 GEV 분포가 적합한 것으로 나타났다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.04a
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• pp.109-116
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• 1993

구조물의 신뢰도를 평가하는 방법을 살펴보고 각각의 장,단점을 비교한다. 각 방법의 정확성을 평가하는 기준으로 Crude Monte Carlo(CMC)방법을 택하여, Importance Sampling(IS)방법, 그리고 Directional Sampling(DS)방법을 살펴 보고, 1차 근사방법은 현재 많이 사용되고 있는 Rackwitz-Fiessler(RF)방법, Chen과 Lind가 제안한 3-parameter방법(CL), Hohenbichler가 제안한 Rosenblatt 변환방법(RT)을, 그리고 2차 근사방법은 Breitung이 제안한 곡률적합 포물선 (Curvature Fitted Paraboloid,CFP)공식과 Kiureghian이 제안한 점적합 포물선(Point Fitted Paraboloid,PFP)공식, 그리고 Log-Likelihood function을 이용하여 원변수공간에서 파괴확률을 구하는 2차 근사공식(LLF)을 비교한다. 그리고 한계상태식이 불명확할 때 효율적으로 사용할 수 있는 반웅웅답법(Response surface method, RSM)을 살펴본다. 각 방법의 효율성 특히 적용 가능성을 예제를 통해 해석한 결과 추출법의 경우는 DS 방법이, 그리고 근사방법에서는 RSM 방법이 효율적임을 알 수 있었다.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.513-523
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• 2016

Fitting a mixture of multivariate skew normal distribution (MSNMix) with multiple skewness parameter vectors via EM algorithm often requires a highly expensive computational cost to calculate the moments and probabilities of multivariate truncated normal distribution in E-step. Subsequently, it is common to fit an asymmetric data set with MSNMix with a simple skewness parameter vector since it allows us to compute them in E-step in an univariate manner that guarantees a cheap computational cost. However, the adaptation of a simple skewness parameter is unrealistic in many situations. This paper proposes an approximate estimation for the MSNMix with multiple skewness parameter vectors that also allows us to treat them in an univariate manner. We additionally provide some experiments to show its effectiveness.

• Journal of the Korean Geophysical Society
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• v.3 no.3
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• pp.161-174
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• 2000

Bayesian inversion is a stable approach to infer the subsurface structure with the limited data from geophysical explorations. In geophysical inverse process, due to the finite and discrete characteristics of field data and modeling process, some uncertainties are inherent and therefore probabilistic approach to the geophysical inversion is required. Bayesian framework provides theoretical base for the confidency and uncertainty analysis for the inference. However, most of the Bayesian inversion require the integration process of high dimension, so massive calculations like a Monte Carlo integration is demanded to solve it. This method, though, seemed suitable to apply to the geophysical problems which have the characteristics of highly non-linearity, we are faced to meet the promptness and convenience in field process. In this study, by the Gaussian approximation for the observed data and a priori information, fast Bayesian inversion scheme is developed and applied to the model problem with electric well logging and dipole-dipole resistivity data. Each covariance matrices are induced by geostatistical method and optimization technique resulted in maximum a posteriori information. Especially a priori information is evaluated by the cross-validation technique. And the uncertainty analysis was performed to interpret the resistivity structure by simulation of a posteriori covariance matrix.

• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.243-257
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• 2017

In this paper, we compare several methods to approximate option prices: Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method using normal inverse gaussian (NIG) distribution, and an asymptotic method using nonlinear regression. We used two different types of approximation. The first (called the RNM method) approximates the risk neutral probability density function of the log return of the underlying asset and computes the option price. The second (called the OPTIM method) finds the approximate option pricing formula and then estimates parameters to compute the option price. For simulation experiments, we generated underlying asset data from the Heston model and NIG model, a well-known stochastic volatility model and a well-known Levy model, respectively. We also applied the above approximating methods to the KOSPI200 call option price as a real data application. We then found that the OPTIM method shows better performance on average than the RNM method. Among the OPTIM, A-type Gram-Charlier expansion and the asymptotic method that uses nonlinear regression showed relatively better performance; in addition, among RNM, the method of using NIG distribution was relatively better than others.

• The Korean Journal of Applied Statistics
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• v.26 no.4
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• pp.611-622
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• 2013

Mudholkar and Tian (2002) proposed an entropy-based test of fit for the inverse Gaussian distribution; however, the test can be applied to only the composite hypothesis of the inverse Gaussian distribution with an unknown location parameter. In this paper, we propose an entropy-based goodness-of-fit test for an inverse Gaussian distribution that can be applied to the composite hypothesis of the inverse Gaussian distribution as well as the simple hypothesis of the inverse Gaussian distribution with a specified location parameter. The proposed test is based on the probability integration transformation. The critical values of the test statistic estimated by simulations are presented in a tabular form. A simulation study is performed to compare the proposed test under some selected alternatives with Mudholkar and Tian (2002)'s test in terms of power. The results show that the proposed test has better power than the previous entropy-based test.

• Computational Structural Engineering
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• v.7 no.1
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• pp.109-116
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• 1994

In this paper, various reliability analysis methods for calculating a probability of failure are investigated for their accuracy and efficiency. Crude Monte Carlo method is used as a basis for the comparison of various numerical results. For the sampling methods, Importance Sampling method and Directional Simulation method are considered for overcoming a drawback of Crude Monte Carlo method. For the approximate methods, conventional Rackwitz-Fiessler method. 3-parameter Chen-Lind method, and Rosenblatt transformation method are compared on the basis of First order reliability method. As a Second-order reliability method, Curvature-Fitting paraboloid method, Point-fitting paraboloid method, and Log-likelihood function method are explored in order to verify the accuracy of the reliability calculation results. These methods mentioned above would have some difficulty unless the limit state equation is expressed explicitly in terms of random design variables. Thus, there is a need to develop some general reliability methods for the case where an implicit limit state equation is given. For this purpose, Response surface method is used where the limit state equation is approximated by regression analysis of the response surface outcomes resulted from the structural analysis. From the application of these various reliability methods to three examples, it is found that Directional Simulation method and Response Surface method are very efficient and recommendable for the general reliability analysis problem cases.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07b
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• pp.724-726
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• 2005

베이지안망(Bayesian network)은 다수의 변수들 사이의 확률적 관계(조건부독립성: conditional independence)를 그래프 구조로 표현하는 모델이다. 이러한 베이지안망은 비감독학습(unsupervised teaming)을 통한 데이터마이닝에 적합하다. 이를 위해 데이터로부터 베이지안망의 구조와 파라미터를 학습하게 된다. 주어진 데이터의 likelihood를 최대로 하는 베이지안망 구조를 찾는 문제는 NP-hard임이 알려져 있으므로, greedy search를 통한 근사해(approximate solution)를 구하는 방법이 주로 이용된다. 하지만 이러한 근사적 학습방법들도 데이터를 구성하는 변수들이 수천 - 수만에 이르는 경우, 방대한 계산량으로 인해 그 적용이 실질적으로 불가능하게 된다. 본 논문에서는 그러한 대규모 데이터에서 학습될 수 있는 계층적 베이지안망(hierarchical Bayesian network) 모델 및 그 학습방법을 제안하고, 그 가능성을 실험을 통해 보인다.

• The Korean Journal of Applied Statistics
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• v.5 no.2
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• pp.271-282
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• 1992

A statistical method to investigate the relationship between the occurrence of Langerahans cells and neoplastic transformation of uterine cerivx. The best fitting submodel which satisfies the selection criterion similar in type to AIC is selected among the possible submodels based on Poisson probability models. A bootstrap method is used to approximate the sampling distribution of the selection criterion and the usual normal approximation is used to find the asymptotic distribution of the estimated rates.