Detecting log-periodicity in a regime-switching model of stock returns

Log-periodic precursors have been identified before most and perhaps all financial crashes of the Twentieth Century, but efforts to statistically validate the leading model of log-periodicity, the Johansen–Ledoit–Sornette (JLS) model, have generally failed. The main feature of this model is that log-harmonic fluctuations in financial prices are driven by similar fluctuations in expected daily returns. Here we search more broadly for evidence of any log-periodic variation in expected daily returns by estimating a regime-switching model of stock returns in which the mean return fluctuates between a high and a low value. We find such evidence prior to the two largest drawdowns in the S&P 500 since 1950. However, if we estimate a log-harmonic specification for the stock index for the same time periods, fixing the frequency and critical time according to the results of the regime-switching model, the parameters do not satisfy restrictions imposed by the JLS model.     

A statistical analysis of log-periodic precursors to financial crashes*

Motivated by the hypothesis that financial crashes are macroscopic examples of critical phenomena associated with a discrete scaling symmetry, we reconsider the evidence of log-periodic precursors to financial crashes and test the prediction that log-periodic oscillations in a financial index are embedded in the mean function of this index (conditional upon no crash having yet occurred). In particular, we examine the first differences of the logarithm of the S&P 500 prior to the October 1987 crash and find the log-periodic component of this time series is not statistically significant if we exclude the last year of data before the crash. We also examine the claim that two separate mechanisms are needed to explain the frequency distribution of draw downs in the S&P 500 and find the evidence supporting this claim to be unconvincing.     

Significance of log-periodic precursors to financial crashes

We clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's criticism ([A article="1469-7688/1/3/306"] Feigenbaum J A 2001 Quantitative Finance 1 346-60 [/A]) and show how it can be refuted. Feigenbaum's main result is as follows: 'the hypothesis that the log-periodic component is present in the data cannot be rejected at the 95% confidence level when using all the data prior to the 1987 crash; however, it can be rejected by removing the last year of data' (e.g. by removing 15% of the data closest to the critical point). We stress that it is naive to analyse a critical point phenomenon, i.e., a power-law divergence, reliably by removing the most important part of the data closest to the critical point. We also present the history of log-periodicity in the present context explaining its essential features and why it may be important. We offer an extension of the rational expectation bubble model for general and arbitrary risk-aversion within the general stochastic discount factor theory. We suggest guidelines for the use of log-periodicity and explain how to develop and interpret statistical tests of log-periodicity. We discuss the issue of prediction based on our results and the evidence of outliers in the distribution of drawdowns. New statistical tests demonstrate that the 1% to 10% quantile of the largest events of the population of drawdowns of the NASDAQ composite index and of the Dow Jones Industrial Average index belong to a distribution significantly different from the rest of the population. This suggests that very large drawdowns may result from an amplification mechanism that may make them more predictable.     

Inferring fundamental value and crash nonlinearity from bubble calibration

Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in general, not directly observable and it is poorly constrained to calculate. Further, it is not possible to distinguish between an exponentially growing fundamental price and an exponentially growing bubble price. In this paper, we present a series of new models based on the Johansen–Ledoit–Sornette (JLS) model, which is a flexible tool to detect bubbles and predict changes of regime in financial markets. Our new models identify the fundamental value of an asset price and a crash nonlinearity from a bubble calibration. In addition to forecasting the time of the end of a bubble, the new models can also estimate the fundamental value and the crash nonlinearity, meaning that identifying the presence of a bubble is enabled by these models. In addition, the crash nonlinearity obtained in the new models presents a new approach to possibly identify the dynamics of a crash after a bubble. We test the models using data from three historical bubbles ending in crashes from different markets. They are the Hong Kong Hang Seng index 1997 crash, the S&P 500 index 1987 crash (Black Monday) and the Shanghai Composite index 2009 crash. All results suggest that the new models perform very well in describing bubbles, forecasting their ending times and estimating fundamental value and the crash nonlinearity. The performance of the new models is tested under both the Gaussian residual assumption and non-Gaussian residual assumption. Under the Gaussian residual assumption, nested hypotheses with the Wilks' statistics are used and the p-values suggest that models with more parameters are necessary. Under the non-Gaussian residual assumption, we use a bootstrap method to obtain type I and II errors of the hypotheses. All tests confirm that the generalized JLS models provide useful improvements over the standard JLS model.     

Contagion as a domino effect in global stock markets

This paper shows that stock market contagion occurs as a domino effect, where confined local crashes evolve into more widespread crashes. Using a novel framework based on ordered logit regressions we model the occurrence of local, regional and global crashes as a function of their past occurrences and financial variables. We find significant evidence that global crashes do not occur abruptly but are preceded by local and regional crashes. Besides this form of contagion, interdependence shows up by the effect of interest rates, bond returns and stock market volatility on crash probabilities. When it comes to forecasting global crashes, our model outperforms a binomial model for global crashes only.     

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.     

Modelling failure rates with machine-learning models: Evidence from a panel of UK firms

In this study, we investigate the ability of machine-learning techniques to predict firm failures and we compare them against alternatives. Using data on business and financial risks of UK firms over 1994–2019, we document that machine-learning models are systematically more accurate than a discrete hazard benchmark. We conclude that the random forest model outperforms other models in failure prediction. In addition, we show that the improved predictive power of the random forest model relative to its counterparts persists when we consider extreme economic events as well as firm and industry heterogeneity. Finally, we find that financial factors affect failure probabilities.     

The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals

Using the concept of the stochastic discount factor with critical behavior, we present a self-consistent model for explosive financial bubbles, which combines a mean-reverting volatility process and a stochastic conditional return which reflects nonlinear positive feedbacks and continuous updates of the investors' beliefs and sentiments. The conditional expected returns exhibit faster-than-exponential acceleration decorated by accelerating oscillations, called “log-periodic power law” (LPPL). Tests on residuals show a remarkable, low rate (0.2%) of false positives when applied to a GARCH benchmark. When tested on the S&P500 US index from Jan. 3, 1950 to Nov. 21, 2008, the model correctly identifies the bubbles ending in Oct. 1987, in Oct. 1997, and in Aug. 1998 and the ITC bubble ending on the first quarter of 2000. Different unit-root tests confirm the high relevance of the model specification. Our model also provides a diagnostic for the duration of bubbles: applied to the period before the Oct. 1987 crash, there is clear evidence that the bubble started at least 4 years earlier. We confirm the validity and universality of the volatility-confined LPPL model on seven other major bubbles that have occurred in the World in the last two decades. Using Bayesian inference, we find a very strong statistical preference for our model compared with a standard benchmark, in contradiction with Chang and Feigenbaum (2006) which used a unit-root model for residuals.     

A statistical model of speculative bubbles,with applications to the stock markets of the United States,Japan, and China

It is common knowledge that the more prices deviate from fundamentals, the more likely it is for prices to reverse. Taking this into account, we propose a simple statistical model to identify speculative bubbles in financial markets. Through the estimates of the time varying parameters, including transition probabilities, we can identify when and how newly born bubbles grow and burst over time. The model can be estimated by recursive computations, which require a huge storage capacity for standard computers. For this reason, we introduce an approximation in the computation, maintaining the recursive nature of our estimation technique. We then apply this model to the stock markets of the United States, Japan, and China, estimate its parameters and the probabilities of a bubble crash, and obtain several interesting results: the time series data of the stock price bubble show an inherently non-stationary development and the probability of a bubble crash indeed increases as the stock price becomes too high or too low.     

Prediction accuracy and sloppiness of log-periodic functions

We show that log-periodic power-law (LPPL) functions are intrinsically very hard to fit to time series. This comes from their sloppiness, the squared residuals depending very much on some combinations of parameters and very little on other ones. The time of singularity that is supposed to give an estimate of the day of the crash belongs to the latter category. We discuss in detail why and how the fitting procedure must take into account the sloppy nature of this kind of model. We then test the reliability of LPPLs on synthetic AR(1) data replicating the Hang Seng 1987 crash and show that even this case is borderline regarding the predictability of the divergence time. We finally argue that current methods used to estimate a probabilistic time window for the divergence time are likely to be over-optimistic.     

Markov Chain Monte Carlo Methods in Financial Econometrics

Markov Chain Monte Carlo (MCMC) methods have become very popular in financial econometrics during the last years. MCMC methods are applicable where classical methods fail. In this paper, we give an introduction to MCMC and present recent empirical evidence. Finally, we apply MCMC methods to portfolio choice to account for parameter uncertainty and to incorporate different degrees of belief in an asset pricing model.     

The role of multivariate skew-Student density in the estimation of stock market crashes

By combining the multivariate skew-Student density with a time-varying correlation GARCH (TVC-GARCH) model, this paper investigates the spread of crashes in the regional stock markets. The regional index series of European, USA, Latin American and Asian markets are modeled jointly, and the maximum likelihood estimates show that a TVC-GARCH model with multivariate skew-Student density outperforms that with multivariate normal density substantially. Depending on the past information set, the conditional 1-day crash probabilities are computed, and the forecast performances of the TVC-GARCH model with both multivariate skew-Student and normal densities are evaluated. In both bilateral and global environments, multivariate skew-Student density has better predictive accuracy than normal density. In global crash probability forecasts, multivariate skew-Student density attains much higher hit rate and Kuipers score than multivariate normal density, thus it can be used to improve early-warning systems.     

Technological bias at the exchange rate market

Prediction of exchange rates has been a topic for debate in economic literature since the late 1980s. The recent development of machine learning techniques has spurred a plethora of studies that further improves the prediction models for currency markets. This high-tech progress may create challenges for market efficiency along with information asymmetry and irrationality of decision-making. This technological bias emerges from the fact that recent innovative approaches have been used to solve trading tasks and to find the best trading strategies. This paper demonstrates that traders can leverage technological bias for financial market forecasting. Those traders who adapt faster to the changes in market innovations will get excess returns. To support this hypothesis we compare the performance of deep learning methods, shallow neural networks with baseline prediction methods and a random walk model using daily closing rate between three currency pairs: Euro and US Dollar (EUR/USD), British Pound and US Dollar (GBP/USD), and US Dollar and Japanese Yen (USD/JPY). The results demonstrate that deep learning achieves higher accuracy than alternate methods. The shallow neural network outperforms the random walk model, but cannot surpass ARIMA accuracy significantly. The paper discusses possible outcomes of the technological shift for financial market development and accounting conforming also to adaptive market hypothesis.     

Interpreting financial market crashes as earthquakes: A new Early Warning System for medium term crashes

We propose a modeling framework which allows for creating probability predictions on a future market crash in the medium term, like sometime in the next five days. Our framework draws upon noticeable similarities between stock returns around a financial market crash and seismic activity around earthquakes. Our model is incorporated in an Early Warning System for future crash days. Testing our EWS on S&P 500 data during the recent financial crisis, we find positive Hanssen–Kuiper Skill Scores. Furthermore our modeling framework is capable of exploiting information in the returns series not captured by well known and commonly used volatility models. EWS based on our models outperform EWS based on the volatility models forecasting extreme price movements, while forecasting is much less time-consuming.     

Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods

This study applies the nonparametric estimation procedure tothe diffusion process modeling the dynamics of short-term interestrates. This approach allows us to operate in continuous time,estimating the continuous-time model, despite the use of discretedata. Three methods are proposed. We apply these methods totwo important financial data. After selecting an appropriatebandwidth for each dataset, empirical comparisons indicate thatthe specification of the drift has a considerable impact onthe pricing of derivatives through its effect on the diffusionfunction. In addition, a novel nonparametric test has been proposedfor specification of linearity in the drift. Our simulationdirects us to reject the null hypothesis of linearity at the5% significance level for the two financial datasets.     

投资者理性预期、流动性约束与股价崩盘传染研究

“传染性”是股价崩盘三大基本特征之一,会加剧股价崩盘负面影响,甚至引发系统性金融风险,因此,本文重点关注股价崩盘传染机制研究。首先,本文基于两阶段理性预期均衡模型,提出股价崩盘传染两大假设,即投资者理性预期与流动性约束导致传染;其次,基于2000-2016年全球28个国家或地区资本市场数据,实证检验股价崩盘传染机制和传染渠道。研究显示:(1)投资者理性预期、流动性约束会导致股价崩盘发生传染;(2)股价崩盘事件会在资本市场关联国家或地区传染;(3)提高资本市场信息透明度、加强金融管制有助于降低受关联国家或地区股价崩盘传染。     

Fair value disclosures and crash risk

In response to the public criticism of the inadequate disclosures mandated by SFAS No. 157, Fair Value Measurements, the FASB issued ASU (Accounting Standards Update) 2010–06, Improving Disclosures about Fair Value Measurements, and ASU 2011–04, Amendments to Achieve Common Fair Value Measurement and Disclosure Requirements, in an effort to increase the reporting transparency. We examine whether the increased fair value disclosures required by these two updates effectively decrease crash risk, defined as the frequency of extreme negative stock returns. In support of the hypothesis, we find that increased transparency from these updates reduces crash risk among U.S. banking firms and that the reduction is greater in banks that have a higher level of Level 3 financial assets.     

Current account sustainability in the US: What did we really know about it?

We analyze the sustainability of the US current account (CA) deficit by means of unit-root tests. First, we argue that there are several reasons to believe that the CA may follow a non-linear mean-reversion behavior under the null of stationarity. Using a non-linear ESTAR model we can reject the null of non-stationarity favoring the sustainability hypothesis. Second, we ask whether unit-root tests are a useful indicator of sustainability by comparing in-sample results for the 1960–2004 period to the developments observed up to the end of 2008. We find that the non-linear model outperforms the linear and random walk models in terms of forecast performance. The large shocks to the CA observed in the last five years induced a faster speed of mean reversion, ensuring the necessary adjustment to meet the inter-temporal budget constraint.     

Do geographically nearby major customers mitigate suppliers’ stock price crash risk?

This study examines the impact of geographically nearby major customers on suppliers' stock price crash risk. Using a sample of Chinese A-share listed firms and their top five (major) customers during the period 2008–2019, we find a significantly negative association. This association is robust in a series of robustness checks, including the use of instrumental variables estimations, propensity score matching procedure, and Heckman two-step sample selection model. The mitigating effect of supplier?customer proximity on crash risk is more pronounced for suppliers with lower corporate transparency and greater operational uncertainty. Finally, we identify two possible mechanisms through which geographically nearby major customers reduce suppliers’ crash risk: fewer financial restatements and higher accounting conservatism of suppliers. The findings of this study indicate that listed firms may choose geographically nearby customers to reduce crash risk.     

A pairs trading strategy based on linear state space models and the Kalman filter

Among many strategies for financial trading, pairs trading has played an important role in practical and academic frameworks. Loosely speaking, it involves a statistical arbitrage tool for identifying and exploiting the inefficiencies of two long-term, related financial assets. When a significant deviation from this equilibrium is observed, a profit might result. In this paper, we propose a pairs trading strategy entirely based on linear state space models designed for modelling the spread formed with a pair of assets. Once an adequate state space model for the spread is estimated, we use the Kalman filter to calculate conditional probabilities that the spread will return to its long-term mean. The strategy is activated upon large values of these conditional probabilities: the spread is bought or sold accordingly. Two applications with real data from the US and Brazilian markets are offered, and even though they probably rely on limited evidence, they already indicate that a very basic portfolio consisting of a sole spread outperforms some of the main market benchmarks.