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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=611720
• 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.

波动率是一种衡量资产价格在给定时期内预期波动幅度的指标。 而且波动性越大，风险就越高。随机变量的滤波和递推参数估计 波动率(SV)模型在金融决策中有着广泛的应用。Sv型号是常用的 在金融应用中，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。 许多应用决策问题，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具有重要作用。持续的波动性一直是 在期权定价的基本Black-Scholes-Merton方法中假定。它们之间存在显著的相关性 对数的平方值返回需要在此恒定波动性之外建模的点。因此， 非线性广义自回归条件异方差(GARCH)共同建模 伴随着非线性随机波动率模型应运而生。 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 在许多资产市场中，模型一直是非常流行和有效的波动动态建模方法。 我们开发了一种数据驱动的期权定价方法，并证明了GARCH/SV的优越性 使用真实数据的期权定价模型。 (A)在这项拟议的研究中，我们研究随机过程的推断问题，例如GARCH模型， 最近提出的ACP(自回归条件泊松)/RCV模型，久期模型，整数 值型模型、非线性随机波动率模型、循环时间序列模型和半鞅模型。 对于连续时间和离散时间模型，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 从期权价格到基于删节数据的推论。 (B)人们对具有无穷方差的随机过程越来越感兴趣，例如FAMA (今年诺贝尔计量经济模型奖获得者)研究了无限回归的估计和预测 模特们。这是由于非正态稳定定律所带来的内在挑战和理论兴趣。 以及根据这些定律构建的过程可能是许多合适的模型 多样的现象。在实践中，任何时间序列表现出急剧的尖峰或偶尔的边远突发 观测结果表明，可以使用具有无穷大方差的稳定误差的模型。对于时间序列 具有无穷方差稳定误差的模型，其密度的闭合形式表达式不可用 因此不能得到最大似然估计。我们使用了组合的正弦和余弦 估计函数，用于研究估计。最近，我开发了一种最大信息量递归方法 并应用于金融数据。在本提案中，我还将研究最大信息过滤/联合递归 利用基于变换的估计函数对无穷大方差过程进行估计。 (C)实施随机利率模型的问题之一是，理论上 模型价格与现有观察到的债券市场价格不符。原因是，在任何时候都会有一个 当前债券价格的向量，只有几个参数的模型根本不能适应整个债券价格集。 有一个利率模型(带有时变参数)是有用的，它可以更好地适应观察到的价格。 准确地说。我们使用非参数估计方法来研究债券价格，这是基于最近提出的 具有时变参数的利率模型。