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We investigate the impact of order flow imbalance (OFI) on price movements in equity markets in a multi-asset setting. First, we propose a systematic approach for combining OFIs at the top levels of the limit order book into an integrated OFI variable which better explains price impact, compared to the best-level OFI. We show that once the information from multiple levels is integrated into OFI, multi-asset models with cross-impact do not provide additional explanatory power for contemporaneous impact compared to a sparse model without cross-impact terms. On the other hand, we show that lagged cross-asset OFIs do improve the forecasting of future returns. We also establish that this lagged cross-impact mainly manifests at short-term horizons and decays rapidly in time. [ABSTRACT FROM AUTHOR]

The measurement of financial risk premia, the amount that a risky asset will outperform a risk-free one, is an important problem in asset pricing. The noisiness and non-stationarity of asset returns makes the estimation of risk premia using machine learning (ML) techniques challenging. In this work, we develop ML models that solve the problems associated with risk premia forecasting by separating risk premia prediction into two independent tasks, a time series model and a cross-sectional model, and using neural networks with skip connections to enable their deep neural network training. These models are tested robustly with different metrics, and we observe that our models outperform several existing standard ML models. A known issue with ML models is their 'black box' nature, i.e. their opaqueness to interpretability. We interpret these deep neural networks using local approximation-based techniques that provide explanations for our model's predictions. [ABSTRACT FROM AUTHOR]

Estimators of integrated and spot variance are tested using the queue-reactive model of the limit order book [ABSTRACT FROM AUTHOR]

In this paper, we investigate how a deep learning machine learning model can be applied to improve Bitcoin price forecasting and trading by incorporating unstructured information from financial news. The two-stage model we propose that includes financial news significantly outperforms machine learning models without financial news. In the first stage, we leverage long short-term memory (LSTM) networks to extract structured information from financial news. In the second stage, we apply machine learning models with structured input from financial news to the prediction of Bitcoin prices. In addition to the superior performance relative to machine learning models without input from financial news, we find that the out-of-time rate of return attained with the proposed forecasting system is substantially higher than for a buy-and-hold strategy. Our study highlights how combining deep learning and financial news offers investors and traders support for the monetization of unstructured data in finance. [ABSTRACT FROM AUTHOR]

We propose an asset allocation strategy that engineers optimal weights before feeding them to a supervised learning algorithm. In contrast to the traditional approaches, the machine is able to learn risk measures, preferences, and constraints beyond simple expected returns, within a flexible, forward-looking, and non-linear framework. Our empirical analysis illustrates that predicting the optimal weights directly instead of the traditional two-step approach leads to more stable portfolios with statistically better risk-adjusted performance measures. [ABSTRACT FROM AUTHOR]

We introduce a parametric dynamic factor specification for high-frequency financial data that simplifies considerably the estimation of the realized covariance matrix in high dimensions. The estimation method is tested in an empirical setting that emphasizes the effect of the curse of dimensionality. Compared to standard parametric approaches, our factor specification is computationally less demanding and provides statistically indistinguishable performances in standard risk management applications. The method is also assessed on Monte-Carlo simulations under several forms of misspecification. [ABSTRACT FROM AUTHOR]

Published anomalies evaluated outside the data sample deliver about 50% of in-sample performance [ABSTRACT FROM AUTHOR]

We propose a data-driven Neural Network (NN) optimization framework to determine the optimal multi-period dynamic asset allocation strategy for outperforming a general stochastic target. We formulate the problem as an optimal stochastic control with an asymmetric, distribution shaping, objective function. The proposed framework is illustrated with the asset allocation problem in the accumulation phase of a defined contribution pension plan, with the goal of achieving a higher terminal wealth than a stochastic benchmark. We demonstrate that the data-driven approach is capable of learning an adaptive asset allocation strategy directly from historical market returns, without assuming any parametric model of the financial market dynamics. The optimal adaptive strategy outperforms the benchmark constant proportion strategy, achieving a higher terminal wealth with a 90% probability, a 46% higher median terminal wealth, and a significantly more right-skewed terminal wealth distribution. [ABSTRACT FROM AUTHOR]

This paper introduces a novel class of volatility forecasting models that incorporate market realized (co)variances and semi(co)variances within the framework of a heterogeneous autoregressive (HAR) model. Our empirical analysis shows statistically and economically significant forecasting gains. For our most parsimonious market-HAR specification, stock volatility forecasting is improved by 9.80% points. Using a mixed sampling frequency market-HAR variant with low (high) sampling frequency for the stock (market) improves forecasting by a further 6.90% points. Our paper also develops noise-robust estimators to facilitate the use of realized semi(co)variances at high sampling frequencies. [ABSTRACT FROM AUTHOR]

This study aims to improve the forecasting performance of technical indicators for crude oil prices by imposing economic constraints on the sign of the shrinkage estimators. The out-of-sample results indicate that our constrained methods deliver significantly stronger forecasts than their standard forms and prevalent predictive models. Moreover, the advantages of the constrained methods are stronger during recessions and weaker during expansions. The superior forecasting performance of the constrained methods is not affected by the consideration of long-horizon forecasts and is robust to a large body of alternative specifications. In addition to the statistical tests, we provide evidence that investors who use the new predictive framework can realize sizable economic gains through asset allocations and market timing. [ABSTRACT FROM AUTHOR]

In many reinforcement learning applications, the underlying environment reward and transition functions are explicitly known differentiable functions. This enables us to use recent research which applies machine learning tools to stochastic control to find optimal action functions. In this paper, we define differentiable reinforcement learning as a particular case of this research. We find that incorporating deep learning in this framework leads to more accurate and stable solutions than those obtained from more generic actor critic algorithms. We apply this deep differentiable reinforcement learning (DDRL) algorithm to the problem of one asset optimal trading strategies in various environments where the market dynamics are known. Thanks to the stability of this method, we are able to efficiently find optimal strategies for complex multi-scale market models. We also extend these methods to simultaneously find optimal action functions for a wide range of environment parameters. This makes it applicable to real life financial signals and portfolio optimization where the expected return has multiple time scales. In the case of a slow and a fast alpha signal, we find that the optimal trading strategy consists in using the fast signal to time the trades associated to the slow signal. [ABSTRACT FROM AUTHOR]

Systematic financial trading strategies account for over 80% of trade volume in equities and a large chunk of the foreign exchange market. In spite of the availability of data from multiple markets, current approaches in trading rely mainly on learning trading strategies per individual market. In this paper, we take a step towards developing fully end-to-end global trading strategies that leverage systematic trends to produce superior market-specific trading strategies. We introduce QuantNet: an architecture that learns market-agnostic trends and use these to learn superior market-specific trading strategies. Each market-specific model is composed of an encoder-decoder pair. The encoder transforms market-specific data into an abstract latent representation that is processed by a global model shared by all markets, while the decoder learns a market-specific trading strategy based on both local and global information from the market-specific encoder and the global model. QuantNet uses recent advances in transfer and meta-learning, where market-specific parameters are free to specialize on the problem at hand, whilst market-agnostic parameters are driven to capture signals from all markets. By integrating over idiosyncratic market data we can learn general transferable dynamics, avoiding the problem of overfitting to produce strategies with superior returns. We evaluate QuantNet on historical data across 3103 assets in 58 global equity markets. Against the top performing baseline, QuantNet yielded 51% higher Sharpe and 69% Calmar ratios. In addition, we show the benefits of our approach over the non-transfer learning variant, with improvements of 15% and 41% in Sharpe and Calmar ratios. A link to QuantNet code is made available in the appendix. [ABSTRACT FROM AUTHOR]

This paper establishes a novel model-free representation of the risk-neutral density in terms of market-observed options prices by combining exact series representations of the Dirac Delta function and the Carr-Madan asset spanning formula. Compared to the widely used method for obtaining the risk-neutral densities via the Breeden–Litzenberger device, our method yields estimates of risk-neutral densities that are model-free, automatically smooth, and in closed-form. The closed-form feature of our new representation makes it ideal for many potential applications including a new model-free representation of the local volatility function in the Dupire's local volatility model. The validity of our method is demonstrated through simulation studies as well as an empirical application using S&P 500 index option data. Extension of the method to higher dimensions is also obtained by extending the spanning formula. [ABSTRACT FROM AUTHOR]

Recent advances in high-frequency financial econometrics enable us to characterize which components of the data generating processes change in crisis, and which do not. This paper introduces a new statistic which captures large discontinuities in the composition of a given price series. Monte Carlo simulations suggest that this statistic is useful in characterizing the tail behavior across different sample periods. An application to US Treasury market provides evidence consistent with identifying periods of stress via flight-to-cash behavior which results in increased abrupt price falls at the short end of the term structure and decreased negative price jumps at the long end. [ABSTRACT FROM AUTHOR]

Index tracking and hedge fund replication aim at cloning the return time series properties of a given benchmark, by either using only a subset of its original constituents or by a set of risk factors. In this paper, we propose a model that relies on the Sorted ℓ 1 Penalized Estimator, called SLOPE, for index tracking and hedge fund replication. We show that SLOPE is capable of not only providing sparsity, but also to form groups among assets depending on their partial correlation with the index or the hedge fund return times series. The grouping structure can then be exploited to create individual investment strategies that allow building portfolios with a smaller number of active positions, but still comparable tracking properties. Considering equity index data and hedge fund returns, we discuss the real-world properties of SLOPE based approaches with respect to state-of-the art approaches. [ABSTRACT FROM AUTHOR]

The forecasting of exchange rate returns has long been an issue in finance literature. The use of the best forecasting model is usually sensitive to the data frequency and the sample period used. Model evaluation is usually based on either minimizing error losses or maximizing profit strategies and other likelihood-based measures. Although, much work has been devoted to model evaluation based on maximizing profits strategies little to no work has been devoted to the issue of estimating a forecast model under the same principles. Here, we propose a Bayesian framework that estimates exchange rate models by considering measures such as directional accuracy and trading rules in a form of asymmetric loss functions. Estimation is implemented using Laplace-type estimators applied in cases where the likelihood function is not of a known form. We illustrate this method using simulated and real weekly exchange rate series. The results demonstrate that the use of profit maximizing strategies within estimation can significantly improve the forecasting ability of certain exchange rate models. [ABSTRACT FROM AUTHOR]

Factor strategies have gained growing popularity in industry with the fast development of machine learning. Usually, multi-factors are fed to an algorithm for some cross-sectional return predictions, which are then further used to construct a long-short portfolio. Instead of predicting the value of the stock return, emerging studies predict a ranked stock list using the mature learn-to-rank technology. In this study, we propose a new listwise learn-to-rank loss function which aims to emphasize both the top and the bottom of a rank list. Our loss function, motivated by the long-short strategy, is endogenously shift-invariant and can be viewed as a direct generalization of ListMLE. Under different transformation functions, our loss can lead to consistency with binary classification loss or permutation level 0-1 loss. A probabilistic explanation for our model is also given as a generalized Plackett-Luce model. Based on a dataset of 68 factors in the China A-share market from 2006 to 2019, our empirical study has demonstrated the strength of our method which achieves an out-of-sample annual return of 38% with Sharpe ratio 2. [ABSTRACT FROM AUTHOR]

There are many well documented behavioral biases in financial markets. Yet, analyzing U.S. equities reveals that less than 1% of returns are predictable in recent years. Given the high number of biases, why are returns not more predictable? We provide new evidence in support of one possible explanation. In the long-run, low correlations across signals that trigger biases may create sufficient antinoise which mutes more sizable patterns in returns. However, in the short-run, correlation spikes coincide with market volatility indicating that behavioral biases may become more visible during crises. [ABSTRACT FROM AUTHOR]

Instead of conducting manual factor construction based on traditional and behavioural finance analysis, academic researchers and quantitative investment managers have leveraged Genetic Programming (GP) as an automatic feature construction tool in recent years, which builds reverse polish mathematical expressions from trading data into new factors. However, with the development of deep learning, more powerful feature extraction tools are available. This paper proposes Neural Network-based Automatic Factor Construction (NNAFC), a tailored neural network framework that can automatically construct diversified financial factors based on financial domain knowledge and a variety of neural network structures. The experiment results show that NNAFC can construct more informative and diversified factors than GP, to effectively enrich the current factor pool. For the current market, both fully connected and recurrent neural network structures are better at extracting information from financial time series than convolution neural network structures. Moreover, new factors constructed by NNAFC can always improve the return, Sharpe ratio, and the max draw-down of a multi-factor quantitative investment strategy due to their introducing more information and diversification to the existing factor pool. [ABSTRACT FROM AUTHOR]

This paper tests for jumps of the price process based on noisy high-frequency data. Under the null hypothesis that the price process is continuous, the test statistic converges to a normal distribution, and under the alternative hypothesis that the price has jumps, the statistic converges to infinity. Compared with the test of Aït-Sahalia et al. [Testing for jumps in noisy high frequency data. J. Econom., 2012, 168(2), 207–222], our proposed statistic uses information on the microstructure noise, tends to infinity more rapidly under the alternative hypothesis and has a better power. A simulation confirms the theoretical results and an empirical study illustrates the practical application of the method. [ABSTRACT FROM AUTHOR]

We propose a method to infer lead-lag networks of traders from the observation of their trade record as well as to reconstruct their state of supply and demand when they do not trade. The method relies on the Kinetic Ising model to describe how information propagates among traders, assigning a positive or negative 'opinion' to all agents about whether the traded asset price will go up or down. This opinion is reflected by their trading behavior, but whenever the trader is not active in a given time window, a missing value will arise. Using a recently developed inference algorithm, we are able to reconstruct a lead-lag network and to estimate the unobserved opinions, giving a clearer picture about the state of supply and demand in the market at all times. We apply our method to a dataset of clients of a major dealer in the Foreign Exchange market at the 5 minute time scale. We identify leading players in the market and define a herding measure based on the observed and inferred opinions. We show the causal link between herding and liquidity in the inter-dealer market used by dealers to rebalance their inventories. [ABSTRACT FROM AUTHOR]

This paper proposes novel approaches to the modeling of attenuation bias effects in volatility forecasting. Our strategy relies on suitable generalizations of the Realized GARCH model by Hansen et al. [Realized garch: A joint model for returns and realized measures of volatility. J. Appl. Econom., 2012, 27(6), 877–906] where the impact of lagged realized measures on the current conditional variance is weighted according to the accuracy of the measure itself at that specific time point. This feature allows assigning more weight to lagged volatilities when they are more accurately measured. The ability of the proposed models to generate accurate forecasts of volatility and related tail risk measures, Value-at-Risk and Expected Shortfall, is assessed by means of an application to a set of major stock market indices. The results of the empirical analysis show that the proposed specifications are able to outperform standard Realized GARCH models in terms of out-of-sample forecast performance under both statistical and economic criteria. [ABSTRACT FROM AUTHOR]

We investigate conditions for the existence of a continuous model on the S&P 500 index (SPX) that jointly calibrates to a full surface of SPX implied volatilities and to the VIX smiles. We present a novel approach based on the SPX smile calibration condition E [ σ t 2 | S t ] = σ l v 2 (t , S t). In the limiting case of instantaneous VIX, a novel application of martingale transport to finance shows that such model exists if and only if, for each time t, the local variance σ l v 2 (t , S t) is smaller than the instantaneous variance σ t 2 in convex order. The real case of a 30-day VIX is more involved, as averaging over 30 days and projecting onto a filtration can undo convex ordering. We show that in usual market conditions, and for reasonable smile extrapolations, the distribution of V I X T 2 in the market local volatility model is larger than the market-implied distribution of V I X T 2 in convex order for short maturities T, and that the two distributions are not rankable in convex order for intermediate maturities. In particular, a necessary condition for continuous models to jointly calibrate to the SPX and VIX markets is the inversion of convex ordering property: the fact that, even though associated local variances are smaller than instantaneous variances in convex order, the VIX squared is larger in convex order in the associated local volatility model than in the original model for short maturities. We argue and numerically demonstrate that, when the (typically negative) spot–vol correlation is large enough in absolute value, (a) traditional stochastic volatility models with large mean reversion, and (b) rough volatility models with small Hurst exponent, satisfy the inversion of convex ordering property, and more generally can reproduce the market term-structure of convex ordering of the local and stochastic squared VIX. [ABSTRACT FROM AUTHOR]

In this study we provide an analytical characterization of the impact of zero returns on the popular realized covariance estimator of Barndorff-Nielsen and Shephard [Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica, 2004, 72(3), 885–925]. In our framework, efficient price processes evolve as a semimartingale with some likelihood of repeated prices. We show that the standard realized covariance estimator is asymptotically affected by a downward bias, and the size of the bias depends on these likelihoods. We demonstrate that this result can be used to construct a consistent estimator of the integrated covariance of a vector semimartingale. The advantages with respect to other estimators are discussed with data. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of the relationship between returns and extreme downside risk in different states of the market by combining the framework of Bali et al. [Is there an intertemporal relation between downside risk and expected returns? Journal of Financial and Quantitative Analysis, 2009, 44, 883–909] with a Markov switching mechanism. We show that the risk-return relationship identified by Bali et al. (2009) is highly significant in the low volatility state but disappears during periods of market turbulence. This is puzzling since it is during such periods that downside risk should be most prominent. We show that the absence of the risk-return relationship in the high volatility state is due to leverage and volatility feedback effects arising from increased persistence in volatility. To better filter out these effects, we propose a simple modification that yields a positive tail risk-return relationship in all states of market volatility. [ABSTRACT FROM AUTHOR]

This paper develops the optimal causal path algorithm and applies it within a fully-fledged statistical arbitrage framework to minute-by-minute data of the S&P 500 constituents from 1998 to 2015. Specifically, the algorithm efficiently determines the optimal non-linear mapping and the corresponding lead–lag structure between two time series. Afterwards, this study explores the use of optimal causal paths as a means for identifying promising stock pairs and for generating buy and sell signals. For this purpose, the established trading strategy exploits information about the leading stock to predict future returns of the following stock. The value-add of the proposed framework is assessed by benchmarking it with variants relying on classic similarity measures and a buy-and-hold investment in the S&P 500 index. In the empirical back-testing study, the trading algorithm generates statistically and economically significant returns of 54.98% p.a. and an annualized Sharpe ratio of 3.57 after transaction costs. Returns are well superior to the benchmark approaches and do not load on any common sources of systematic risk. The strategy outperforms in the context of cryptocurrencies even in recent times due to the fact that stock returns contain substantial information about the future bitcoin returns. [ABSTRACT FROM AUTHOR]

In this article, we propose an efficient approach for inverting computationally expensive cumulative distribution functions. A collocation method, called the Stochastic Collocation Monte Carlo sampler (SCMC sampler), within a polynomial chaos expansion framework, allows us the generation of any number of Monte Carlo samples based on only a few inversions of the original distribution plus independent samples from a standard normal variable.We will show that with this path-independent collocation approach the exact simulation of the Heston stochastic volatility model, as proposed in Broadie and Kaya [Oper. Res., 2006, 54, 217-231], can be performed efficiently and accurately. We also show how to efficiently generate samples from the squared Bessel process and perform the exact simulation of the SABR model. [ABSTRACT FROM AUTHOR]

In this work we derive new closed-form pricing formulas for VIX options in the jump-diffusion SVJJ model proposed by Duffie et al. [Econometrica, 2000, 68, 1343-1376]. Our approach is based on the classic methodology of approximating a density function with an orthogonal expansion of polynomials weighted by a kernel. Orthogonal expansions based on the Gaussian distribution, such as Edgeworth or Gram-Charlier expansions, have been successfully employed by a number of authors in the context of equity options. However, these expansions are not quite suitable for volatility or variance densities as they inherently assign positive mass to the negative real line. Here we approximate option prices via expansions that instead are based on kernels defined on the positive real line. Specifically, we consider a flexible family of distributions, which generalizes the gamma kernel associated with the classic Laguerre expansions. The method can be employed whenever the moments of the underlying variance distribution are known. It provides fast and accurate price computations, and therefore it represents a valid and possibly more robust alternative to pricing techniques based on Fourier transform inversions. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic equilibrium model that can provide a unified explanation for the stylized facts observed in stock index markets such as the fat tails of the risk-neutral return distribution relative to the physical distribution, negative expected returns on deep OTM call options and negative realized variance risk premiums. In particular, we focus on the U-shaped pricing kernel against the stock index return, which is closely related to the negative call returns. We assume that the stock index return follows a time-changed Lévy process and that a representative investor has power utility over the aggregate consumption that forms a linear regression of the stock index return and its stochastic activity rate. This model offers a macroeconomic interpretation of the stylized facts from the perspective of the sensitivity of the activity rate and stock index return on aggregate consumption as well as the investor’s risk aversion. [ABSTRACT FROM AUTHOR]

Basic financial theory indicates that the ratio of the conditional density of the future value of a market index and the corresponding risk neutral density should be monotone, but a sizeable empirical literature finds otherwise. We therefore consider an option augmented density forecast of the market return obtained by transforming a baseline density forecast estimated from past excess returns so as to monotonize its ratio with a risk neutral density estimated from current option prices. To evaluate our procedure, we compare baseline and option augmented monthly density forecasts for the S&P 500 index over the period 1997-2013. We find that monotonizing the pricing kernel leads to a modest improvement in the calibration of density forecasts. Supplementary results supportive of this finding are given for market indices in France, Germany, Hong Kong, Japan and the UK. [ABSTRACT FROM AUTHOR]

The integrated volatility plays an important role in risk management and portfolio selection, the estimation methods regarding the quantity have been widely investigated, either under low-frequency data or high-frequency data, or a combination of both. In this paper, we propose a measure for the integrated volatility via limit order book data with possible presence of multiple records. The estimator is valid under mild conditions and it is easily implemented. The finite sample performance of the proposed estimator has been verified by simulation studies and we apply the method to some real high-frequency data-sets as well. [ABSTRACT FROM PUBLISHER]

We present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994,7, 18–20], [Int. J. Theor. Appl. Finance, 1998,1, 61–110] models. In particular, we consider the stochastic local volatility model—see e.g. Lipton et al. [Quant. Finance, 2014,14, 1899–1922], Piterbarg [Risk, 2007,April, 84–89], Tataru and Fisher [Quantitative Development Group, Bloomberg Version 1, 2010], Lipton [Risk, 2002,15, 61–66]—and the local volatility model incorporating stochastic interest rates—see e.g. Atlan [ArXiV preprint math/0604316, 2006], Piterbarg [Risk, 2006,19, 66–71], Deelstra and Rayée [Appl. Math. Finance, 2012, 1–23], Ren et al. [Risk, 2007,20, 138–143]. For both model classes a particular (conditional) expectation needs to be evaluated which cannot be extracted from the market and is expensive to compute. We establish accurate and ‘cheap to evaluate’ approximations for the expectations by means of the stochastic collocation method [SIAM J. Numer. Anal., 2007,45, 1005–1034], [SIAM J. Sci. Comput., 2005,27, 1118–1139], [Math. Models Methods Appl. Sci., 2012,22, 1–33], [SIAM J. Numer. Anal., 2008,46, 2309–2345], [J. Biomech. Eng., 2011,133, 031001], which was recently applied in the financial context [Available at SSRN 2529691, 2014], [J. Comput. Finance, 2016,20, 1–19], combined with standard regression techniques. Monte Carlo pricing experiments confirm that our method is highly accurate and fast. [ABSTRACT FROM PUBLISHER]

Investment tasks include forecasting volatilities and correlations of assets and portfolios. One of the tools widely utilized is stochastic factor analysis on a set of correlated time-series (e.g. asset returns). Published time-series factor models require either sufficiently wide time windows of observed data or numeric solutions by simulations. We developed a ‘variational sequential Bayesian factor analysis’ (VSBFA) algorithm to make online learning of time-varying stochastic factor structure. The VSBFA is an analytic filter to estimate unknown factor scores, factor loadings and residual variances. The covariance matrix of the time-series predicted by the VSBFA can be decomposed into loadings-based covariance and specific variances, and the former can be expressed by ‘explanatory factors’ such as systematic components of various financial market indices. We compared the VSBFA with the most practiced factor model relying on wide data windows, the rolling PCA (principal components analysis), by applying them to 9-year daily returns of 200 simulated stocks with the ‘true’ daily data-generating model completely known, and by using them to forecast volatilities of long-only and long/short global stock portfolios with 25-year monthly returns of more than 800 stocks worldwide. Accuracy of the forecast covariance matrices is measured by a (symmetrized) Kullback–Leibler distance, and accuracy of the forecast portfolio volatilities is measured by bias statistic, log-likelihood,Q-statistic, and portfolio volatility minimization. The factor-based covariance and specific variances predicted by the best VSBFA are significantly more accurate than those by the best rolling PCA. [ABSTRACT FROM PUBLISHER]

This paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jumps in the logarithm of VIX, we derive a linear relationship between the stochastic volatility factor and the VVIX index. We detect the existence of a co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. Using the VVIX index as a proxy for stochastic volatility, we use the MCMC method to estimate the dynamics of VIX. Comparing nested models of VIX, we show that the jump in VIX and the volatility factor are statistically significant. The jump intensity is also stochastic. We analyse the impact of the jump factor on VIX dynamics. [ABSTRACT FROM PUBLISHER]

In this paper, market microstructure models are considered to assess the influence of the key components that drive asset prices. Synchronization techniques and sampling methods are reviewed. Alternatives to normally distributed asset returns, specifically subordinated Brownian motion, are considered. The influential components of the price processes are then combined under tick time to recover normality of asset returns via subordination, a process I denote as ‘natural time’. Normally distributed returns are obtained with the natural time approach which is also found to dominate GARCH results. [ABSTRACT FROM AUTHOR]

We estimate the daily integrated variance and covariance of stock returns using high-frequency data in the presence of jumps, market microstructure noise and non-synchronous trading. For this we propose jump robust two time scale (co)variance estimators and verify their reduced bias and mean square error in simulation studies. We use these estimators to construct theex-postportfolio realized volatility (RV) budget, determining each portfolio component’s contribution to the RV of the portfolio return. These RV budgets provide insight into the risk concentration of a portfolio. Furthermore, the RV budgets can be directly used in a portfolio strategy, called the equal-risk-contribution allocation strategy. This yields both a higher average return and lower standard deviation out-of-sample than the equal-weight portfolio for the stocks in the Dow Jones Industrial Average over the period October 2007–May 2009. [ABSTRACT FROM AUTHOR]

Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies have examine whether there is significantly greater risk premium in VIX option prices compared with S&P 500 option prices. We address this issue by proposing and analysing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX-implied volatilities, as has been documented. We show that the incorporation of sharp regime shifts can bridge this shortcoming. We take advantage of asymptotic and Fourier methods to make the extension tractable, and we present a fit to data, both in times of crisis and relative calm, which shows the effectiveness of the regime switching. [ABSTRACT FROM AUTHOR]