A Stochastic Volatility Model With Realized Measures for Option Pricing

Abstract

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options.     

An analytical approximation method for pricing barrier options under the double Heston model

Abstract

The purpose of the paper is to provide an efficient pricing method for single barrier options under the double Heston model. By rewriting the model as a singular and regular perturbed BS model, the double Heston model can separately mimic a fast time-scale and a slow time-scale. With the singular and regular perturbation techniques, we analytically derive the first-order asymptotic expansion of the solution to a barrier option pricing partial differential equation. The convergence and efficiency of the approximate method is verified by Monte Carlo simulation. Numerical results show that the presented asymptotic pricing method is fast and accurate.     

Stochastic Spanning

ABSTRACT

This study develops and implements methods for determining whether introducing new securities or relaxing investment constraints improves the investment opportunity set for all risk averse investors. We develop a test procedure for “stochastic spanning” for two nested portfolio sets based on subsampling and linear programming. The test is statistically consistent and asymptotically exact for a class of weakly dependent processes. A Monte Carlo simulation experiment shows good statistical size and power properties in finite samples of realistic dimensions. In an application to standard datasets of historical stock market returns, we accept market portfolio efficiency but reject two-fund separation, which suggests an important role for higher-order moment risk in portfolio theory and asset pricing. Supplementary materials for this article are available online.     

Perspectives on Job Stress in the Serials Information World

Abstract

Adam Chesler describes his experiences and observations of job stress in the serials publishing industry. While stresses, such as the challenges of supervision have always existed, others are new, such as serial publishers scrambling to adapt service and pricing models for providing Internet content. Advice is offered on coping with these stresses.     

Multi-modal tempered stable distributions and prosses with applications to finance

Abstract

The assumption of underlying return distribution plays an important role in asset pricing models. While the return distribution used in the traditional theories of asset pricing is the unimodal distribution, numerous studies which have investigated the empirical behavior of asset returns in financial markets use multi-modal distribution. We introduce a new parsimonious multi-modal distribution, referred to as the multi-modal tempered stable (MMTS) distribution. In this article we also generate the exponential Lévy market models and derive the value-at-risk (VaR) induced from them. To demonstrate the advantages, we will present the results of the parameter estimation and the VaRs for financial data.     

Empirical Performance and Asset Pricing in Hidden Markov Models

Abstract

To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address leptokurtic feature, volatility smile, and volatility clustering effects of the asset return distributions. However, analytical tractability remains a problem for most alternative models. In this article, we study a class of hidden Markov models including Markov switching models and stochastic volatility models, that can incorporate leptokurtic feature, volatility clustering effects, as well as provide analytical solutions to option pricing. We show that these models can generate long memory phenomena when the transition probabilities depend on the time scale. We also provide an explicit analytic formula for the arbitrage-free price of the European options under these models. The issues of statistical estimation and errors in option pricing are also discussed in the Markov switching models.     

Pricing longevity-linked derivatives using a stochastic mortality model

Abstract

We propose a 2-factor MBMM model with exponential Lévy process to develop a stochastic mortality process. The two components are fitted by two independent NIG distributions. Compared to Lee–Carter model or 1-factor MBMM model, our mortality model explains more variation and improves the goodness of fit by including the second time component. Based on the improved model, we price three longevity-linked financial instruments, namely the longevity bond, q-forward and s-forward. The pricing is demonstrated on English and Welsh males aged 65 in 2013. Results indicate that the 2-factor MBMM model gives the highest price for mortality-related type of contract.     

Pareto Regression: A Bayesian Analysis

Abstract

In this article, a new model is presented that is based on the Pareto distribution of the second kind, when the location parameter depends on covariates as well as unobserved heterogeneity. Bayesian analysis of the model can be performed using Markov Chain Monte Carlo techniques. The new procedures are illustrated in the context of artificial data as well as international output data.     

On a nonlinear Birnbaum–Saunders model based on a bivariate construction and its characteristics

Abstract

The Birnbaum-Saunders (BS) distribution is an asymmetric probability model that is receiving considerable attention. In this article, we propose a methodology based on a new class of BS models generated from the Student-t distribution. We obtain a recurrence relationship for a BS distribution based on a nonlinear skew–t distribution. Model parameters estimators are obtained by means of the maximum likelihood method, which are evaluated by Monte Carlo simulations. We illustrate the obtained results by analyzing two real data sets. These data analyses allow the adequacy of the proposed model to be shown and discussed by applying model selection tools.     

New shrinkage-type estimators in a linear regression model when multicollinearity is severe

For the linear regression model y=Xβ+e with severe multicollinearity, we put forward three shrinkage-type estimators based on the ordinary least-squares estimator including two types of independent factor estimators and a seemingly convex combination. The simulation study shows that the new estimators are not good enough when multicollinearity is mild to moderate, but perform very well when multicollinearity is severe to very severe.     

Extended binomial AR(1) processes with generalized binomial thinning operator

Abstract

In this article, we introduce an extended binomial AR(1) model based on the generalized binomial thinning operator. This operator relaxes the independence assumption of the binomial thinning operator and contains dependent Bernoulli counting series. The new model contains the binomial AR(1) model as a particular case. Some probabilistic and statistical properties are explored. Estimators of the model parameters are derived by conditional maximum likelihood (CML), conditional least squares (CLS) and weighted conditional least squares (WCLS) methods. Some asymptotic properties and numerical results of the estimators are studied. The good performance of the new model is illustrated, among other competitive models in the literature, by an application to the monthly drunken driving counts.     

The exponentiated-log-logistic geometric distribution: Dual activation

ABSTRACT

The log-logistic distribution is commonly used to model lifetime data. We propose a wider distribution, named the exponentiated log-logistic geometric distribution, based on a double activation approach. We obtain the quantile function, ordinary moments, and generating function. The method of maximum likelihood is used to estimate the model parameters. We propose a new extended regression model based on the logarithm of the exponentiated log-logistic geometric distribution. This regression model can be very useful in the analysis of real data and could provide better fits than other special regression models. The potentiality of the new models is illustrated by means of two applications to real lifetime data sets.     

Valuation of contingent claims with stochastic interest rate and mortality driven by Lévy processes

Abstract

In this paper, we consider a model with stochastic interest rate and stochastic mortality, which is driven by a Lévy process. Under the assumption that the stochastic mortality and interest rate are dependent, we discuss the valuation of life insurance contracts. Employing the method of change of measure together with the Bayes’ rule, we present the pricing formulas in closed form for the survival and death benefit models. Finally, numerical experiments illustrate the effects of some parameters.     

Valuing equity-indexed annuities with icicled barrier options

Inspired by the recent popularity of autocallable structured products, this paper intends to enhance equity-indexed annuities (EIAs) by introducing a new class of barrier options, termed icicled barrier options. The new class of options has a vertical (icicled) barrier along with the horizontal one of the ordinary barrier options, which may act as an additional knock-in or knock-out trigger. To improve the crediting method of EIAs, we propose a new EIA design, termed autocallable EIA, with payoff structure similar to the autocallable products except for the minimum guarantee, and further investigate the possibility of embedding various icicled barrier options into the plain point-to-point or the ratchet EIAs. Explicit pricing formulas for the proposed EIAs and the icicled barrier options are obtained under the Black–Scholes model. To the purpose, we derive the joint distribution of the logarithmic returns at the icicled time and the maturity, and their running maximum. As an application of the well-known reflection principle, the derivation itself is an interesting probability problem and the joint distribution plays a key role in the subsequent pricing stage. Our option pricing result can be easily transferred to EIAs or other equity-linked products. The pricing formulas for the EIAs and the options are illustrated through numerical examples.     

Statistical inference for oscillation processes

ABSTRACT

A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonparametric curve characterizing the pattern, leading together to a generalized state space model. Identifiability of the model is proved and a method for statistical inference based on a particle smoother and a nonparametric EM algorithm is developed. In particular, the oscillation pattern and the unobserved phase process are estimated. The proposed algorithms are computationally efficient and their performance is assessed through simulations and an application to human electrocardiogram recordings.     

A new semiparametric Weibull cure rate model: fitting different behaviors within GAMLSS

ABSTRACT

We propose a new semiparametric Weibull cure rate model for fitting nonlinear effects of explanatory variables on the mean, scale and cure rate parameters. The regression model is based on the generalized additive models for location, scale and shape, for which any or all distribution parameters can be modeled as parametric linear and/or nonparametric smooth functions of explanatory variables. We present methods to select additive terms, model estimation and validation, where all computational codes are presented in a simple way such that any R user can fit the new model. Biases of the parameter estimates caused by models specified erroneously are investigated through Monte Carlo simulations. We illustrate the usefulness of the new model by means of two applications to real data. We provide computational codes to fit the new regression model in the R software.     

Generalized modified slash distribution with applications

Abstract

In this article a generalization of the modified slash distribution is introduced. This model is based on the quotient of two independent random variables, whose distributions are a normal and a one-parameter gamma, respectively. The resulting distribution is a new model whose kurtosis is greater than other slash distributions. The probability density function, its properties, moments, and kurtosis coefficient are obtained. Inference based on moment and maximum likelihood methods is carried out. The multivariate version is also introduced. Two real data sets are considered in which it is shown that the new model fits better to symmetric data with heavy tails than other slash extensions previously introduced in literature.     

Robust bootstrap densities for dynamic conditional correlations: implications for portfolio selection and Value-at-Risk

ABSTRACT

Many financial decisions such as portfolio allocation, risk management, option pricing and hedge strategies are based on the forecast of the conditional variances, covariances and correlations of financial returns. Although the decisions depend on the forecasts covariance matrix little is known about effects of outliers on the uncertainty associated with these forecasts. In this paper we analyse these effects on the context of dynamic conditional correlation models when the uncertainty is measured using bootstrap methods. We also propose a bootstrap procedure to obtain forecast densities for return, volatilities, conditional correlation and Value-at-Risk that is robust to outliers. The results are illustrated with simulated and real data.     

Pricing of Digital Resources

Abstract

In this interview, Simon Tanner, senior consultant with Higher Education Digitization Services at the University of Hertfordshire in the United Kingdom, discusses the economics and market issues related to pricing of digital resources. Serials Review 2003; 29:121–126.