Inference for Stochastic Processes and Applications

随机过程的推理和应用

• 批准号: RGPIN-2014-05581
• 负责人: Thavaneswaran, Aerambamoorthy
• 金额: $ 0.8万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=567258
• 关键词: Inference; Stochastic; Processes; Applications

Volatility is a measure of the amount by which an asset price is expected to fluctuate over a given period, and the greater the volatility, the higher the risk. Filtering and recursive parameter estimation for stochastic volatility (SV) models have many applications in financial decision making. SV models are commonly used in financial applications as their dynamics are flexible enough to model observed asset and derivative prices. Many applied decision making problems such as portfolio selection and option pricing are recursive in nature. Inference for the volatility plays an important role in option pricing applications. Constant volatility has been assumed in the basic Black-Scholes-Merton approach to option pricing. Significant correlation among the squared values of the log returns points at a need to model beyond this constant volatility. As a consequence, the world of nonlinear generalized autoregressive conditional heterocedastic (GARCH) modeling together with nonlinear stochastic volatility models has emerged. Practitioners use random coefficient volatility (RCV) models in finance and economics. Nonlinear GARCH models have been very popular and effective for modeling volatility dynamics in many asset markets. We have developed a data driven method for option pricing and demonstrated the superiority of GARCH/SV option pricing models using real data. (a) In this proposed research, we study inference problems for stochastic processes such as GARCH models, recently proposed ACP ( autoregressive conditionally Poisson)/RCV models, duration models, integer valued models, nonlinear stochastic volatility models, circular time series models and semimartingale models. The unified method of estimating function theory for continuous time as well as for discrete time models will be used to obtain joint maximum informative recursive estimates/filtered estimates and will be applied to inferences from option prices and to inference based on censored data. (b) There has been a growing interest in stochastic processes with infinite variance, for example Fama (Nobel Price Winner for econometric modelling this year) studied estimation and prediction for infinite regression models. This is due to the inherent challenge and theoretical interest provided by the non-normal stable laws as well as the possibility that the processes constructed from these laws may be appropriate models for many diverse phenomena. In practice, any time series which exhibits sharp spikes or occasional bursts of outlying observations suggests the possible use of a model with stable errors having infinite variance. For time series models with infinite variance stable errors, for which closed form expressions for the density are not available and hence the maximum likelihood estimate cannot be obtained.We have used combined sine and cosine estimating functions to study estimation. Recently I developed a maximum informative recursive method and applied to financial data. In this proposal, I will also study maximum informative filtering/joint recursive estimation for infinite variance processes using transformation based estimating functions. (c) One of the problems with the implementations of stochastic interest rate models was that the theoretical model prices did not fit the existing observed market prices of bonds. The reason is that at any time there is a vector of current bond prices, and a model with a few parameters simply cannot fit the entire set of bond prices. It is useful to have an interest rate model (with time varying parameters) which can fit the observed prices more accurately. We use the nonparametric estimation method to study bond prices based on recently proposed interest rate models with time varying parameters.

波动性是衡量资产价格在给定时期内预期波动的幅度，波动性越大，风险越高。随机波动率模型的滤波和参数递推估计在金融决策中有着广泛的应用。SV模型通常用于金融应用，因为它们的动态足够灵活，可以对观察到的资产和衍生品价格进行建模。许多实用的决策问题，如投资组合选择和期权定价，本质上是递归的。波动率的推断在期权定价应用中起着重要的作用。在期权定价的基本Black-Scholes-Merton方法中，假设波动率为常数。对数回报率的平方值之间的显著相关性表明，需要在这种恒定波动性之外建立模型。因此，世界上的非线性广义自回归条件异方差（GARCH）建模与非线性随机波动率模型已经出现。从业者在金融和经济学中使用随机系数波动率（RCV）模型。非线性GARCH模型在许多资产市场波动动力学建模中非常流行和有效。本文提出了一种基于数据驱动的期权定价方法，并利用真实的数据证明了GARCH/SV期权定价模型的优越性。(a)在这项建议的研究中，我们研究的随机过程，如高斯模型，最近提出的ACP（自回归条件泊松）/RCV模型，持续时间模型，整数值模型，非线性随机波动模型，循环时间序列模型和半鞅模型的推理问题。连续时间以及离散时间模型的估计函数理论的统一方法将用于获得联合最大信息递归估计/过滤估计，并将应用于期权价格的推断和基于删失数据的推断。(b)人们对具有无穷方差的随机过程越来越感兴趣，例如法马（今年的诺贝尔经济学奖赢家）研究了无穷回归模型的估计和预测。这是由于固有的挑战和理论兴趣提供的非正常稳定的法律，以及可能性，从这些法律构建的过程可能是适当的模型，许多不同的现象。在实践中，任何时间序列，表现出尖锐的尖峰或偶尔爆发的离群观测表明可能使用的模型与稳定的误差具有无穷大的方差。对于具有无穷方差稳定误差的时间序列模型，由于其密度的封闭形式表达式不可得，因而无法得到极大似然估计，本文采用组合正弦和余弦估计函数来研究估计问题。最近，我开发了一个最大信息递归方法，并应用于金融数据。在这个建议中，我还将研究最大信息滤波/联合递归估计无穷方差过程中使用基于变换的估计函数。(c)实施随机利率模型的问题之一是，理论模型价格不适合现有的债券市场价格。原因在于，在任何时候，都存在一个当前债券价格的向量，只有几个参数的模型根本无法拟合整个债券价格集合。有一个利率模型（具有随时间变化的参数）可以更准确地拟合观察到的价格是有用的。我们使用非参数估计方法来研究债券价格的基础上最近提出的利率模型与时变参数。