Bayesian Markov Chain Monte Carlo algorithm for Feller square-root stochastic volatility models = Feller제곱근 확률변동성모형에 대한 베이지언 MCMC알고리듬

국문 초록 (Abstract)

본 연구는 Feller제곱근 확률변동성모형에 대한 새로운 베이지언 추론 알고리듬, 알고리듬의 성과에 대한 모의실험 결과, 그리고 알고리듬을 이용한 실증분석 결과를 제시한다. 본 연구의 알고리듬은 수익률과 조건부분산의 결합확률밀도함수로부터 유도되는 조건부분산의 GIG분포 확률커널을 정규분포로 근사하는 방법을 이용하므로 도약과정이나 두꺼운 꼬리를 가지는 수익률 분포를 포함하는 확장모형에도 쉽게 적용될 수 있다. 또한 본 연구의 알고리듬과 파티클필터를 통해 얻은 PIT를 이용하는 확률변동성모형 진단 통계량들의 사이즈와 검정력을 비교하는 모의실험 결과를 제시한다. 파라미터 추정에 따른 불확실성에 영향을 받지 않는 대표적인 비모수 검정인 Hong and Li (2005) 검정과 일반화된 잔차의 정규성을 이용하는 고전적 진단통계량들의 사이즈와 검정력에 대한 모의실험 결과, 고전적 진단통계량들의 사이즈왜곡이 심각하지 않을 수 있으며 검정력 또한 Hong-Li옴니버스검정(Q)보다 좋을 수 있는 것으로 나타났다.

다국어 초록 (Multilingual Abstract)

We develop a new Bayesian Markov Chain Monte Carlo algorithm for Euler-discretized Feller square-root stochastic volatility models and demon-strate the performance of our algorithm through simulations and empirical anal-yses. Specifically, our algorithm use the Laplace approximation of the posterior density of conditional variance, which is the probability kernel of the generalized inverse gaussian distribution, derived from the joint density of return and condi-tional variance so that it can be easily applied to the extended stochastic volatility models with such as fat-tailed distributions or Le´vy jump processes. In addition, we conduct the simulation experiment investigating and comparing the size and power of the parametric specification tests checking certain finite-dimensional moment conditions without correction for parameter estimation uncertainty with that of the nonparametric Hong and Li (2005)’s omnibus test which is not af-fected by parameter estimation uncertainty. The parametric and nonparametric tests are based on the probability integral transform of the prediction densities of returns obtained using auxiliary particle filter algorithms. Our experiment re-sult shows that the classical parametric specification test may have no worse size distortion and better power than Hong and Li (2005)’s test.

목차 (Table of Contents)

• 1. 서론
• 2. Feller제곱근 확률변동성모형에 대한 베이지언 MCMC알고리듬
• 4. 모의실험 및 실증분석
• 5. 결론

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