CAJ | 학술논문

在股票价潞中引入漂移率、波动率和随机跳跃三种状态，建立动态状态空间模型，并通过局部风险中性定价关系（RNVR）推导无套利定价模型．以非高斯条件ARMA—NGARCH为基准模型，构建S＆P500指数的离散动态Levy过程，并基于序贯贝叶斯的参数学习方法，进行模型估计和期权定价研究．结果表明：动态L6vy过程能够联合刻画时变漂移率、条件波动率和无穷活动率等特征，且贝叶斯方法的引入提高了期权隐含波动率的定价精度．同时，无穷活动率模型在期权定价方面具有显著优势．在五类滤波中，无损粒子滤波估计精度最高，速降调和稳态过程（RDTS）的期权定价误差最小，而非高斯模型在收益率预测方面没有表现出显著的差异．
재고표개로중인입표이솔、파동솔화수궤도약삼충상태，건립동태상태공간모형，병통과국부풍험중성정개관계（RNVR）추도무투리정개모형．이비고사조건ARMA—NGARCH위기준모형，구건S＆P500지수적리산동태Levy과정，병기우서관패협사적삼수학습방법，진행모형고계화기권정개연구．결과표명：동태L6vy과정능구연합각화시변표이솔、조건파동솔화무궁활동솔등특정，차패협사방법적인입제고료기권은함파동솔적정개정도．동시，무궁활동솔모형재기권정개방면구유현저우세．재오류려파중，무손입자려파고계정도최고，속강조화은태과정（RDTS）적기권정개오차최소，이비고사모형재수익솔예측방면몰유표현출현저적차이．
In this paper, we consider a three-dimension state space model for establishing a discrete-time dynamic Levy process, including time-varying drift, conditional volatility and stochastic jump activity. Then we obtain the equivalent non-arbitrage pricing model through local risk-neutral valuation relationship （RNVR）. Taking non-Gaussian ARMA-NGARCH model as our benchmark, we construct a discrete time dynamic Levy process with GARCH effect for modeling S~P500 index. Furthermore we jointly estimate the parameters of the model and study the option pricing performance based on Bayesian learning approach. Research results show that our dynamic Lgvy process can depict the time-varying drift rate, conditional volatility and infinite activity styles. Meanwhile, Bayesian approach improves the option valuation ability of our model. Infinite jump models are significant superior and increase the pricing accuracy of implied volatility. We also find that unscented particle filtering （UPF） has the best estimation performance, non- Gaussian models in the yield prediction are of no significant difference, but the rapidly decreasing tempered stable processes （RDTS） have minimum errors for option pricing.