Fitting prices with a complete model

The aim of this paper is to introduce some methodologies for parameter estimation in Hobson and Rogers stochastic volatility model (1998). We pay a specific attention to the so-called feedback parameter, which is shown to be crucial for the model to fit correctly the smile curve of implied volatility and we introduce different procedures for the estimation of the volatility parameters. We finally test the pricing capability of the model on market options prices on the FTSE100 and the S&P500 Indexes, according to the estimation methodologies introduced.     

Parameter estimation risk in asset pricing and risk management: A Bayesian approach

Parameter estimation risk is non-trivial in both asset pricing and risk management. We adopt a Bayesian estimation paradigm supported by the Markov Chain Monte Carlo inferential techniques to incorporate parameter estimation risk in financial modelling. In option pricing activities, we find that the Merton's Jump-Diffusion (MJD) model outperforms the Black-Scholes (BS) model both in-sample and out-of-sample. In addition, the construction of Bayesian posterior option price distributions under the two well-known models offers a robust view to the influence of parameter estimation risk on option prices as well as other quantities of interest in finance such as probabilities of default. We derive a VaR-type parameter estimation risk measure for option pricing and we show that parameter estimation risk can bring significant impact to Greeks' hedging activities. Regarding the computation of default probabilities, we find that the impact of parameter estimation risk increases with gearing level, and could alter important risk management decisions.     

Gradient-based simulated maximum likelihood estimation for Lévy-driven Ornstein–Uhlenbeck stochastic volatility models

This paper studies the parameter estimation problem for Ornstein–Uhlenbeck stochastic volatility models driven by Lévy processes. Estimation is regarded as the principal challenge in applying these models since they were proposed by Barndorff-Nielsen and Shephard [J. R. Stat. Soc. Ser. B, 2001, 63(2), 167–241]. Most previous work has used a Bayesian paradigm, whereas we treat the problem in the framework of maximum likelihood estimation, applying gradient-based simulation optimization. A hidden Markov model is introduced to formulate the likelihood of observations; sequential Monte Carlo is applied to sample the hidden states from the posterior distribution; smooth perturbation analysis is used to deal with the discontinuities introduced by jumps in estimating the gradient. Numerical experiments indicate that the proposed gradient-based simulated maximum likelihood estimation approach provides an efficient alternative to current estimation methods.     

两因子随机死亡率状态空间模型及长寿风险测度

引入状态空间模型对传统两因子CBD模型拟合阶段和预测阶段进行联合建模,并基于卡尔曼滤波方法对模型参数进行估计。进一步考虑到死亡率数据的小样本特征,结合Bootstrap仿真技术和生存年金组合折现模型对长寿风险进行测度。利用1996~2011年数据展开实证研究,结果表明:结合模型解释能力、参数估计结果和误差项正态分布检验结果,两因子状态空间模型要优于传统CBD模型;年金组合规模的扩大可以消除微观长寿风险,但不能消除宏观长寿风险和参数风险;宏观长寿风险占据着不可分散风险的主导地位。     

Risk parity portfolio optimization under a Markov regime-switching framework

We formulate and solve a risk parity optimization problem under a Markov regime-switching framework to improve parameter estimation and to systematically mitigate the sensitivity of optimal portfolios to estimation error. A regime-switching factor model of returns is introduced to account for the abrupt changes in the behaviour of economic time series associated with financial cycles. This model incorporates market dynamics in an effort to improve parameter estimation. We proceed to use this model for risk parity optimization and also consider the construction of a robust version of the risk parity optimization by introducing uncertainty structures to the estimated market parameters. We test our model by constructing a regime-switching risk parity portfolio based on the Fama–French three-factor model. The out-of-sample computational results show that a regime-switching risk parity portfolio can consistently outperform its nominal counterpart, maintaining a similar ex post level of risk while delivering higher-than-nominal returns over a long-term investment horizon. Moreover, we present a dynamic portfolio rebalancing policy that further magnifies the benefits of a regime-switching portfolio.     

Gibbs posterior inference on value-at-risk

ABSTRACT

Accurate estimation of value-at-risk (VaR) and assessment of associated uncertainty is crucial for both insurers and regulators, particularly in Europe. Existing approaches link data and VaR indirectly by first linking data to the parameter of a probability model, and then expressing VaR as a function of that parameter. This indirect approach exposes the insurer to model misspecification bias or estimation inefficiency, depending on whether the parameter is finite- or infinite-dimensional. In this paper, we link data and VaR directly via what we call a discrepancy function, and this leads naturally to a Gibbs posterior distribution for VaR that does not suffer from the aforementioned biases and inefficiencies. Asymptotic consistency and root-n concentration rate of the Gibbs posterior are established, and simulations highlight its superior finite-sample performance compared to other approaches.     

Sequential estimation problems for the scale parameter of a Pareto distribution

Abstract

The Pareto distribution plays a central role in many areas of econometrics. So, we first consider sequential point estimation problems for the scale parameter of a Pareto distribution. Under a very general loss structure, we derive several asymptotic results regarding the associated “risk” and “regret” functions. Then, we consider the problem of constructing a fixed-ratio confidence interval for the scale parameter, and we propose various sampling techniques to achieve the intended goal. Most of our theoretical findings are asymptotic in nature for either problem, and thus we have presented extensive simulation studies to examine moderate sample performances of all the procedures. The findings in the point estimation problem are also supposed to fill many important gaps left in the paper of Wang (1973).     

Predictive regression: An improved augmented regression method

This paper proposes three modifications to the augmented regression method (ARM) for bias-reduced estimation and statistical inference in the predictive regression. They are in relation to improved bias-correction, stationarity-correction, and the use of matrix formulae for bias-correction and covariance matrix estimation. The improved ARM parameter estimators are unbiased to the order of n^− 1, and always satisfy the condition of stationarity. With the matrix formulae, the improved ARM can easily be implemented for a high order model with multiple predictors. From an extensive Monte Carlo experiment, it is found that the improved ARM delivers substantial gain in parameter estimation, statistical inference, and out-of-sample forecasting in small samples. As an application, the improved ARM is applied to monthly US stock return data to evaluate the predictive power of dividend yield in univariate and bivariate predictive models.     

Understanding Delta-Hedged Option Returns in Stochastic Volatility Environments

In this paper, we provide a novel representation of delta-hedged option returns in a stochastic volatility environment. The representation of delta-hedged option returns provided in this paper consists of two terms: volatility risk premium and parameter estimation risk. In an empirical analysis, we examine delta-hedged option returns based on the result of a historical simulation with the USD-JPY currency option market data from October 2003 to June 2010. We find that the delta-hedged option returns for OTM put options are strongly affected by parameter estimation risk as well as the volatility risk premium, especially in the post-Lehman shock period.     

The flexible coefficient multinomial logit (FC‐MNL) model of demand for differentiated products

We show FC‐MNL is flexible in the sense of Diewert ( 1974 ), thus its parameters can be chosen to match a well‐defined class of possible own‐ and cross‐price elasticities of demand. In contrast to models such as Probit and Random Coefficient‐MNL models, FC‐MNL does not require estimation via simulation; it is fully analytic. Under well‐defined and testable parameter restrictions, FC‐MNL is shown to be an unexplored member of McFadden's class of Multivariate Extreme Value discrete‐choice models. Therefore, FC‐MNL is fully consistent with an underlying structural model of heterogeneous, utility‐maximizing consumers. We provide a Monte‐Carlo study to establish its properties and we illustrate its use by estimating the demand for new automobiles in Italy.     

Jackknife empirical likelihood for parametric copulas

For fitting a parametric copula to multivariate data, a popular way is to employ the so-called pseudo maximum likelihood estimation proposed by Genest, Ghoudi, and Rivest. Although interval estimation can be obtained via estimating the asymptotic covariance of the pseudo maximum likelihood estimation, we propose a jackknife empirical likelihood method to construct confidence regions for the parameters without estimating any additional quantities such as the asymptotic covariance. A simulation study shows the advantages of the new method in case of strong dependence or having more than one parameter involved.     

Unconditional return disturbances: A non-parametric simulation approach

Simulation methods are extensively used in Asset Pricing and Risk Management. The most popular of these simulation approaches, the Monte Carlo, requires model selection and parameter estimation. In addition, these approaches can be extremely computer intensive. Historical simulation has been proposed as a non-parametric alternative to Monte Carlo. This approach is limited to the historical data available.In this paper, we propose an alternative historical simulation approach. Given a historical set of data, we define a set of standardized disturbances and we generate alternative price paths by perturbing the first two moments of the original path or by reshuffling the disturbances. This approach is either totally non-parametric when constant volatility is assumed; or semi-parametric in presence of GARCH(1, 1) volatility. Without a loss in accuracy, it is shown to be much more powerful in terms of computer efficiency than the Monte Carlo approach. It is also extremely simple to implement and can be an effective tool for the valuation of financial assets.We apply this approach to simulate pay off values of options on the S&P 500 stock index for the period 1982–2003. To verify that this technique works, the common back-testing approach was used. The estimated values are insignificantly different from the actual S&P 500 options payoff values for the observed period.     

小波分析结合ARIMA组合模型的2014~2017年石油贸易量预测研究

选取2002~2013年我国石油进出口贸易量的数据进行建模分析。首先运用小波分析理论将贸易量数据进行分解,识别出数据的主要特征和细节特征,针对不同特征进行识别和平稳性检测和参数估计,建立相应的ARIMA模型,并进行预测加权合成。仿真结果表明,小波分析结合ARIMA组合模型的预测精度远远大于为改进的ARIMA预测模型,从而为科学合理的决策提供更为精确的预测模型。     

A solution to an estimation problem involving models with rational expectations

Recently Flood and Garber (1980) have shown that the use of Fair's (1970) estimation technique in the context of a rational expectations errors in variables model yields inconsistent parameter estimates. In this paper we explain why this happens and suggest two consistent estimation procedures.     

Forecasting trends with asset prices

The question of interest in this paper is the estimation of the trend of a financial asset, and the impact of its misspecification on investment strategies. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein–Uhlenbeck process. Motivated by the use of Kalman filtering as a forecasting tool, we address the problem of parameter estimation, and measure the effect of parameter misspecification. Numerical examples illustrate the difficulty of trend forecasting in financial time series.     

Bayesian comparison of several continuous time models of the Australian short rate

This paper provides an empirical analysis of a range of alternative single‐factor continuous time models for the Australian short‐term interest rate. The models are nested in a general single‐factor diffusion process for the short rate, with each alternative model indexed by the level effect parameter for the volatility. The inferential approach adopted is Bayesian, with estimation of the models proceeding through a Markov chain Monte Carlo simulation scheme. Discrimination between the alternative models is based on Bayes factors. A data augmentation approach is used to improve the accuracy of the discrete time approximation of the continuous time models. An empirical investigation is conducted using weekly observations on the Australian 90 day interest rate from January 1990 to July 2000. The Bayes factors indicate that the square root diffusion model has the highest posterior probability of all models considered.     

Multivariate Tweedie lifetimes: the impact of dependence

Systematic longevity risk is increasingly relevant for public pension schemes and insurance companies that provide life benefits. In view of this, mortality models should incorporate dependence between lives. However, the independent lifetime assumption is still heavily relied upon in the risk management of life insurance and annuity portfolios. This paper applies a multivariate Tweedie distribution to incorporate dependence, which it induces through a common shock component. Model parameter estimation is developed based on the method of moments and generalized to allow for truncated observations. The estimation procedure is explicitly developed for various important distributions belonging to the Tweedie family, and finally assessed using simulation.     

Statistical tests of contingent-claims asset-pricing models: A new methodology

A new methodology for statistically testing contingent-claims asset-pricing models based on asymptotic statistical theory is proposed. It is introduced in the context of the Black-Scholes option-pricing model, for which some illustrative estimation, inference, and simulation results are also presented. The proposed methodology is then extended to arbitrary contingent claims by first considering the estimation problem for general Itô processes and then deriving the asymptotic distribution of a general contingent claim which depends upon such Itô processes.     

How much should portfolios shrink?

This paper develops a portfolio model that penalizes the deviation from a reference portfolio. The proposed model renders a robust portfolio that performs superior under parameter uncertainty. Penalizing the deviation also improves the performance of existing shrinkage portfolio models that are suboptimal due to model parameter uncertainty. The equal-weight portfolio turns out to be a better reference portfolio than the currently holding portfolio even in the presence of transaction costs. A data-driven method for determining the degree of penalization is offered. Comprehensive simulation and empirical studies suggest that the proposed model significantly outperforms various existing models.