Strong Mean Reversion Research Articles

Stationary increments reverting to a Tempered Fractional Lévy Process (TFLP)

Stationary Increment Tempered Fractional Lévy Processes (TFLP) introduced by Boniece et al. [On fractional Lévy processes: Tempering, sample path properties and stochastic integration. J. Stat. Phys., 2020, 178, 954–985] are applied to financial data. They are used to model the stochastic drift rate of a mean reverting equation. The new processes are called OU processes with a TFLP drift rate. Expressions for the characteristic functions, variance, skewness and kurtosis at arbitrary horizons are developed. Estimations are conducted for daily return data on ten underlying assets. It is observed that the processes may be consistent with high levels of excess kurtosis in perpetuity. Enquiring further into the possible source of the excess kurtosis it is observed that stochastic drifts that are highly fluctuating with strong mean reversion towards them can generate excess kurtosis at all horizons. Such features may well be characteristic of financial markets and provide an explanation for the persistence of excess kurtosis that has already been documented in the literature. Extensions to matrix tempered multivariate fractional Lévy processes are also considered with estimations reported in the bivariate case.

Electricity pricing using a periodic GARCH model with conditional skewness and kurtosis components

Abstract This paper extends the investigation of the stochastic properties of electricity price growth rates beyond their first two conditional moments allowing for the impact of seasonality on their parameters. The main contributions include the breakdown of electricity price risk into its pure and skewness price components and the development of a risk neutral forecasting equation for electricity prices. Empirical results using ten-years of hourly wholesale prices from the Day-Ahead electricity market in Germany depict the presence of seasonality, strong mean reversion and up-to third degree time-varying moments.

TÜRKİYE PAY PİYASALARINDA ORTALAMAYA DÖNME EĞİLİMİ VE ZAMANLA DEĞİŞEN PİYASA RİSK PRİMİ

Mean reversion in stock markets has been an open question for the decades it has been meticulously tested. This study first aims at shedding further light on this unsettled issue by assessing mean reversion in a broad Turkish stock data via a non-parametric and model-free methodology. Variance ratio computations and distribution-free statistical tests based on randomization are used on dollar and lira denominated nominal, real and excess returns of Borsa Istanbul equity market. As a strong mean reversion is apparent in the empirical tests, the study secondly tries to identify a possible cause of this apparent anomaly. CAPM-based equity risk premium estimations generated via two-pass cross-sectional regressions reveal that the mean reversion might be explained by the dynamic nature of equity risk-premium. The results indicate that the mean reversion in Turkish equity market is a result of time-varying behavior of rational investors rather than market inefficiency.

Review of stochastic differential equations in statistical arbitrage pairs trading

The use of stochastic differential equations offers great advantages for statistical arbitrage pairs trading. In particular, it allows the selection of pairs with desirable properties, e.g., strong mean-reversion, and it renders traditional rules of thumb for trading unnecessary. This study provides an exhaustive survey dedicated to this field by systematically classifying the large body of literature and revealing potential gaps in research. From a total of more than 80 relevant references, five main strands of stochastic spread models are identified, covering the ‘Ornstein–Uhlenbeck model’, ‘extended Ornstein–Uhlenbeck models’, ‘advanced mean-reverting diffusion models’, ‘diffusion models with a non-stationary component’, and ‘other models’. Along these five main categories of stochastic models, we shed light on the underlying mathematics, hereby revealing advantages and limitations for pairs trading. Based on this, the works of each category are further surveyed along the employed statistical arbitrage frameworks, i.e., analytic and dynamic programming approaches. Finally, the main findings are summarized and promising directions for future research are indicated.

Half-Life Volatility Measure of the Returns of Some Cryptocurrencies

This paper explores the half-life volatility measure of three cryptocurrencies (Bitcoin, Litecoin and Ripple). Two GARCH family models were used (PGARCH (1, 1) and GARCH (1, 1)) with the student-t distribution. It was realised that, the PGARCH (1, 1) was the most appropriate model. Therefore, it was used in determining the half-life of the three returns series. The results revealed that, the half-life was 3 days, 6 days and 4 days for Bitcoin, Litecoin and Ripple respectively. This shows that, the three coins have strong mean reversion and short half-life and that it takes the respective days for volatility in each of coin to return half way back without further volatility.

On optimal investment with processes of long or negative memory

We consider the problem of utility maximization for investors with power utility functions. Building on the earlier work Larsen et al. (2016), we prove that the value of the problem is a Fréchet-differentiable function of the drift of the price process, provided that this drift lies in a suitable Banach space.We then study optimal investment problems with non-Markovian driving processes. In such models there is no hope to get a formula for the achievable maximal utility. Applying results of the first part of the paper we provide first order expansions for certain problems involving fractional Brownian motion either in the drift or in the volatility. We also point out how asymptotic results can be derived for models with strong mean reversion.

Inflation-targeting and real interest rate parity: A bias correction approach

This paper investigates whether inflation-targeting influences real interest rate parity (RIP) by a bias correction approach under cross-sectional dependence. The recursive mean adjustment (RMA) method proposed by So and Shin (1999) and Shin and So (2001) is employed to correct the downward bias in the panel unit root tests and in the half-life estimates of real interest rate differentials for traded and non-traded goods. The empirical findings differ depending on whether we apply the RMA. More importantly, the empirical results show that as more homogeneous economies become involved in terms of inflation-targeting regime, stronger mean reversion and much a tighter confidence interval are present. Thus, inflation-targeting plays an important role in providing favorable evidence for long-run RIP.

An Analysis of the Performance of Genetic Programming for Realised Volatility Forecasting

Abstract Traditionally, the volatility of daily returns in financial markets is modeled autoregressively using a time-series of lagged information. These autoregressive models exploit stylised empirical properties of volatility such as strong persistence, mean reversion and asymmetric dependence on lagged returns. While these methods can produce good forecasts, the approach is in essence atheoretical as it provides no insight into the nature of the causal factors and how they affect volatility. Many plausible explanatory variables relating market conditions and volatility have been identified in various studies but despite the volume of research, we lack a clear theoretical framework that links these factors together. This setting of a theory-weak environment suggests a useful role for powerful model induction methodologies such as Genetic Programming (GP). This study forecasts one-day ahead realised volatility (RV) using a GP methodology that incorporates information on market conditions including trading volume, number of transactions, bid-ask spread, average trading duration (waiting time between trades) and implied volatility. The forecasting performance from the evolved GP models is found to be significantly better than those numbers of benchmark forecasting models drawn from the finance literature, namely, the heterogeneous autoregressive (HAR) model, the generalized autoregressive conditional heteroscedasticity (GARCH) model, and a stepwise linear regression model (SR). Given the practical importance of improved forecasting performance for realised volatility this result is of significance for practitioners in financial markets.

Asymmetry and Persistence of Stock Returns: A Case of the Ghana Stock Exchange

Measuring and estimating volatility of asset return is bubbly for risk management, asset allocation, and option pricing. This paper investigated the asymmetry and persistence of the return of some stocks on the Ghana Stock Exchange using univariate TGARCH-M (1, 1) and half-life measure of the daily returns of eight stocks from 02/01/2004 to 20/12/2014. It was realized that, volatility was persistent (explosive process) in all the stocks. The persistence in volatility was extended in investigating the half-life measure of the stocks and it was realized that almost all the stocks had strong mean reversion and short half-life measure with the exception of Fan Milk Limited. Also all the returns series exhibited a positive leverage effect parameter indicating that bad news influenced volatility than good news of the same magnitude.

Real interest rate parity in Asian countries: evidence from the quantile unit root test

ABSTRACTThis article studies the real interest rate parity (RIP) for several Asian countries. This is done by examining the stationarity in the real interest rate differentials (rids) with respect to the US using the quantile unit root test. Our results show that rids exhibits unit-root behaviours in the lower quantile levels, and mean reversion in the upper quantile levels. Furthermore, large positive shocks tend to induce strong mean reversion and the adjustment towards the long-run equilibrium level is faster as rids gets larger, with shorter half-lives in the extreme quantile levels.

Semi-Markov Model for Market Microstructure

We introduce a new model based on Markov renewal processes (MRP) describing the fluctuations of a tick-by-tick single asset price. We consider a point process associated to the timestamps of the price jumps, with marks associated to price increments. By modelling the marks with a suitable Markov chain, we can reproduce the strong mean-reversion of price returns, a phenomenon known as microstructure noise. Moreover, using MRP, we can model the alternating of time intervals with high and low market activity, and consider dependence between price increments and jump times. We also provide simple parametric and nonparametric statistical procedures for the estimation of our model. We obtain closed-form formula for the mean signature plot, and show the diffusive behaviour of our model at large-scale limit. We illustrate our results by numerical simulations, and find that our model is consistent with available empirical data.

Fundamental Relations between Market and Accounting Values

This study examines the implied underlying relation between market and accounting values in a long-run time-series approach based on error correction principles. Recent studies have suggested problems with the current approaches to linear valuation modelling (Ohlson and Kim, 2015). The results this study show that firm market values show slight mean-reversionary characteristics, i.e. returning to a long term level. Economy-wide equity values, through the index, show a significant short-run relationship with individual firm market values but none of the Ohlson-type model accounting variables of book value, earnings and dividends show the same level of short-run explanatory ability for firm market values. Of these four explanatory variables, only dividends show a clear ability to predict firm market value one period ahead. Reported earnings exhibit quite strong mean reversion, suggesting the possibility of earnings management. The implications for testing the Ohlson-Penman theory of market value are also discussed.

Asymmetry and Persistence of Energy Price Volatility

Th is study estimates and compares the asymmetry and persistence of volatility of crude oil, natural gas and coal- three main sources of energy. This study also evaluates the effect of recent Global Financial Crisis (GFC) on the return and volatility of these energy prices. Threshold GA RCH (TGA RCH) and fract ionally integrated GA RCH (FIGA RCH) model are employed to facilitate the study. The estimated results show that coal return volatility exhib its strong mean reversion whereas crude oil and natural gas return volatility endures shocks for relatively higher period. The estimated results also confirm that volatility of crude oil and natural gas increases after positive shocks in prices.

Empirical Asset Pricing with Nonlinear Risk Premia

We introduce a new model for the joint dynamics of the S&P 100 index and the VXO implied volatility index. The nonlinear specification of the variance process is designed to simultaneously accommodate extreme persistence and strong mean reversion. This grants superior forecasting power over the standard (linear) specifications for implied variance forecasting. We obtain statistically significant predictions in an out-of-sample exercise spanning several market crashes starting 1986 and including the recent subprime crisis. The model specification is possible through a simple continuous-time no-arbitrage asset pricing framework that combines semi-analytic pricing with a nonlinear specification for the market price of risk.

Semi Markov Model for Market Microstructure

We introduce a new model for describing the fluctuations of a tick-by-tick single asset price. Our model is based on Markov renewal processes. We consider a point process associated to the timestamps of the price jumps, and marks associated to price increments. By modeling the marks with a suitable Markov chain, we reproduce the strong mean-reversion of price returns known as microstructure noise. Moreover, by using Markov renewal processes, we can model the presence of spikes in intensity of market activity, i.e. the volatility clustering, and consider dependence between price increments and jump times. We also provide simple parametric and nonparametric statistical procedures for the estimation of our model. We obtain closed-form formula for the mean signature plot, and show the diffusive behavior of our model at large scale limit. We illustrate our results by numerical simulations, and find that our model is consistent with empirical data on the Euribor future.

Quantifying natural gas storage optionality: a two-factor tree model

We find evidence of strong mean-reversion in U.S. natural gas prices and proceed to test a valuation model of natural gas storage leases based on mean-reversion’s eects. The model utilizes a two-factor tree in which both factors mean-revert, and the model calibrates to current market conditions, accounts for volume constraints, and can be applied to historical data. In applying the model to data on U.S. natural gas, we find that the model can consistently capture large amounts of optionality based on the premise of strongly mean-reverting prices: On historical price data spanning 1999 to 2006, simulated trading using our model obtained average values (not including the cost of the lease) of $1.244 per million British-thermal-units over intrinsic value for fastcycle storage leases and $0.397 per million British-thermal-units over intrinsic for slow-cycle leases. Results relating stored inventory to storage lease optionality are also shown.

Modelling microstructure noise with mutually exciting point processes

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By suitably coupling the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable us to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro–Bund and Euro–Bobl in several situations.

Stein's Overreaction Puzzle: Option Anomaly or Perfectly Rational Behavior?

Empirical studies have shown that implied volatilities of long-term options react quite strongly to changes in implied volatilities of short-term options and do not display the rationally expected smoothing behavior. Given the observed strong mean-reversion in volatility, those findings have been interpreted as evidence for overreaction in the options market. Focusing on a stochastic variance process in a rational expectation framework, we theoretically show that under normal market conditions the risk-neutral volatility dynamics are substantially more persistent than the physical one. As a result, the empirical observation of a strong reaction of long-term volatility would be consistent with perfectly rational behavior. We additionally show that the degree of persistence depends on investors’ risk aversion. Using daily data on S&P 500 index options, we confirm previous findings for the 2000-2010 period, which is characterized by an overall moderate level of risk aversion. Once we identify periods of high and low risk aversion, in line with the predictions of our theoretical model, empirical results only hold for periods, when investors are highly risk averse. During periods of low risk aversion, results are insignificant. Robustness checks reveal that the results are remarkably stable over the complete term structure. Therefore, we provide strong evidence that the empirical observation is not overreaction, but in line with perfectly rational behavior.

Efficiency of Crude Oil Futures Markets: New Evidence from Multifractal Detrending Moving Average Analysis

In this paper, we examine the weak-form efficient market hypothesis of crude oil futures markets by testing for the random walk behavior of prices. Using a method borrowed from statistical physics, we find that crude oil price display weak persistent behavior for time scales smaller than a year. For time scales larger than a year, strong mean-reversion behaviors can be found. That is, crude oil futures markets are not efficient in the short-term or in the long-term. By quantifying the market inefficiency using a "multifractality degree", we find that the futures markets are more inefficient in the long-term than in the short-term. Furthermore, we investigate the "stylized fact" of volatility dynamics on market efficiency. The simulating and empirical results indicate that volatility clustering, volatility memory and extreme volatility have adverse effects on market efficiency, especially in the long-term.

On the time series measure of conservatism: a threshold autoregressive model

In this note we propose an alternative test specification for Basu’s (1997) time series measure of conservatism that is related to the threshold unit root test of Enders and Granger (1998). We argue that a regression of changes in earnings on the lagged levels—rather than lagged changes—, including an interaction term for negative values, has three conceptual advantages compared to the conventional setup: (1) a smooth, non-oscillating impulse-response pattern to an unexpected shock in earnings (2) a more efficient estimate of persistence in the long run and (3) it can be extended to higher order autoregressive processes. We apply both approaches to a common dataset of firms from the S&P500 index. We confirm the conventional finding that negative shocks are transitory and display stronger mean reversion than positive shocks. However, while most of the literature reports mixed evidence on positive shocks, we find clear evidence that positive shocks are transitory as well. In a Monte Carlo simulation we explain this finding by documenting that larger standard errors in the Basu specification can lead to incorrect inference when the decision between persistent and transitory shocks is close.