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Timetable (INIW93)

Computerised Trading at Low & High Frequency

Tuesday 19th November 2013 to Thursday 21st November 2013

Tuesday 19th November 2013
08:20 to 08:50 Registration
08:50 to 09:00 Welcome by John Toland, Director of the Institute INI 2
09:00 to 09:50 The Impact of Computer-Based Trading on Market Quality and Some Policy Responses
We review some of the statistical evidence regarding the impact of computer based trading on market quality. We discuss some policy responses.
09:50 to 10:40 Robust Market Making
Co-authors: Alvaro (Cartea), Ryan (Donnelly)

Because market makers (MMs) acknowledge that their models are incorrectly specified, in this paper, we allow for ambiguity in their choices to make their models robust to misspecification in (i) the arrival rate of market orders (MOs), (ii) the fill probability of limit orders, and (iii) the dynamics of the fundamental value of the asset they deal. We demonstrate that MMs adjust their quotes to reduce inventory risk and adverse selection costs. Moreover, robust market making increases the Sharpe ratio of market making strategies and allows for the MM to fine tune the tradeoff between the mean and the standard deviation of expected profits. Our framework adopts the robust optimal control approach of Hansen and Sargent (2007) and we provide analytical solutions for the robust optimal strategies as well as a verification theorem. We also find that in many circumstances ambiguity averse MMs act differently from MMs who are risk averse.

10:40 to 11:00 Morning Coffee
11:00 to 11:50 T Pennanen (King's College London)
Optimal investment and contingent claim valuation under temporary price impacts and margin requirements
We explore how certain fundamental results in financial mathematics are affected when moving from the classical model of perfectly liquid financial markets towards nonlinear models that incorporate portfolio constraints and nonlinear trading costs that arise in limit order markets. We extend basic results on arbitrage bounds, attainable claims and duality to general convex market models and general swap contracts where both claims and premiums may have multiple payout dates.
11:50 to 12:40 Modern Bayesian machine learning methods and their application to finance and econometrics
Uncertainty, data, and inference play a fundamental role in modelling. Probabilistic approaches to modelling have transformed scientific data analysis, artificial intelligence and machine learning, and have made it possible to exploit the many opportunities arising from the recent explosion of big data problems arising in the sciences, society and commerce. Once a probabilistic model is defined, Bayesian statistics (which used to be called "inverse probability") can be used to make inferences and predictions from the model. Bayesian methods work best when they are applied to models that are flexible enough to capture the complexity of real-world data. Recent work on non-parametric Bayesian machine learning provides this flexibility.

I will give an overview of some of our recent work in nonparametric Bayesian modelling, with an emphasis on models that might be useful in computerised trading, finance and econometrics. Some topics I will cover include scalable and interpretable time series forecasting with Gaussian process regression models, modelling switching and non-stationarity in time series with infinite HMMs, and multivariate stochastic volatility via Wishart processes and dynamic covariance models.

12:40 to 13:30 Lunch at Wolfson Court
14:00 to 14:50 R Almgren (New York University)
Using a Market Simulator to Develop High-Frequency Execution Algorithms
A market simulator is an essential tool for the development of high-frequency trading strategies. We will discuss the principles of constructing a simulator for interest rates futures products, taking account of the special features of these markets such as pro rata matching, implied liquidity, and pricing signals. Comparison with actual trade executions lets us do a quantitative assessment of the validity of the simulator.
14:50 to 15:40 D Sornette (ETH Zürich)
Diagnostic and forecast of future bubbles and crashes
We report recent advances on the calibration of financial bubbles, defined as transient super-exponential stochastic price trajectories that reflect positive feedbacks. The results include advanced methods of calibration to address the quasi-degenerate or soft-mode problem in the estimation procedure, the FTS-GARCH model (finite-time singularity GARCH) and the use of self-consistent rational expectation bubble models with stochastic finite-time singularities. We also present results of the Financial Crisis Observatory ( at ETH Zurich, which aims at testing and quantifying rigorously, in a systematic way and on a large scale the hypothesis that financial bubbles can diagnosed with a rigorous scientific methodology before they burst.
15:40 to 16:00 Afternoon Tea
16:50 to 18:00 Welcome Drinks Reception
Wednesday 20th November 2013
09:00 to 09:50 Do empirical (high and low frequency) measures of price impact capture informed trading?
Co-author: Vyacheslav Fos (University of Illinois at Urbana Champaign)

This talk is based on two papers.

The first paper ("Do prices reveal the presence of informed trading?") tests empirical measures or price impact. Using a comprehensive sample of trades by Schedule 13D filers, who possess valuable private information when they accumulate stocks of targeted companies, this paper studies whether several empirical (high and low frequency) measures of adverse selection reveal the presence of informed trading. The evidence suggests that on days when Schedule 13D filers accumulate shares, both high-frequency and low-frequency measures of stock liquidity and adverse selection indicate higher stock liquidity and lower adverse selection, even though prices are positively a ected. We document three channels that help explain this phenomenon: (a) informed traders select times of higher liquidity when they trade, (b) liquidity increases in response to informed traders' trades, (c) informed traders use limit orders.

The second paper ("Insider Trading, Stochastic Liquidity and Equilibrium Prices") proposes a theoretical model to explain the empirical findings. In that paper, we extend Kyle's (1985) model of insider trading to the case where liquidity provided by noise traders follows a general stochastic process. Even though the level of noise trading volatility is observable, in equilibrium, measured price impact is stochastic. If noise trading volatility is mean-reverting, then the equilibrium price follows a multivariate stochastic volatility `bridge' process. More private information is revealed when volatility is higher. This is because insiders choose to optimally wait to trade more aggressively when noise trading volatility is higher. In equilibrium, market makers anticipate this, and adjust prices accordingly. In time series, insiders trade more aggressively, when measured price impact is lower. Therefore, aggregate execution costs to uninformed traders can be higher when price impact is lower. The model provides some guidance about how to improve existing empirical measures of adverse selection.

09:50 to 10:40 Intraday ecology of electronic limit order market: empirical evidence and multiscale modelling
The advent of computerized trading is often associated with higher frequency of order arrivals and higher rate of trade executions. However, empirical study of order flows submitted by market participants in electronic limit order markets shows a key feature of these market to be a widening of spectrum of frequencies, with a high heterogeneity of order activity across participants. Based on empirical evidence from the S&P futures markets, we show that order flow of 'high-frequency' participants is qualitatively different from that of low frequency ones, both in terms of directionality, inventory and their impact of the limit order book. In particular, there is evidence that a category of HFT, while contributing a major component of order volume, may not necessarily increase market depth.

Based on this empirical evidence, we argue that any model for examining the impact of HFT on market dynamics should allow for order flows occurring at (widely) differing frequencies. We present such a stochastic model, which mimics the features observed in intraday data, and show that the separation of frequencies leads to an asymptotic regime in which the evolution of the limit order book may be described by a simple stochastic equation.

10:40 to 11:00 Morning Coffee
11:00 to 11:50 Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market consisting of a money market account and a single stock whose trading is subject to proportional transaction cost and whose price dynamic is modeled by a family of probability measures, possibly non-dominated. Under a continuity assumption, we prove using a backward-forward scheme that the absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. A parallel statement between robust no-arbitrage and strictly consistent price systems is also obtained.
11:50 to 12:40 Algorithmic Trading with Learning: Informed versus Uninformed
High-frequency traders often take a view on the market and then act accordingly: buy an asset if they predict an upward trend or sell an asset if they expect a downward trend. However, if they are not fully confident in their prediction, how can they optimally trade? Here, we develop a framework to address this problem by first modeling the asset mid-price with a randomized Brownian bridge. The randomization encodes the trader's prior estimate of the asset's future midprice distribution, e.g., a two point discrete random variable corresponds to upward/downward movements. We pose and solve the optimal control and stopping problem for how the trader should post limit orders at the touch and/or cross the spread and execute market orders. The optimal trading strategy indeed learns from the dynamics of the asset's midprice which trend is being realized and modifies its behavior accordingly. By comparing the performance three traders who differ in the accuracy of their predictions and whether they learn or not, we demonstrate that traders can significantly benefit from using our approach.

Authors: Alvaro Cartea, Ryan Donnelly, Sebastian Jaimungal

12:40 to 13:30 Lunch at Wolfson Court
14:00 to 14:50 News Trading and Speed
Co-authors: Johan Hombert (HEC), Ioanid Rosu (HEC)

Speed matters: we show that an investor's optimal trading strategy is significantly different when he observes news faster than others versus when he does not, holding the precision of his signals constant. When the investor has fast access to news, his trades are much more sensitive to news, account for a much bigger fraction of trading volume, and forecasts short run price changes. Moreover, in this case, an increase in news informativeness increases liquidity, volume, and the fast investor's share of trading volume. Last, price changes are more correlated with news and trades contribute more to volatility when the investor has fast access to news.

14:50 to 15:40 Liquidity resilience in the limit order book with survival models
Joint with Efsathios Panayi, Gareth Peters and Jon Danielsson
15:40 to 16:00 Afternoon Tea
16:00 to 16:50 Ultra-Fast Activity and Market Quality
This paper analyses the relationship between ultra-fast activity taking place in the stock market, and different dimensions of market quality. For us "ultra-fast activity" includes the actions of both high-frequency proprietary trading as well as automated buy- and sell-side algos. In order to measure this ultra-fast activity empirically we define a new measure, which uses information on messages sent to the exchange, We then, use this measure as proxy for ultra-fast activity, and analyze its relationship with standard measures of market quality, during the month of march for every year between 2005 and 2011 (inclusive). Our analysis finds evidence that higher ultra-fast activity is associated with lower market quality: less depth in limit order book, higher effective spreads, and higher quoted spreads.
19:00 to 22:00 Conference Dinner at Gonville and Caius College
Thursday 21st November 2013
09:00 to 09:50 Smooth solutions to portfolio liquidation problems under price-sensitive market impact
Co-authors: Paulwin Graewe, Eric Sere

We establish existence and uniqueness of a classical solution to a semilinear parabolic partial dierential equation with singular initial condition. This equation describes the value function of the control problem of a nancial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price dependent impact functions describing the trading costs in the primary market and price dependent adverse selection costs associated with dark pool trading. We establish the explicit asymptotic behavior of the value function at the terminal time and give the optimal trading strategy in feedback form.

09:50 to 10:40 Liquidity Suppliers and High Frequency Trading
We use a liquidity model to study mathematically the effect of ultra high frequency traders, and to show how the markets have changed since ultra high frequency traders (UHFTs) burst onto the scene a half decade ago. In particular we show how they exploit the limit order book to ensure that most algorithmic traders trade at the limits of their market orders. The UHFTs pocket the liquidity profits that were traditionally the province of institutional traders, and in addition exploit their speed advantage and clever tricks to make the purchase of stocks via limit orders as expensive as possible, and the sale of stocks to be at the lowest price the institutional traders are willing to pay.
10:40 to 11:00 Morning Coffee
11:00 to 11:50 Fast Aggressive Trading
Co-authors: Ian Marsh (Cass Business School), Torben Latza (Blackrock)

We study .....

12:40 to 14:00 Sandwich lunch at INI
14:00 to 15:40 Round table discussion
15:40 to 16:00 Afternoon Tea
16:00 to 16:50 Round table discussion
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons