Long-run Mean Research Articles

Persistence or reversal? The effects of abnormal trading volume on stock returns

Having established that portfolios derived from the extreme deciles of Abnormal Trading Volume (ATV) generate positive (negative) returns in the short (long) run, we devise a measure of Persistence in ATV (PATV) and provide an investor sentiment-based explanation for this return predictability. PATV leads to portfolio returns continuing to drift in the short run. However, the trading volumes of individual stocks in the portfolios gradually revert to their long-run means, accompanied by portfolio returns falling and turning negative as mispricing is corrected. We dismiss liquidity shocks, continuing overreaction, and investor disagreement and attention as explanations for the observed return predictability.

Overextrapolation of disaster probabilities and asset pricing in a production economy

In this paper, the overextrapolation belief about the jump intensity of disaster risk is incorporated into an equilibrium asset pricing model in a production economy. The theoretical results, which are dependent on the level of the jump intensity, show that overextrapolation may induce over/underinvestment and under/overconsumption. Moreover, it is predicted that the overextrapolative agent will always overreact on investment and consumption, which results in higher volatility in the economy and generates a higher equity risk premium under the equilibrium model. However, the effects of overextrapolation on the interest rate are ambiguous. Finally, we find that the overextrapolative agent suffers significant welfare loss due to the distortion of investment and consumption, especially when the jump intensity is far from the long-run mean.

Delta hedging and volatility-price elasticity: A two-step approach

We incorporate a time-varying negative relationship for implied volatility and underlying price into the delta hedging problem, where traders aim to minimize the variance of changes in the value of an option position by trading an appropriate amount of the underlying asset. We show that volatility-price elasticity is mean-reverting and embed predictions of the elasticity in a hedge ratio model that incorporates the negative volatility-price relationship. Our tests show that when applied to index options data, the proposed approach improves hedging performance over methods that rely solely on the long-run mean of the volatility-price relationship.

Comparison of the Performances for the Mean-Reversion Strategy for Exchange Rate

Mean-reversion theory predicts that historical returns and asset price volatility will eventually return to the long-run mean or average level of the entire dataset. The mean-reversion strategy applies the fundamental idea of selling high and attracting low to stock market investment. Researchers studying the international exchange market have shown that foreign exchange rates display momentum and mean reversion behavior. This study aims to assess the effectiveness of the mean-reversion approach on exchange rates and improve it. Using historical data, the author assessed the mean-reversion method's impact on the exchange rate. According to the study, the method offers a risk-to-reward ratio that is conservative. The clear disadvantage is that for most of the exchange rate, mean-reversion methods yield lesser profits. Furthermore, the return is significantly influenced by the mean-reversion lookback period. Quantitatively, exchange rates with significant volatility and variation often outperform when using the mean-reversion approach. Overall, these results shed light on guiding further exploration of mean-revision strategy.

The Impact of Climate Change on Gender Inequality in the Labour Market: A Case Study of South Africa

South Africa has been exposed to climate change and has been experiencing associated extreme climatic events such as droughts, floods, and heat waves. These have impacted water and fuel sources, habitats, human health, and economic productivity. Poorer populations and particularly females are more affected. The main objective of this study is therefore to assess gender inequalities in employment resultant from the effects of climate change and extreme climatic events. The study employs binary, ordered, and multinomial logistic models to analyse the effects on employment, intensity of employment and the effects in economic sectors, respectively. The study computes temperature deviations from its long-run mean as climate change variable and uses the Keetch–Byram Drought Index and number of heatwave days per year as proxies for extreme climatic events. Data for the work are from the South African Weather Services database and the National Income Dynamic Survey. The findings suggest that climate change reduces the probability of being employed more for males than females, but extreme events have more negative effects on female employment than males. We suggest that while climate change mitigations and adaptation measures geared towards the labour market should take priority in general, when extreme climate events occur, labour market support measures should weigh more towards females.

A new nonlinear stochastic volatility model with regime switching stochastic mean reversion and its applications to option pricing

We establish a new nonlinear stochastic volatility model by modeling the volatility long-run mean with a particular stochastic process, whose parameters can jump between different regimes according to a Markov chain. Introducing the regime switching factor is consistent with the empirical evidence of the economic cycle and nonlinear volatility mean-reversion observed from market data. A closed-form solution that can be used to value European options has been successfully obtained based on the characteristic function approach, followed by some numerical examples comparing the models with and without regime switching.

Closed-form pricing formulas for variance swaps in the Heston model with stochastic long-run mean of variance

The Heston model is a popular stochastic volatility model in mathematical finance and it has been extended or modified in several ways by researchers to overcome the shortcomings of the model in the context of pricing derivatives. However, the extended models usually do not lead to a closed-form formula for the derivative prices. This paper is focused on a stochastic extension of the constant long-run mean of variance in the Heston model for the pricing of variance swaps. The extension is given by a positive function perturbed by an amplitude-modulated Brownian motion or Ito integral. We obtain two closed-form formulas for the fair strike prices of a variance swap under two corresponding underlying models. The formulas are explicitly given by elementary functions without any integral terms involved. Further, the two models show better performance than the Heston model when the market implied volatility has a concave-down pattern as shown in an unstable market circumstance caused by the COVID-19 pandemic.

Bayesian Filtering for Dynamic Anomaly Detection and Tracking

This article presents a Bayesian approach for sequential detection of anomalies in the motion of a target and joint tracking. The anomaly is modeled as a binary (on/off) switching unknown control input that goes into action (begins to exist, or “switches on”) thereby modifying the object dynamics; and by ceasing its activity (becoming nonexistent, or “switching off”) returns the dynamics to nominal. The developed Bayesian framework brings together random finite set (RFS) theory to represent the switching nature of the anomaly, and optimal joint input and state estimation to sequentially update a hybrid state that incorporates a random vector for the kinematic state and a Bernoulli RFS for the unknown control input. In addition, a closed-form solution, the Gaussian-mixture hybrid Bernoulli filter (GM-HBF), has been developed to provide a customized solution for dynamic anomaly detection in the maritime domain characterized by linear Gaussian target dynamics. Based on the Ornstein–Uhlenbeck dynamic model for vessels, where the evolution of the object velocity is governed by a piecewise mean-reverting stochastic process, the anomaly can be represented by a change in the long-run mean velocity (i.e., the unknown control input) from the nominal condition that forces the vessel to deviate from its standard route. We demonstrate the effectiveness of the proposed GM-HBF in both simulated and real-world maritime surveillance applications and test its performance in the face of false measurements, detection uncertainty, and sensor data gaps.

The quantity theory of stock prices

ABSTRACT We determine the implications of the Modern Quantity Theory of Money for the nominal pricing of equity stocks. Our analysis is compatible with the hypothesis that the ratio of the quantity of money in circulation to a comprehensive index of stock prices evolves in terms of an elastic (that is, mean reverting) random walk. Using annual U.S. data covering the period from 1871 until 2018 shows that the ‘half-life’ of the period it takes for the money to stock price ratio to converge towards its long-run mean, is around fifteen years. Our empirical analysis also shows that unexpected inflation has a disruptive impact on the output and investment decisions implemented by firms and leads to an increase in the money to stock price ratio (equivalently, the stock price index falls relative to the quantity of money in circulation). We also develop a framework for determining how economic agents can rebalance their investment portfolios in response to disequilibria in the money to stock price ratio and thereby maximise the expected discounted utility obtained from their future consumption.

Time Discretized Variational Iteration Method for the Stochastic Volatility Process with Jumps

A model for both stochastic jumps and volatility for equity returns in the area of option pricing is the stochastic volatility process with jumps (SVPJ). A major advantage of this model lies in the area of mean reversion and volatility clustering between returns and volatility with uphill movements in price asserts. Thus, in this article, we propose to solve the SVPJ model numerically through a discretized variational iteration method (DVIM) to obtain sample paths for the state variable and variance process at various timesteps and replications in order to estimate the expected jump times at various iterates resulting from executing the DVIM as n increases. These jumps help in estimating the degree of randomness in the financial market. It was observed that the average computed expected jump times for the state variable and variance process is moderated by the parameters (variance process through mean reversion), Θ (long-run mean of the variance process), σ (volatility variance process) and λ (constant intensity of the Poisson process) at each iterate. For instance, when = 0.0, Θ = 0.0, σ = 0.0 and λ = 1.0, the state variable cluttered maximally compared to the variance process with less volatility cluttering with an average computed expected jump times of 52.40607869 as n increases in the DVIM scheme. Similarly, when = 3.99, Θ = 0.014, σ = 0.27 and λ = 0.11, the stochastic jumps for the state variable are less cluttered compared to the variance process with maximum volatility cluttering as n increases in the DVIM scheme. In terms of option pricing, the value 52.40607869 suggest a better bargain compared to the value 20.40344029 due to the fact that it yields less volatility rate. MAPLE 18 software was used for all computations in this research.

An analytical option pricing formula for mean-reverting asset with time-dependent parameter

We present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided. doi:10.1017/S1446181121000262

Testing the Predictive Ability of Possibly Persistent Variables under Asymmetric Loss

Tests of no predictability under an asymmetric power loss function are considered. While this task does not pose difficulties for stationary predictors, non-standard limiting distributions may arise for standard inferential tools when the putative predictors are endogenous (i.e. there is contemporaneous dependence between the shocks of the regressor and of the dependent variable) and of high persistence (i.e. the predictor is reverting slowly to its long-run mean, if at all). It is argued that endogeneity should be interpreted in relation to the relevant loss-function; thus, no endogeneity under MSE loss does not imply, and is not implied by, lack of endogeneity under an asymmetric loss function. To deal with other loss functions than the MSE loss, an overidentified instrumental variable-based test is proposed. The test statistic uses an instrument of high persistence, yet exogenous, and a possibly endogenous one, yet less persistent. The statistic follows a limiting null chi-squared distribution irrespective of the actual degree of persistence of the predictor. The proposed methodology is applied with the forward premium puzzle by providing evidence that asymmetric losses are of empirical relevance and by subsequently conducting robust inference of the rational expectations hypothesis.

Modeling Wind Speed Based on Fractional Ornstein-Uhlenbeck Process

The primary task of the design and feasibility study for the use of wind power plants is to predict changes in wind speeds at the site of power system installation. The stochastic nature of the wind and spatio-temporal variability explains the high complexity of this problem, associated with finding the best mathematical modeling which satisfies the best solution for this problem. In the known discrete models based on Markov chains, the autoregressive-moving average does not allow variance in the time step, which does not allow their use for simulation of operating modes of wind turbines and wind energy systems. The article proposes and tests a SDE-based model for generating synthetic wind speed data using the stochastic differential equation of the fractional Ornstein-Uhlenbeck process with periodic function of long-run mean. The model allows generating wind speed trajectories with a given autocorrelation, required statistical distribution and provides the incorporation of daily and seasonal variations. Compared to the standard Ornstein-Uhlenbeck process driven by ordinary Brownian motion, the fractional model used in this study allows one to generate synthetic wind speed trajectories which autocorrelation function decays according to a power law that more closely matches the hourly autocorrelation of actual data. In order to demonstrate the capabilities of this model, a number of simulations were carried out using model parameters estimated from actual observation data of wind speed collected at 518 weather stations located throughout Russia.

Pricing power exchange options with default risk, stochastic volatility and stochastic interest rate

This paper investigates the pricing issue of power exchange options with default risk, in which the dynamics of the underlying assets and the counterparty asset follow three correlated stochastic volatility models with stochastic interest rate. We assume that the volatility risk is decomposed into short-term and long-term volatility. The stochastic interest rate is driven by the CIR (Cox-Ingersoll-Ross) process. Based on the proposed model, we derive a closed-form solution for the price of power exchange option with default risk by means of Fourier transform. Besides, the price of power exchange option with default risk can be quickly computed by employing the fast Fourier transform (FFT) algorithm. The results of Monte Carlo simulations demonstrate that the FFT is fast and accurate. More importantly, the pricing model also shows that: (i) a higher long-run mean of the underlying asset price's instantaneous variance induces a higher value of power exchange option with default risk; (ii) the long-run mean of instantaneous variance in counterparty's asset value has a negative impact on the price of power exchange option with default risk; and (iii) the higher the long-run mean of stochastic interest rate, the higher the power exchange option price.

Mean-Reversion in Commodity Futures Volatility: An Analysis of Daily Range-Based Stochastic Volatility Models

We analyse the dynamic behavior of conditional volatility in commodity markets using a novel, manually collected dataset of daily price ranges over a time span of more than 140 years, which allows more precise daily volatility estimates than are otherwise prevalent in the commodity literature. We find that a one-factor range-based EGARCH-model (REGARCH) is not adequate to capture the very distinct long-run and short-run dynamic volatility components. While the long memory effect of volatility is numerically very small, it strongly affects the parameters of the short-run dynamics which become more stable and plausible in size. Moreover, long-run persistency in volatility shocks is practically unaffected after controlling for regimes which indicates that the stochastic movement of the long-run mean is not a statistical artefact. We also find that consistent with the theory of storage, long run volatility is positively related to lagged returns. Thus, asymmetry in volatility is not a short-run phenomenon.

AN ANALYTICAL OPTION PRICING FORMULA FOR MEAN-REVERTING ASSET WITH TIME-DEPENDENT PARAMETER

AbstractWe present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided.

Mapping the sensitivity of agriculture to drought and estimating the effect of irrigation in the United States, 1950–2016

Drought is a devastating natural hazard posing great threats to agriculture. Identifying the spatial pattern of agricultural sensitivity to drought can provide scientific information for decision-makers to prepare droughts, allocate resources, and mitigate impacts. Here, we use long-term state- and county-level crop data for the 10 major crops: corn grain, soybeans, hay, spring wheat, winter wheat, cotton, corn silage, sorghum, barley, and rice in the United States from 1950 to 2016. First, we perform a correlation analysis between crop yield anomalies and two drought indices (Standardized Precipitation Evapotranspiration Index (SPEI) and Standardized Precipitation Index (SPI)) to identify the sub-seasonal pattern of agricultural sensitivity to drought stress. SPEI performs better than SPI. For most crops, the sensitivity to drought increases in the early period, peaks at the critical months, and then declines. July is the most critical month for crop growth for most crops. Among all crops, soybean and corn grain are most sensitive to drought. Second, we develop an Agriculture Drought Sensitivity Index (ADSI) to quantitatively measure the sensitivity of agriculture to drought stress based on the statistical relationship between the ten major crops and SPEI. We demonstrate that there exists a very strong spatial correspondence between higher sensitivity to drought and the lower percentage of acres irrigated, and vice versa. Also, for those regions with limited irrigation, the sensitivity is higher in arid/semi-arid regions and lower in humid regions in summer. Third, given the importance of irrigation, an analysis of covariance (ANCOVA) shows that the irrigated crop yields have much higher long-run mean yields than non-irrigated crop yields. Fourth, to investigate how irrigation affects drought sensitivity, a panel data regression model shows that the responses of crop growth to drought are non-linear for all crops. Non-irrigated crops are more sensitive to droughts than the irrigated crops, particularly in severe drought conditions. This provides quantitative incentive to use irrigation as an important adaptation and coping strategy to mitigate the drought impacts on agriculture in the US.

Minimizing Mean Response Time in Nonobservable Distributed Processing Systems with Nodes Operating under Egalitarian Processor-Sharing Policy

Abstract—Consideration is given to the dispatching problem in an almost nonobservable distributed processing system with M, M ≥ 2, single-server queues operating in parallel, each under the processor-sharing discipline. Jobs having the same job size distribution arrive one-by-one to the dispatcher, which immediately routes it to one of the queues. When making a routing decision, the dispatcher has no online information about the system (like current queues sizes, size of arriving job, etc.). The only information available to the dispatcher is job-size distribution, job-interarrival-time distribution, server speeds, time instants of previously arrived jobs, and previous routing decisions. Under these conditions, one is interested in the routing policies that minimize the job long-run mean response time. A new class of dispatching policies is proposed that, according to the numerical experiments, may significantly outperform all classical dispatching policies available for such system: (optimal) probabilistic policy and the round-robin policy.

Fundamentals versus speculation in oil market: The role of asymmetries in price adjustment?

The recent literature on financialisation of oil markets highlights the destabilizing impact of speculative activity on the oil price formation. Time-series studies using linear unit root tests might suggest absence of long-run mean reversion in oil prices, implying dominance of speculation over fundamental factors. However, the price adjustment could take a nonlinear form due to certain characteristics inherent to the oil markets. This study examines the presence of nonlinear adjustment behaviour in nominal and real crude oil prices towards a long-run equilibrium using two specific types of smooth transition models, capturing size and sign asymmetries. The results suggest asymmetric mean-reversion of oil prices towards the trend over the cycle and potential structural breaks leading to trend-shifts. In sum, taking cognizance of asymmetries suggests an adjustment behaviour largely based on fundamentals in long-run, pointing out relatively limited impact of speculation due to financialisation in oil market. Furthermore, the analysis suggest higher forecasting power of the proposed smooth transition models for nominal oil prices compared to alternative linear benchmarks.

Pricing Vulnerable Options with Stochastic Volatility and Stochastic Interest Rate

This paper considers the pricing issue of vulnerable European options when the price process of the underlying asset follows the GARCH diffusion model with stochastic interest rate. Based on the proposed model, we obtain an approximate solution for the vulnerable European option price via means of Fourier transform. In addition, the Greeks of vulnerable option price are derived explicitly. Besides, the approximate solution of vulnerable option price can be quickly computed by using the fast Fourier transform (FFT) algorithm. The results of Monte Carlo simulations indicate that FFT is accurate, fast and easy to implement. More important, the pricing model also reveals that: (i) a negative correlation of volatility with the spot return creates a fat left tail and thin right tail in the distribution of continuously compounded spot returns. Thus, for in-the-money options, the vulnerable option prices of the proposed model are higher than those of Klein (J Bank Finance 20(7):1211–1229, 1996). While for deep-out-of-the-money options, the vulnerable option prices of the proposed model are smaller; (ii) the higher long-run mean of the underlying asset price’s instantaneous variance, the higher vulnerable option price; (iii) the long-run mean of the stochastic interest rate exerts a positive effect on the value of vulnerable European option.