# Bitcoin orderbooks and high frequency market microstructure

Under the assumption that the best competing response is exponentially distributed around a commonly discerned fair market price we examine properties of the market maker's optimal behavior. We show that simple adjustments to skew and width accommodate customer arrival imbalance. We derive a straightforward relationship between the market marker's fill probability and direct holding costs.

A simple formula for optimal bidding in terms of non-myopic inventory cost is presented. Large-dimensional factor modeling based on high-frequency observations Markus Pelger Stanford This paper develops a statistical theory to estimate an unknown factor structure based on financial high-frequency data.

I derive an estimator for the number of factors and consistent and asymptotically mixed-normal estimators of the loadings and factors under the assumption of a large number of cross-sectional and high-frequency observations. The estimation approach can separate factors for continuous and rare jump risk.

The estimators for the loadings and factors are based on the principal component analysis of the quadratic covariation matrix.

The estimator for the number of factors uses a perturbed eigenvalue ratio statistic. The results are obtained under general conditions, that allow for a very rich class of stochastic processes and for serial and cross-sectional correlation in the idiosyncratic components. I apply the approach to the U. Gox to analyze the dynamics of the price of bitcoin on the period June to November The data set gives us a rare opportunity to observe the emergence of a retail-focused, highly speculative and unregulated market at a tick frequency with trader identifiers at the transaction level.

Jumps are frequent events and they cluster in time. They are predicted by the order flow imbalance and the preponderance of aggressive traders, as well as a widening of the bid-ask spread. Jumps have short-term positive impact on market activity and illiquidity and see a persistent change in the price.

We use this modification to evaluate the empirical plausibility of recent predictions from high frequency financial theory regarding the small-time movements of an Ito semimartingale. The theory indicates that the probability distribution of the small moves should be locally stable around the origin. It makes no predictions regarding large rare jumps, which get filtered out. Our exact Bayesian procedure imposes support conditions on parameters as implied by this theory. The evidence is consistent with a locally stable distribution valid over most of the support of the observed data while mildly failing in the extreme tails, about which the theory makes no prediction.

We undertake diagnostic checks on all aspects of the procedure. In particular, we evaluate the distributional assumptions regarding a semi-pivotal statistic, and we test by Monte Carlo that the posterior distribution is properly centered with short credibility intervals.

Taken together, our results suggest a more important role than previously thought for pure jump-like models with diminished, if not absent, diffusive component. Nonparametric Option-based Volatility Estimation Viktor Todorov Kellogg In this talk we first review the different methods for recovering volatility non-parametrically from high-frequency return data. We then derive analogues of some of these methods for recovering volatility from options written on the underlying asset.

The option data is observed with error and we prove the consistency of the option-based volatility estimators. We further derive a Central Limit Theorem for the estimators. The limiting distribution is mixed-Gaussian and depends on the quality of the option data on the given date as well as on the overall state of the economy. We compare the option and return based volatility estimators and present numerical experiments documenting the superior performance of the former. It is a challenging problem to obtain reliable estimate of VaR, since there is often a lack of sufficient amount of observations to accurately estimate the tail quantile.

In this talk we propose a general approach of pooling data from other 'similar' companies to increase the available data and to make more accurate estimation. A similarity measure is proposed to identify the nearest neighbors and a bandwidth selection procedure is developed for practical guidance. Simulation and real data examples are presented. Uniform Inference on Volatility Dacheng Xiu Chicago Booth In this paper, we propose a general framework of volatility inference with noisy high-frequency data.

Our estimator is obtained by maximizing the likelihood of a misspecified MA model with homoscedastic innovations. We show that this quasi-likelihood estimator is consistent with respect to the quadratic variation of the semimartingale, and that the estimator is asymptotically mixed normal.

We thereby provide uniform inference on volatility over small and large noises. Finally, we present the semiparametric efficiency bound on volatility estimation, from which our estimator deviates slightly. To implement our likelihood estimator, we adopt Kalman filter and a state-space representation, which is tuning-free and warrants a positive estimate in finite sample.

In contrast, we show that the classical Whittle approximation is inconsistent under in-fill asymptotics. Structured often as a proprietary trading business, most HFT trading firms try to remain an ultra-low profile to protect their trade secrets. This mysteriousness does not help their public image, unfortunately, though HFT is more of a result from combining finance, science and engineering than any other investment or trading methods.

In this talk, Mr. Xu will demystify what HFT really is, correct some common misconceptions, explain basic principles behind HFT trading, introduce some common HFT strategy types, and explain why, in his mind, HFT has existed, will exist and must exist in one form or another in a free market place.

In , he joined Jump Trading as a trader specialized in index futures trading. In , he joined HTG Capital Partners now renamed to Hehmeyer LLC as a partner and built a trading group specialized in trading index futures, treasury futures, commodity futures and options.

Steve is president of the Chinese Trading and Derivatives Association. A reduced-form model for level-1 limit order books Tzu-Wei Yang Minnesota One popular approach to model the limit order books dynamics of the best bid and ask at level-1 is to use the reduced-form diffusion approximations.

It is well known that the biggest contributing factor to the price movement is the imbalance of the best bid and ask. We investigate the data of the level-1 limit order books of a basket of stocks and study the numerical evidence of drift, correlation, volatility and their dependence on the imbalance.

Based on the numerical discoveries, we develop a nonparametric discrete model for the dynamics of the best bid and ask, which can be approximated by a reduced-form model with analytical tractability that can fit the empirical data of correlation, volatilities and probability of price movement simultaneously.

This is a joint work with Prof. Generalized Autoregressive Conditional Frechet Models for Maxima Zhengjun Zhang Wisconsin This talk introduces a novel dynamic framework to integrate the static generalized extreme value GEV distribution with dynamic modeling approach for the modeling of maxima in financial time series. The GACF model provides a direct and accurate modeling of the time varying behavior of maxima and offers a new angle to study the tail risk dynamics in financial markets.

Probabilistic properties of GACF are fully studied and an irregular maximum likelihood estimator is used for model estimation, with its statistical properties investigated. Simulation study shows the flexibility of GACF and confirms the reliability of its estimators. The results of two real data examples in which GACF is used for market tail risk monitoring and VaR calculation are presented, where significant improvement over static GEV has been observed.

Empirical result of GACF is consistent with the findings of the dynamic peak-over-threshold POT literature, that the tail index of financial markets varies through time a joint work with Zifeng Zhao and Rong Chen. A Hawkes Process Approach Lingjiong Zhu Florida State Dark pools are automated trading facilities which do not display bid and ask quotes to the public.

In this talk, we use the Hawkes process to model the clustered arrival of trades in a dark pool and analyze various performance metrics including time-to-first-fill, time-to-complete-fill and the expected fill rate of a resting dark order. This is based on the joint work with Xuefeng Gao and Xiang Zhou. Uniform Inference on Volatility. We then develop a non-parametric test statistic that allows for the identification of drift bursts from noisy high-frequency data. We apply this methodology to a comprehensive set of tick data and show that drift bursts form an integral part of the price dynamics across equities, fixed income, currencies and commodities.

A majority of the identified drift bursts are accompanied by price reversion and can therefore be regarded as "flash crashes. We find that currencies whose changes are more sensitive to negative market jumps provide significantly higher expected returns. The positive risk premium constitutes compensation for the extreme losses during periods of market turmoil. Using the empirical finding, we propose a jump modified carry trade strategy, which has approximately 2-percent point per annum higher returns than the regular carry trade strategy.

These findings result from the fact that negative jump betas are significantly related to the riskiness of currencies and business conditions. Market Making as a Sequence of Sealed-Bid Auctions, with Analytic Results Andrew Papanicolaou NYU Tandon We provide analytic results for the optimal control problem faced by a market maker who can only obtain and dispose of inventory via a sequence of sealed-bid auctions.

Under the assumption that the best competing response is exponentially distributed around a commonly discerned fair market price we examine properties of the market maker's optimal behavior. We show that simple adjustments to skew and width accommodate customer arrival imbalance. We derive a straightforward relationship between the market marker's fill probability and direct holding costs.

A simple formula for optimal bidding in terms of non-myopic inventory cost is presented. Large-dimensional factor modeling based on high-frequency observations Markus Pelger Stanford This paper develops a statistical theory to estimate an unknown factor structure based on financial high-frequency data. I derive an estimator for the number of factors and consistent and asymptotically mixed-normal estimators of the loadings and factors under the assumption of a large number of cross-sectional and high-frequency observations.

The estimation approach can separate factors for continuous and rare jump risk. The estimators for the loadings and factors are based on the principal component analysis of the quadratic covariation matrix. The estimator for the number of factors uses a perturbed eigenvalue ratio statistic. The results are obtained under general conditions, that allow for a very rich class of stochastic processes and for serial and cross-sectional correlation in the idiosyncratic components.

I apply the approach to the U. Gox to analyze the dynamics of the price of bitcoin on the period June to November The data set gives us a rare opportunity to observe the emergence of a retail-focused, highly speculative and unregulated market at a tick frequency with trader identifiers at the transaction level.

Jumps are frequent events and they cluster in time. They are predicted by the order flow imbalance and the preponderance of aggressive traders, as well as a widening of the bid-ask spread. Jumps have short-term positive impact on market activity and illiquidity and see a persistent change in the price.

We use this modification to evaluate the empirical plausibility of recent predictions from high frequency financial theory regarding the small-time movements of an Ito semimartingale. The theory indicates that the probability distribution of the small moves should be locally stable around the origin. It makes no predictions regarding large rare jumps, which get filtered out. Our exact Bayesian procedure imposes support conditions on parameters as implied by this theory.

The evidence is consistent with a locally stable distribution valid over most of the support of the observed data while mildly failing in the extreme tails, about which the theory makes no prediction. We undertake diagnostic checks on all aspects of the procedure. In particular, we evaluate the distributional assumptions regarding a semi-pivotal statistic, and we test by Monte Carlo that the posterior distribution is properly centered with short credibility intervals.

Taken together, our results suggest a more important role than previously thought for pure jump-like models with diminished, if not absent, diffusive component.

Nonparametric Option-based Volatility Estimation Viktor Todorov Kellogg In this talk we first review the different methods for recovering volatility non-parametrically from high-frequency return data.

We then derive analogues of some of these methods for recovering volatility from options written on the underlying asset. The option data is observed with error and we prove the consistency of the option-based volatility estimators. We further derive a Central Limit Theorem for the estimators. The limiting distribution is mixed-Gaussian and depends on the quality of the option data on the given date as well as on the overall state of the economy.

We compare the option and return based volatility estimators and present numerical experiments documenting the superior performance of the former. It is a challenging problem to obtain reliable estimate of VaR, since there is often a lack of sufficient amount of observations to accurately estimate the tail quantile. In this talk we propose a general approach of pooling data from other 'similar' companies to increase the available data and to make more accurate estimation.

A similarity measure is proposed to identify the nearest neighbors and a bandwidth selection procedure is developed for practical guidance. Simulation and real data examples are presented.

Uniform Inference on Volatility Dacheng Xiu Chicago Booth In this paper, we propose a general framework of volatility inference with noisy high-frequency data.

Our estimator is obtained by maximizing the likelihood of a misspecified MA model with homoscedastic innovations. We show that this quasi-likelihood estimator is consistent with respect to the quadratic variation of the semimartingale, and that the estimator is asymptotically mixed normal. We thereby provide uniform inference on volatility over small and large noises.

Finally, we present the semiparametric efficiency bound on volatility estimation, from which our estimator deviates slightly. To implement our likelihood estimator, we adopt Kalman filter and a state-space representation, which is tuning-free and warrants a positive estimate in finite sample.

In contrast, we show that the classical Whittle approximation is inconsistent under in-fill asymptotics. Structured often as a proprietary trading business, most HFT trading firms try to remain an ultra-low profile to protect their trade secrets. This mysteriousness does not help their public image, unfortunately, though HFT is more of a result from combining finance, science and engineering than any other investment or trading methods.

In this talk, Mr. Xu will demystify what HFT really is, correct some common misconceptions, explain basic principles behind HFT trading, introduce some common HFT strategy types, and explain why, in his mind, HFT has existed, will exist and must exist in one form or another in a free market place.

In , he joined Jump Trading as a trader specialized in index futures trading. In , he joined HTG Capital Partners now renamed to Hehmeyer LLC as a partner and built a trading group specialized in trading index futures, treasury futures, commodity futures and options. Steve is president of the Chinese Trading and Derivatives Association.

A reduced-form model for level-1 limit order books Tzu-Wei Yang Minnesota One popular approach to model the limit order books dynamics of the best bid and ask at level-1 is to use the reduced-form diffusion approximations. It is well known that the biggest contributing factor to the price movement is the imbalance of the best bid and ask. We investigate the data of the level-1 limit order books of a basket of stocks and study the numerical evidence of drift, correlation, volatility and their dependence on the imbalance.

Based on the numerical discoveries, we develop a nonparametric discrete model for the dynamics of the best bid and ask, which can be approximated by a reduced-form model with analytical tractability that can fit the empirical data of correlation, volatilities and probability of price movement simultaneously. This is a joint work with Prof. Generalized Autoregressive Conditional Frechet Models for Maxima Zhengjun Zhang Wisconsin This talk introduces a novel dynamic framework to integrate the static generalized extreme value GEV distribution with dynamic modeling approach for the modeling of maxima in financial time series.

The GACF model provides a direct and accurate modeling of the time varying behavior of maxima and offers a new angle to study the tail risk dynamics in financial markets.