Long-Range Dependence in the Risk-Neutral Measure for the Market on Lehman Brothers Collapse

This paper discusses the long-range dependence in the risk-neutral stock return process of the S&P 500 index option market. To observe the long-range dependence together with fat-tails, I define the parametric model of fractional Lévy process. Since the continuous time fractional Lévy process allows arbitrage, I use discrete time option pricing model based on the fractional Lévy process. By model calibration, we can capture the long-range dependence in the S&P 500 index option market. The paper finds that the long range dependence becomes stronger for the volatile market caused by the Lehman Brothers Collapse, comparing with other less volatility markets.     

Assessing gender and top-management-team pay in the S&P Mid-Cap and Small-Cap companies using data envelopment analysis

In this study, we use data envelopment analysis (DEA) to study gender equity in top-management-team compensation in the S&P Mid-Cap and Small-Cap companies. We find that female and male executives in these companies receive comparable compensation when controlling for differences in company performance, company size, and company pay philosophy.     

Cost minimization and the stochastic discount factor

It is shown that a cost function subject to internal costs of adjustment induces a stochastic discount factor (pricing kernel) that is a function of random output, input and output prices, existing capital stock, and investment. The only assumption on firm preferences is that they are increasing in current period consumption and future stochastic consumption. This ensures that the firm will always act to minimize current period cost of providing future consumption, and it is the first-order conditions for this cost minimization problem that generate the stochastic discount factor, which itself can be interpreted as the marginal variable cost of varying stochastic output. A cost-based pricing kernel is estimated using annual time-series data on macroeconomic variables and returns data for the S&P 500 and commercial paper.     

Normal tempered stable copula

In this paper, we discuss a copula defined by the Gaussian subordination method. The copula can capture the dependence between extreme events, and asymmetric dependence, which are observed in empirical financial return distributions. We further perform an empirical test for this new copula against the standard Gaussian copula using 10 years daily returns of the Standard&Poor’s 500 (S&P500) and the Deutscher Aktien Index (DAX) equity market indices.     

On idiosyncratic stochasticity of financial leverage effects

We model leverage as stochastic but independent of return shocks and of volatility and perform likelihood-based inference via the recently developed iterated filtering algorithm using S&P500 data, contributing new evidence to the still slim empirical support for random leverage variation.     

N-tuple S&P patterns across decades, 1950–2011

Numerous studies have analyzed the movements of the S&P 500 index using several methodologies such as technical analysis, econometric modeling, time series techniques and theories from behavioral finance. In this paper we take a novel approach. We use daily closing prices for the S&P 500 index for a very long period from 1/3/1950 to 7/19/2011 for a total of 15,488 daily observations. We then investigate the up and down movements and their combinations for 1–7 days giving us multiple possible patterns for over six decades. Some patterns of each type are more dominant across decades. We split the data into training and validation sets and then select the dominant patterns to build conditional forecasts in several ways, including using a decision tree methodology. The best model is correct 51 % of the time on the validation set when forecasting a down day, and 61 % when forecasting an up day. We show that certain conditional forecasts outperform the unconditional random walk model.     

Nonparametric prediction of stock returns based on yearly data: The long-term view

One of the most studied questions in economics and finance is whether empirical models can be used to predict equity returns or premiums. In this paper, we take the actuarial long-term view and base our prediction on yearly data from 1872 through 2014. While many authors favor the historical mean or other parametric methods, this article focuses on nonlinear relationships between a set of covariates. A bootstrap test on the true functional form of the conditional expected returns confirms that yearly returns on the S&P500 are predictable. The inclusion of prior knowledge in our nonlinear model shows notable improvement in the prediction of excess stock returns compared to a fully nonparametric model. Statistically, a bias and dimension reduction method is proposed to import more structure in the estimation process as an adequate way to circumvent the curse of dimensionality.     

Self-criticality and stochasticity of an S&P 500 index time series

In this paper, three time series representative of the daily high, low and closing prices of S&P 500 index time series, as from 1 December 1988 to 1 April 1998 are studied. The hypothesis advanced by Osborne that the stock market time series satisfy a log-normal distribution is rejected. The self-critical behavior of these time series is investigated. A fractional Brownian motion model for such time series is supported. Arguments are directed torwards a negation of a chaotic explanation of these time series.     

Delta hedging strategies comparison

In this paper we implement dynamic delta hedging strategies based on several option pricing models. We analyze different subordinated option pricing models and we examine delta hedging costs using ex-post daily prices of S&P 500. Furthermore, we compare the performance of each subordinated model with the Black–Scholes model.     

Compensation differences between male and female CEOs for publicly traded firms: a nonparametric analysis

A recent article in the popular press suggested that gender is one determining factor of corporate executives' pay. The average compensation for the top 20 men was more than 10 times larger than for the top 20 women. We would expect, however, that direct compensation from salary and bonuses would be similar for both genders given the public nature of the data. There have been few academic articles on the topic of gender pay differences among top executives. One paper found marginally significant statistical evidence that women CEOs are paid more than their male counterparts. In this paper, we extend the literature by looking at compensation differences of male and female CEOs. Our sample includes over 40 female CEOs for publicly traded companies and matched pairs of comparable male CEOs. In addition, we use data envelopment analysis to derive a gap measure representing the difference between male and female compensation. The results suggest that there is a statistical difference between male and female potential compensation.     

Modeling country risk ratings using partial orders

In order to evaluate the creditworthiness of various countries, a learning model is induced from the 1998 Standard and Poor’s country risk ratings, using the 1998 values of nine economic and three political indicators. This learning model allows the construction of a partially ordered set describing the relative superiority of countries on the basis of their creditworthiness, and it is shown that the Condorcet linear extensions of this poset match closely the S&P ratings. Moreover, the ratings derived from the model correlate highly with those of other rating agencies. The model is shown to provide excellent ratings even when applied to the following years’ data or to the ratings of previously unrated countries. Rating changes implemented by S&P in subsequent years resolved most of the (few) discrepancies between the constructed poset and S&P’s initial ratings.     

Data-driven hedging of stock index options via deep learning

We develop deep learning models to learn the hedge ratio for S&P500 index options from options data. We compare different combinations of features and show that with sufficient training data, a feedforward neural network model with time to maturity, the Black-Scholes delta and market sentiment as inputs performs the best in the out-of-sample test under daily hedging. This model significantly outperforms delta hedging and a data-driven hedging model. Our results also demonstrate the importance of market sentiment for hedging.     

Weak convergence of non-stationary multivariate marked processes with applications to martingale testing

This paper establishes the weak convergence of a class of marked empirical processes of possibly non-stationary and/or non-ergodic multivariate time series sequences under martingale conditions. The assumptions involved are similar to those in Brown's martingale central limit theorem. In particular, no mixing conditions are imposed. As an application, we propose a test statistic for the martingale hypothesis and we derive its asymptotic null distribution. Finally, a Monte Carlo study shows that the asymptotic results provide good approximations for small and moderate sample sizes. An application to the S&P 500 is also considered.     

Evaluating capacity management tactics for a legacy manufacturing plant

Robust capacity improvement tactics, namely acquisition of assets and enhanced flexibility in product manufacturing, that alleviate mismatches between required and available capacity are revealed by data analytics. Improvement brought about by these tactics as measured by two performance metrics, production makespan and product availability, is assessed using optimization methodology. This paper demonstrates the value of analysing demand and product specification data to inform capacity re-calibration in an S&P 500 company in the chemical industry. The tactic recommended for implementation, which yielded up to a doubling of the capacity, emerged from an empirical analysis of data for five prototypical planning periods.     

Inducing Stock Screening Rules for Portfolio Construction

This study describes a technique originated from the emerging field of machine learning and demonstrates its effectiveness in stock screening. We have derived screening rules by applying a rule induction method, constructed portfolios using the rules, and evaluated the portfolios' performance using the Sharpe, Treynor and Jensen indexes. Results indicate that regularities among stocks can be identified, and portfolios so constructed outperformed the NYSE Composite index and the S&P 500 over the same period.     

Bayesian Filtering for Jump-Diffusions With Application to Stochastic Volatility

In this article, the problem of sequentially learning parameters governing discretely observed jump-diffusions is explored. The estimation framework involves the introduction of latent points between every pair of observations to allow a sufficiently accurate Euler–Maruyama approximation of the underlying (but unavailable) transition densities. Particle filtering algorithms are then implemented to sample the posterior distribution of the latent data and the model parameters online. The methodology is applied to the estimation of parameters governing a stochastic volatility (SV) model with jumps. As well as using S&P 500 Index data, a simulation study is provided. Supplemental materials for this article are available online.     

Iterative estimation maximization for stochastic linear programs with conditional value-at-risk constraints

We present a new algorithm, iterative estimation maximization (IEM), for stochastic linear programs with conditional value-at-risk constraints. IEM iteratively constructs a sequence of linear optimization problems, and solves them sequentially to find the optimal solution. The size of the problem that IEM solves in each iteration is unaffected by the size of random sample points, which makes it extremely efficient for real-world, large-scale problems. We prove the convergence of IEM, and give a lower bound on the number of sample points required to probabilistically bound the solution error. We also present computational performance on large problem instances and a financial portfolio optimization example using an S&P 500 data set.     

Regime switching volatility calibration by the Baum-Welch method

Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate regime switching models instead. We demonstrate the Baum-Welch algorithm and discuss the significant advantages that it provides compared to the Hamilton filter. We provide computational results of calibrating and comparing the performance of the Baum-Welch and the Hamilton filter to S&P 500 and Nikkei 225 data, examining their performance in and out of sample.     

Simulated likelihood inference for stochastic volatility models using continuous particle filtering

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models: it has the attractive feature of inheriting unconditional properties similar to the standard GARCH model but being conditionally heavier tailed. Second, we propose a likelihood-based inference technique for a large class of SV models relying on the recently introduced continuous particle filter. The approach is robust and simple to implement. The technique is applied to daily returns data for S&P 500 and Dow Jones stock price indices for various spans.     

Estimating value at risk with semiparametric support vector quantile regression

Value at Risk (VaR) has been used as an important tool to measure the market risk under normal market. Usually the VaR of log returns is calculated by assuming a normal distribution. However, log returns are frequently found not normally distributed. This paper proposes the estimation approach of VaR using semiparametric support vector quantile regression (SSVQR) models which are functions of the one-step-ahead volatility forecast and the length of the holding period, and can be used regardless of the distribution. We find that the proposed models perform better overall than the variance-covariance and linear quantile regression approaches for return data on S&P 500, NIKEI 225 and KOSPI 200 indices.