The price impact of order book events: market orders,limit orders and cancellations

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective impact on future price changes. We define and extract from the data the ‘bare’ impact these events would have if they were to happen in isolation. For large tick stocks, we show that a model where the bare impact of all events is permanent and non-fluctuating is in good agreement with the data. For small tick stocks, however, bare impacts must contain a history-dependent part, reflecting the internal fluctuations of the order book. We show that this effect can be accurately described by an autoregressive model of the past order flow. This framework allows us to decompose the impact of an event into three parts: an instantaneous jump component, the modification of the future rates of the different events, and the modification of the jump sizes of future events. We compare in detail the present formalism with the temporary impact model that was proposed earlier to describe the impact of market orders when other types of events are not observed. Finally, we extend the model to describe the dynamics of the bid–ask spread.     

Volatility estimation via hidden Markov models

We propose a stochastic volatility model where the conditional variance of asset returns switches across a potentially large number of discrete levels, and the dynamics of the switches are driven by a latent Markov chain. A simple parameterization overcomes the commonly encountered problem in Markov-switching models that the number of parameters becomes unmanageable when the number of states in the Markov chain increases. This framework presents some interesting features in modelling the persistence of volatility, and that, far from being constraining in data fitting, it performs comparably well as other popular approaches in forecasting short-term volatility.     

Time-variations in commodity price jumps

In this paper, we study jumps in commodity prices. Unlike assumed in existing models of commodity price dynamics, a simple analysis of the data reveals that the probability of tail events is not constant but depends on the time of the year, i.e. exhibits seasonality. We propose a stochastic volatility jump–diffusion model to capture this seasonal variation. Applying the Markov Chain Monte Carlo (MCMC) methodology, we estimate our model using 20 years of futures data from four different commodity markets. We find strong statistical evidence to suggest that our model with seasonal jump intensity outperforms models featuring a constant jump intensity. To demonstrate the practical relevance of our findings, we show that our model typically improves Value-at-Risk (VaR) forecasts.     

Universal features of price formation in financial markets: perspectives from deep learning

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary relation between order flow history and the direction of price moves. The universal price formation model exhibits a remarkably stable out-of-sample accuracy across a wide range of stocks and time periods. Interestingly, these results also hold for stocks which are not part of the training sample, showing that the relations captured by the model are universal and not asset-specific.

The universal model—trained on data from all stocks—outperforms asset-specific models trained on time series of any given stock. This weighs in favor of pooling together financial data from various stocks, rather than designing asset- or sector-specific models, as is currently commonly done. Standard data normalizations based on volatility, price level or average spread, or partitioning the training data into sectors or categories such as large/small tick stocks, do not improve training results. On the other hand, inclusion of price and order flow history over many past observations improves forecast accuracy, indicating that there is path-dependence in price dynamics.     

Capturing model risk and rating momentum in the estimation of probabilities of default and credit rating migrations

We present two methodologies on the estimation of rating transition probabilities within Markov and non-Markov frameworks. We first estimate a continuous-time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computational time needed for the Wald confidence interval by a factor of a half. We provide an efficient procedure for transferring such uncertainties from the generator matrix of the Markov chain to the corresponding rating migration probabilities and, crucially, default probabilities. For our second contribution, we assume access to the full (continuous) data set and propose a tractable and parsimonious self-exciting marked point processes model able to capture the non-Markovian effect of rating momentum. Compared to the Markov model, the non-Markov model yields higher probabilities of default in the investment grades, but also lower default probabilities in some speculative grades. Both findings agree with empirical observations and have clear practical implications. We use Moody's proprietary corporate credit rating data set. Parts of our implementation are available in the R package ctmcd.     

Information, Trading, and Product Market Interactions: Cross-sectional Implications of Informed Trading

I present a simple model of informed trading in which asset values are derived from imperfectly competitive product markets and private information events occur at individual firms. The model predicts that informed traders may have incentives to make information‐based trades in the stocks of competitors, especially when events occur at firms with large market shares. In the context of 759 earnings announcements, I use intraday transactions data to test the hypothesis that net order flow and returns in the stocks of nonannouncing competitors have information content for announcing firms.     

Markovian Approaches to Joint-Life Mortality

Abstract

Many insurance products provide benefits that are contingent on the combined survival status of two lives. To value such benefits accurately, we require a statistical model for the impact of the survivorship of one life on another. In this paper we first set up two models, one Markov and one semi-Markov, to model the dependence between the lifetimes of a husband and wife. From the models we can measure the extent of three types of dependence: (1) the instantaneous dependence due to a catastrophic event that affect both lives, (2) the short-term impact of spousal death, and (3) the long-term association between lifetimes. Then we apply the models to a set of jointlife and last-survivor annuity data from a large Canadian insurance company. Given the fitted models, we study the impact of dependence on annuity values and examine the potential inaccuracy in pricing if we assume lifetimes are independent. Finally, we compare our Markovian models with two copula models considered in previous research on modeling joint-life mortality.     

Time-varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques

This paper investigates the time-varying behavior of systematic risk for 18 pan-European sectors. Using weekly data over the period 1987–2005, six different modeling techniques in addition to the standard constant coefficient model are employed: a bivariate t-GARCH(1,1) model, two Kalman filter (KF)-based approaches, a bivariate stochastic volatility model estimated via the efficient Monte Carlo likelihood technique as well as two Markov switching models. A comparison of ex-ante forecast performances of the different models indicate that the random walk process in connection with the KF is the preferred model to describe and forecast the time-varying behavior of sector betas in a European context.     

Time-varying long-run mean of commodity prices and the modeling of futures term structures

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder et al. [J. Finance, 1995, 50, 361–375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson–Schwartz [J. Finance, 1990, 45, 959–976] model and the Casassus–Collin-Dufresne [J. Finance, 2005, 60, 2283–2331] model with a constant interest rate. An application for option pricing is also presented in this paper.     

Telling from Discrete Data Whether the Underlying Continuous–Time Model Is a Diffusion

Can discretely sampled financial data help us decide which continuous-time models are sensible? Diffusion processes are characterized by the continuity of their sample paths. This cannot be verified from the discrete sample path: Even if the underlying path were continuous, data sampled at discrete times will always appear as a succession of jumps. Instead, I rely on the transition density to determine whether the discontinuities observed are the result of the discreteness of sampling, or rather evidence of genuine jump dynamics for the underlying continuous-time process. I then focus on the implications of this approach for option pricing models.     

Mortality Regimes and Pricing

Abstract

Mortality dynamics are characterized by changes in mortality regimes. This paper describes a Markov regime-switching model that incorporates mortality state switches into mortality dynamics. Using the 1901-2005 U.S. population mortality data, we illustrate that regime-switching models can perform better than well-known models in the literature. Furthermore, we extend the 1992 Lee-Carter model in such a way that the time-series common risk factor to all cohorts has distinct mortality regimes with different means and volatilities. Finally, we show how to price mortality securities with this model.     

How does news sentiment affect the states of Japanese stock return volatility?

This paper examines the impact of public news sentiment on the volatility states of firm-level returns on the Japanese Stock market. We firstly adopt a novel Markov Regime Switching Long Memory GARCH (MRS-LMGARCH), which is employed to estimate the latent volatility states of intraday stock return. By using the RavenPack Dow Jones News Analytics database, we fit discrete choice models to investigate the impact of news sentiment on changes of volatility states of the constituent stocks in the TOPIX Core 30 Index. Our findings suggest that news occurrence and sentiment, especially those of macro-economic news, are a key factor that significantly drives the volatility state of Japanese stock returns. This provides essential information for traders of the Japanese stock market to optimize their trading strategies and risk management plans to combat volatility.     

Second order approximations for limit order books

In this paper, we derive a second order approximation for an infinite-dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g. the volume standing at the top of the book). We study the fluctuations of the price and volume process relative to their first order approximation given in ODE–PDE form under two different scaling regimes. In the first case, we suppose that price changes are really rare, yielding a constant first order approximation for the price. This leads to a measure-valued SDE driven by an infinite-dimensional Brownian motion in the second order approximation of the volume process. In the second case, we use a slower rescaling rate, which leads to a non-degenerate first order approximation and gives a PDE with random coefficients in the second order approximation for the volume process. Our results can be used to derive confidence intervals for models of optimal portfolio liquidation under market impact.     

Option Pricing for Pure Jump Processes with Markov Switching Compensators

This paper proposes a model for asset prices which is the exponential of a pure jump process with an N-state Markov switching compensator. We argue that such a process has a good chance of capturing all the empirical stylized regularities of stock price dynamics and we provide a closed form representation of its characteristic function. We also provide a parsimonious representation of the (not necessarily unique) risk neutral density and show how to price and hedge a large class of options on assets whose prices follow this process.     

Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds

Empirical evidence shows that there is a close link between regime shifts and business cycle fluctuations. A standard term structure of interest rates, such as the Cox et al. (1985 Econometrica, 53, 385–407; CIR) model, is sharply rejected in the Treasury bond data. Only Markov regime-switching models on the entire yield curve of the Treasury bond data can account for the observed behavior of the yield curve. In this paper, we examine the impact of regime shifts on AAA-rated and BBB-rated corporate bonds through the use of a reduced-form model. The model is estimated by the Efficient Method of Moments (EMM). Our empirical results suggest that regime-switching risk has significant implications for corporate bond prices and hence has a material impact on the entire corporate bond yield curve, providing evidence for the approach of rating through the cycle employed by rating agencies.     

Financial leverage and export quality: Evidence from France

Does corporate financial structure matter for a firm’s ability to compete in international markets through output quality? This study answers this question by using firm-level export and balance sheet data covering a large sample of French manufacturing exporters over the period 1997–2007. The main result is that there is a negative causal relation between a firm’s leverage and export quality, where quality is inferred from the estimation of a discrete choice model of foreign consumers’ demand. This result is robust across different specifications and estimation techniques. In addition, by estimating investment models we find that the negative impact of leverage on quality is consistent with theories predicting that the agency cost of debt determines suboptimal investment.     

How many factors are important in U.K. stock returns?

I use the sequential approach of Harvey and Liu ([2018]. Lucky factors (Working Paper). Duke University) to build linear factor models in U.K. stock returns among a set of 13 candidate factors using individual stocks and three groups of test portfolios between July 1983 and December 2017. My study finds that the Market factor is the dominant factor in reducing mispricing in individual stocks and test portfolios regardless of the pricing error metric used. The Market factor has a bigger impact when using a value weighting pricing error metric. Whether a second factor is used or not depends upon which metric is used for mispricing and the time period examined. My study finds support for a two-factor model for the whole sample period of the Market factor and the Conservative Minus Aggressive (CMA) factor of Fama and French ([2015]. “A five-factor asset pricing model.” Journal of Financial Economics 116: 1–22) when giving greater weight to the mispricing of larger companies.     

Out-West Products, Inc.: A financial modeling and decision analysis case

The Out-West Products, Inc. instructional case requires students to build a comprehensive financial model to support planning and decision-making. Part 1 of this team-oriented Excel project requires students to construct a baseline model, while Part 2 provides sensitivity analysis and decision-making extensions. The case incorporates cost-volume-profit, accounting income versus cash flow, and benchmarking analyses. Case objectives provide students with a realistic financial modeling experience that includes: building models; linking data across financial statements; testing solutions and analyzing scenarios; and improving critical thinking skills. These objectives closely align to the AICPA Core Competency Framework for Entry into the Accounting Profession. The case can be used in introductory and upper-division managerial accounting, upper-division cost accounting, and MBA managerial accounting courses, and can be modularized to achieve instructor-specific objectives.