Using predicted cumulative probability distribution of hidden Markov Model for European option pricing

Youngchul Han,Jungwoo Lee,Jeong-Hoon Kim 한국재무학회 2013 한국재무학회 학술대회 Vol.2013 No.11

In this paper, we proposed model for European option pricing using predicted cumulative probability distribution of hidden Markov Model. The Black-Scholes model is based on Gaussian distribution and the model's main shortfall is fat-tail problem. Because of fat-tail problem, the implied volatility surface is shaped skew, smirk or other forms. To correct model's drawback, we extract predicted cumulative distribution using hidden Markov Model and simulate the underlying price paths using Monte Carlo method. In the results, our model re ect current implied volatility surface suciently.

Non-Cooperative Game Joint Hidden Markov Model for Spectrum Allocation in Cognitive Radio Networks

Yan Jiao 한국인터넷방송통신학회 2018 Journal of Advanced Smart Convergence Vol.7 No.1

Spectrum allocation is a key operation in cognitive radio networks (CRNs), where secondary users (SUs) are usually selfish – to achieve itself utility maximization. In view of this context, much prior lit literature proposed spectrum allocation base on non-cooperative game models. However, the most of them proposed non-cooperative game models based on complete information of CRNs. In practical, primary users (PUs) in a dynamic wireless environment with noise uncertainty, shadowing, and fading is difficult to attain a complete information about them. In this paper, we propose a non-cooperative game joint hidden markov model scheme for spectrum allocation in CRNs. Firstly, we propose a new hidden markov model for SUs to predict the sensing results of competitors. Then, we introduce the proposed hidden markov model into the non-cooperative game. That is, it predicts the sensing results of competitors before the non-cooperative game. The simulation results show that the proposed scheme improves the energy efficiency of networks and utilization of SUs.

확률적 변동성을 가진 은닉마르코프 모형을 통한 비트코인 가격의 변동성 추정

강태현,황범석 한국통계학회 2023 응용통계연구 Vol.36 No.1

The stochastic volatility (SV) model is one of the main methods of modeling time-varying volatility. In particular, SV model is actively used in estimation and prediction of financial market volatility and option pricing. This paper attempts to model the time-varying volatility of the bitcoin market price using SV model. Hidden Markov model (HMM) is combined with the SV model to capture characteristics of regime switching of the market. The HMM is useful for recognizing patterns of time series to divide the regime of market volatility. This study estimated the volatility of bitcoin by using data from Upbit, a cryptocurrency trading site, and analyzed it by dividing the volatility regime of the market to improve the performance of the SV model. The MCMC technique is used to estimate the parameters of the SV model, and the performance of the model is verified through evaluation criteria such as MAPE and MSE. Stochastic volatility (SV) 모형은 시변 변동성을 모델링하는 주요한 수단 중 하나이며, 특히 금융시장 변동성의 추정 및 예측, 옵션의 가격 결정 등의 분야에서 활발하게 사용되고 있다. 본 논문은 SV 모형을 활용하여 비트코인 시장의 시변 변동성을 모델링하고자 한다. 시장의 변동성은 국면 전환의 특성을 갖고 있다고 알려져 있으며, 시장의 변동 국면을 나누기 위해 시계열의 패턴을 인식하는 작업에 유용한 hidden Markov model (HMM)을 결합하여 사용하고자 한다. 본 연구는 암호화폐 거래 사이트 업비트의 비트코인 데이터를 활용하여 비트코인의 변동성 모형을 추정하였으며 SV 모형의 성능을 높이기 위하여 시장의 변동 국면을 나누어 분석을 진행하였다. MCMC 기법이 SV 모델의 모수를 추정하는 데 사용되며 MAPE, MSE 등의 평가 기준을 통하여 모델의 성능을 확인하고자 한다.

HMM근사를 이용한 빠르고 효율적인 확률코퓰러모형 최우추정

김태형,박정민 한국금융학회 2023 금융연구 Vol.37 No.3

The association or interdependence between asset returns plays a crucial role in financial and managerial theories and practices, such as asset pricing, portfolio construction, risk management, and derivative pricing. The Pearson correlation coefficient, a representative measure of linear interdependence under the elliptical distribution, has been widely used in theory and practice. However, after the US financial crisis of 2008, various limitations of the correlation coefficient as a measure of interdependence have been exposed. Since Patton (2006a), The copula function, which has been actively researched in the field of financial econometrics in order to overcome the limitations of the linear measure of interdependence, that is, correlation coefficient. Unlike the linear measure of interdependence, the copula function can capture nonlinear, asymmetric, and tail dependence. Various study results have shown that the interdependence between asset returns, such as time-varying conditional variance and asymmetric behavior, varies over time and with different degrees of asymmetry. To capture such asymmetric time-varying interdependence, various conditional dynamic copula models have been proposed, such as Patton's (2006a) Copula-GARCH model, Creal et al's (2011, 2013) GAS model (generalized autoregressive score models), and Hafner and Manner's (2012) stochastic copula model. In the case of the Copula-GARCH and GAS models, similar to the GARCH models, the dynamic equation of association parameter is a deterministic function of parameters and returns of previous periods. In contrast, the stochastic copula model is a nonlinear, non-normal state space model in which the association parameter is a nonlinear function of a latent state variable as in the stochastic volatility model. As in the maximum likelihood estimation of the volatility model, it is necessary to integrate out unobserved state variables in order to perform maximum likelihood estimation of the Copula model and it is well known that integrating-out of such state variables can be challenging. Efficient Importance Sampling (EIS), proposed by Liesenfeld and Richard (2003) and Richard and Zhang (2007), was used by Hafner and Manner (2012) to obtain the likelihood function required for estimating the stochastic volatility model. Almeida and Czado (2012), Kim and Park (2018), and Kreuzer and Czado (2020), among others, have proposed MCMC algorithms for Bayesian inference on stochastic copula models. Although those simulation-based estimation methods are efficient, they have the disadvantage of taking a considerable amount of time for model estimation. For a small number of state variables, it is possible to calculate the likelihood function of a general discrete-time continuous state-space model using numerical integration. Kitagawa (1987) proposed a method of numerical integration by partitioning continuous state variables for the estimation of discrete-time non-normal state-space models. Similarly, Fridman and Harris (1998), Bartolucci and De Luca (2001, 2003), and others have proposed methods of approximating the likelihood function of stochastic volatility models using quadrature methods. The maximum likelihood estimation using the likelihood function obtained by numerical integration may take a considerable amount of time for numerical integration as the number of observed data and the dimension of the state variable increases due to the curse of dimensionality. Therefore, numerical integration-based maximum likelihood estimation is not commonly used for the estimation of stochastic volatility models. Langrock et al. (2012) used the HMM (hidden Markov model) approximation to obtain an approximate likelihood function of the stochastic volatility model by partitioning the state variable into multiple intervals and approximating the transition probability density function of the discrete-time continuous state variable with the transition probability of the discrete sta...

Chow-Liu Tree 모형과 동질성 Hidden Markov Model을 연계한 다지점 일강수량 모의기법 개발

권현한,김태정,김운기,이동률 한국수자원학회 2013 한국수자원학회논문집 Vol.46 No.10

본 연구에서는 유역의 공간상관성을 고려한 다지점 일단위 강수량을 동시에 모의할 수 있는 일강수량 모의기법을 개발하였다. 기존 Hidden Markov Chain Model(HMM)은 단일지점 강수모의에 적용되어 왔으나 관측지점간의 유역상관성을 충분히 고려하지 못하는 문제점을 가지고 있다. 따라서 본 연구에서는 Chow-Liu Tree(CLT) 모형을 적용하여 다변량(multivariate) 형태로써 유역내에 위치한 강우관측소간의 상호종속성을 고려하기 위하여 기존의 동질성 HMM 강우모의기법과 CLT 알고리즘을 결합한 동질성 CLT-HMM 모형을 개발하였다. 본 연구에서 개발된 동질성 CLT-HMM 모형을 사용하여 장기간의 수문자료를 보유하고 있는 기상청 산하의 한강유역 강수네트워크에 대해서 적합성을 검토하였다. 동질성 CLT-HMM 모형을 적용하여 모의 된 결과를 보면 일강수량의 계절적 특성뿐만 아니라 일강수량 모의 시 강수시계열의 통계적인 특성들까지 우수하게 모의하였다. 추가적으로 상관행렬(correlation matrix)을 이용하여 기상관측소간의 공간상관 재현성을 검토한 결과 관측지점들 사이의 공간상관성도 비교적 우수하게 재현하는 것을 확인할 수 있었다. This study aims to develop a multivariate daily rainfall simulation model considering spatial coherence across watershed. The existing Hidden Markov Model(HMM) has been mainly applied to single site case so that the spatial coherences are not properly addressed. In this regard, HMM coupled with Chow-Liu Tree(CLT) that is designed to consider inter-dependences across rainfall networks was proposed. The proposed approach is applied to Han-River watershed where long-term and reliable hydrologic data is available, and a rigorous validation is finally conducted to verify the model’s capability. It was found that the proposed model showed better performance in terms of reproducing daily rainfall statistics as well as seasonal rainfall statistics. Also, correlation matrix across stations for observation and simulation was compared and examined. It was confirmed that the spatial coherence was well reproduced via CLT-HMM model.

Applications of the Conway-Maxwell-Poisson Hidden Markov models for analyzing traffic accident

Hee-Young Kim(Hee-Young Kim) 한국자료분석학회 2022 Journal of the Korean Data Analysis Society Vol.24 No.5

This paper documents the application of the Conway-Maxwell-Poisson(CMP) hidden Markov model for modelling motor vehicle crashes. The CMP distribution is a twoparameter extension of the Poisson distribution that generalizes some well-known discrete distributions(Poisson, Bernoulli and geometric). Also it leads to the generalizations of distributions derived from theses discrete distributions, that is, the binomial and negative binomial distributions. The advantage of CMP distribution is its ability to handle both under and over-dispersion through controlling one special parameter in the distribution, which makes it more flexible than Poisson distribution. We consider the data consisting of the daily number of injuries on the road in 2020 from the TAAS(Traffic Accident Analysis System). We apply CMP hidden Markov model to data, the parameters are estimated via maximim likelihood, and find that this model achieves better performance than commonly used Poisson hidden Markov model. For the decoding procedure, the Viterbi algorithm is implemented.

고객만족, NPS, Bayesian Inference 및 Hidden Markov Model로 구현하는 명품구매에 관한확률적 추적 메카니즘

황선주,이정수 한국산업정보학회 2018 한국산업정보학회논문지 Vol.23 No.6

The purpose of this study is to specify a probabilistic tracking mechanism for customer luxury purchase implemented by hidden Markov model, Bayesian inference, customer satisfaction and net promoter score. In this paper, we have designed a probabilistic model based on customer's actual data containing purchase or non-purchase states by tracking the SPC chain : customer satisfaction -> customer referral -> purchase/non-purchase. By applying hidden Markov model and Viterbi algorithm to marketing theory, we have developed the statistical model related to probability theories and have found the best purchase pattern scenario from customer's purchase records.

장애인의 노동 시장 진입과 일자리 질의 변화 궤적에 관한 연구 - 잠재 마르코프 모형(Hidden Markov Model)을 활용한 고용 궤적 유형화와 집단 간 비교를 중심으로 -

노법래(Roh, Beop-Rae),문영민(Mun, Yeongmin) 한국사회복지학회 2021 한국사회복지학 Vol.73 No.3

본 연구의 목적은 장애인 고용 이행 궤적을 일자리에 따라 유형화하고, 장애인 고용 상황의 잠재이행구조를 규명하는 것이다. 이를 위하여 본 연구는 Hidden Markov Model을 활용해 장애인의 고용 상태 변화에 영향을 미치는 잠재 구조가 무엇인지를 추정하고, 장애정도와 성별에 따른 경로구조의 차이를 비교하였다. 나아가 Mixture Hidden Markov Model을 활용해 고용이행 구조에 미치는 개인 특성 요인을 분석하였다. 분석 결과 장애인 노동시장 참여에는 노동시장 참여-미참여, 안정-불안정의 2중 분절 구조가 관찰되었다. 또한 분절 구조 사이에 이동성이 거의 관찰되지 않았으며, 분절구조를 가르는 개인 특성은 여성이거나 저학력인 것으로 나타났다. 연구결과를 바탕으로 분절구조를 완화할 수 있는 가교 일자리를 확대할 것과, 취약한 장애 특성을 가진 집단에 대한 지원이 필요하다는 것, 그리고 근로 및 실업빈곤집단에 대하여 다양한 정책 레퍼토리를 개발할 것을 제언하였다. The purpose of this study is to classify the employment transition trajectory for people with disabilities according to their quality of jobs and identify the latent transition structure of employment status. To this end, we used the Hidden Markov Model to estimate what potential structures affect changes in the employment status of people with disabilities and compare the differences of path structure between disability degree and gender. Furthermore, we analyzed personal characteristic factors on the employment transition structure using the Mixture Hidden Markov Model. According to the analysis, the labor market participation for people with disabilities was observed to have a dual segmentation of labor market participation-nonparticipation and stability-instability. In addition, little mobility has been observed between segment structures, and individual characteristics that divide segmentation have been shown to be female or undereducated. Based on the results of the study, it was suggested to expand the number of bridge jobs that can mitigate the segmentation structure and support groups with vulnerable disability characteristics.

3차원 손 모델링 기반의 실시간 손 포즈 추적 및 손가락 동작 인식

석흥일(Heung-Il Suk),이지홍(Ji-Hong Lee),이성환(Seong-Whan Lee) 한국정보과학회 2008 정보과학회논문지 : 소프트웨어 및 응용 Vol.35 No.12

손 포즈 모델링 및 추적은 컴퓨터 시각 분야에서 어려운 문제로 알려져 있다. 손 포즈 3차원 복원을 위한 방법에는 사용되는 카메라의 수에 따라 다중 카메라 또는 스테레오 카메라 기반 방식과 단일 카메라 기반 방식이 있다. 다중 카메라의 경우 여러 대의 카메라를 설치하거나 동기화를 시키는 등에 대한 제약사항이 따른다. 본 논문에서는 확률 그래프 모델에서 신뢰 전파 (Belief Propagation) 알고리즘을 이용하여 단안 카메라에서 획득된 2차원 입력 영상으로부터 3차원 손 포즈를 추정하는 방법을 제안한다. 또한, 은닉 마르코프 모델(Hidden Markov Model)을 인식기로 하여 손가락 클릭 동작을 인식한다. 은닉 노드로 손가락의 관절 정보를 표현하고, 2차원 입력 영상에서 추출된 특징을 관측 노드로 표현한 확률 그래프 모델을 정의한다. 3차원 손 포즈 추적을 위해 그래프 모델에서의 신뢰 전파 알고리즘을 이용한다. 신뢰 전파 알고리즘을 통해 3차원 손 포즈를 추정 및 복원하고, 복원된 포즈로부터 손가락의 움직임에 대한 특징을 추출한다. 추출된 정보는 은닉 마르코프 모델의 입력값이 된다. 손가락의 자연스러운 동작을 위해 본 논문에서는 한 손가락의 클릭 동작 인식에 여러 손가락의 움직임을 함께 고려한다. 제안한 방법을 가상 키패드 시스템에 적용한 결과 300개의 동영상 테스트 데이타에 대해 94.66%의 높은 인식률을 보였다. Modeling hand poses and tracking its movement are one of the challenging problems in computer vision. There are two typical approaches for the reconstruction of hand poses in 3D, depending on the number of cameras from which images are captured. One is to capture images from multiple cameras or a stereo camera. The other is to capture images from a single camera. The former approach is relatively limited, because of the environmental constraints for setting up multiple cameras. In this paper we propose a method of reconstructing 3D hand poses from a 2D input image sequence captured from a single camera by means of Belief Propagation in a graphical model and recognizing a finger clicking motion using a hidden Markov model. We define a graphical model with hidden nodes representing joints of a hand, and observable nodes with the features extracted from a 2D input image sequence. To track hand poses in 3D, we use a Belief Propagation algorithm, which provides a robust and unified framework for inference in a graphical model. From the estimated 3D hand pose we extract the information for each finger's motion, which is then fed into a hidden Markov model. To recognize natural finger actions, we consider the movements of all the fingers to recognize a single finger's action. We applied the proposed method to a virtual keypad system and the result showed a high recognition rate of 94.66% with 300 test data.

Hidden Markov Model을 이용한 스마트폰 다중 동작에서의 보행 항법 이동방향 개선 알고리즘

박소영,이재홍,박찬국 제어·로봇·시스템학회 2020 제어·로봇·시스템학회 논문지 Vol.26 No.9

In this paper, we propose a solution for mismatching between the walking direction and device heading in a PDR (Pedestrian Dead Reckoning) system using a smartphone and the HMM (Hidden Markov Model). The PA (Parametric Approach)-based PDR system consists of step detection, step length estimation, and heading estimation. In general, the device heading is regarded as the walking direction, but device heading and walking direction are sometimes mismatched due to the smartphone user assuming various poses. In these cases, the PA-based PDR produces an position error from the mismatched angle. The solution proposed in this paper is an IA(Integration Approach)-based PDR system and a walking direction estimation method using HMM. The IA-based PDR system estimates the position by integrating the acceleration twice. To correct the error produced by this system, the travel distance and the walking direction are used as measurements, and are obtained from the step length model of PA and walking direction from HMM, respectively. Through experiments, it is shown that the performance of the proposed algorithm can overcome the limitations of existing smartphone-based algorithms. .