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  • A New Approach for Detecting High-Frequency Trading from Order and Trade Data
  • Mean Reversion Trading with Sequential Deadlines andTransaction Costs abstract We study the optimal timing strategies for trading a mean-reverting price process with afinite deadline to enter and a separate finite deadline to exit the market. The price process is modeled by a diffusion with an affine drift that encapsulates a number of well-known models,including the Ornstein-Uhlenbeck (OU) model, Cox-Ingersoll-Ross (CIR) model, Jacobi model,and inhomogeneous geometric Brownian motion (IGBM) model.We analyze three types of trading strategies: (i) the long-short (long to open, short to close) strategy; (ii) the short-long(short to open, long to close) strategy, and (iii) the chooser strategy whereby the trader has the added flexibility to enter the market by taking either a long or short position, and subsequently close the position. For each strategy, we solve an optimal double stopping problem with sequential deadlines, and determine the optimal timing of trades. Our solution methodology utilizes the local time-space calculus of Peskir (2005) to derive nonlinear integral equations of Volterra-type that uniquely characterize the trading boundaries. Numerical implementation ofthe integral equations provides examples of the optimal trading boundaries.
  • Modeling the price of Bitcoin with fractional Brownian motion: a Monte Carlo approach abstract The long-term dependence of Bitcoin (BTC), manifesting itself through a Hurst exponent $H>0.5$, is exploited in order to predict future BTC/USD price. A Monte Carlo simulation with $10^5$ fractional Brownian motion realisations is performed as extensions on historical data. The accuracy of statistical inferences is 20\%. The most probable Bitcoin price in 180 days is 4537 USD.
  • Mean Reversion Trading with Sequential Deadlines and Transaction Costs
  • Regime-Based Tactical Allocation for Equity Factors and Balanced Portfolios
  • Asymptotics for Greeks under the constant elasticity of variance model abstract This paper is concerned with the asymptotics for Greeks of European-style options and the risk-neutral density function calculated under the constant elasticity of variance model. Formulae obtained help financial engineers to construct a perfect hedge with known behaviour and to price any options on financial assets.
  • Dynamic Quantile Function Models abstract We offer a novel way of thinking about the modelling of the time-varying distributions of financial asset returns. Borrowing ideas from symbolic data analysis, we consider data representations beyond scalars and vectors. Specifically, we consider a quantile function as an observation, and develop a new class of dynamic models for quantile-function-valued (QF-valued) time series. In order to make statistical inferences and account for parameter uncertainty, we propose a method whereby a likelihood function can be constructed for QF-valued data, and develop an adaptive MCMC sampling algorithm for simulating from the posterior distribution. Compared to modelling realised measures, modelling the entire quantile functions of intra-daily returns allows one to gain more insight into the dynamic structure of price movements. Via simulations, we show that the proposed MCMC algorithm is effective in recovering the posterior distribution, and that the posterior means are reasonable point estimates of the model parameters. For empirical studies, the new model is applied to analysing one-minute returns of major international stock indices. Through quantile scaling, we further demonstrate the usefulness of our method by forecasting one-step-ahead the Value-at-Risk of daily returns.
  • Instantaneous order impact and high-frequency strategy optimization in limit order books abstract We propose a limit order book (LOB) model with dynamics that account for both the impact of the most recent order and the shape of the LOB. We present an empirical analysis showing that the type of the last order significantly alters the submission rate of immediate future orders, even after accounting for the state of the LOB. To model these effects jointly we introduce a discrete Markov chain model. Then on these improved LOB dynamics, we find the policy for optimal order choice and placement in the share purchasing problem by framing it as a Markov decision process. The optimal policy derived numerically uses limit orders, cancellations and market orders. It looks to exploit the state of the LOB summarized by the volume at the bid/ask and the type of the most recent order to obtain the best execution price, avoiding non-execution and adverse selection risk simultaneously. Market orders are used aggressively when the mid-price is expected to move adversely. Limit orders are placed under favorable LOB conditions and canceled when non-execution or adverse selection probability is high. Using ultra high-frequency data from the NASDAQ stock exchange we compare our optimal policy with other submission strategies that use a subset of all available order types and show that ours significantly outperforms them.
  • The Bitcoin price formation: Beyond the fundamental sources abstract Much significant research has been done to investigate various facets of the link between Bitcoin price and its fundamental sources. This study goes beyond by looking into least to most influential factors-across the fundamental, macroeconomic, financial, speculative and technical determinants as well as the 2016 events-which drove the value of Bitcoin in times of economic and geopolitical chaos. We use a Bayesian quantile regression to inspect how the structure of dependence of Bitcoin price and its determinants varies across the entire conditional distribution of Bitcoin price movements. In doing so, three groups of determinants were derived. The use of Bitcoin in trade and the uncertainty surrounding China's deepening slowdown, Brexit and India's demonetization were found to be the most potential contributors of Bitcoin price when the market is improving. The intense anxiety over Donald Trump being the president of United States was shown to be a positive determinant pushing up the price of Bitcoin when the market is functioning around the normal mode. The velocity of bitcoins in circulation, the gold price, the Venezuelan currency demonetization and the hash rate were found to be the fundamentals influencing the Bitcoin price when the market is heading into decline.
  • Robust Technical Trading with Fuzzy Knowledge-Based Systems
  • Banking risk as an epidemiological model: an optimal control approach abstract The process of contagiousness spread modelling is well-known in epidemiology. However, the application of spread modelling to banking market is quite recent. In this work, we present a system of ordinary differential equations, simulating data from the largest European banks. Then, an optimal control problem is formulated in order to study the impact of a possible measure of the Central Bank in the economy. The proposed approach enables qualitative specifications of contagion in banking obtainment and an adequate analysis and prognosis within the financial sector development and macroeconomic as a whole. We show that our model describes well the reality of the largest European banks. Simulations were done using MATLAB and BOCOP optimal control solver, and the main results are taken for three distinct scenarios.
  • Option Pricing in a Regime Switching Stochastic Volatility Model abstract In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model has been successfully used where the volatility is expressed as a stochastic differential equation. In addition, we consider a regime switching model where the stock volatility dynamics depends on an underlying process which is possibly a non-Markov pure jump process. Under this model assumption, we find the locally risk minimizing pricing of European type vanilla options. The price function is shown to satisfy a Heston type PDE.
  • Stock Price Patterns When Overconfident Traders Overestimate Their Ability and Underestimate the Competition
  • Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model abstract In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial time series and our model covers both. To illustrate the relevance of our proposed methodology, we first compare the proposed model with the well-known hidden Markov model via likelihood ratio tests and a novel goodness-of-fit test on the S\&P 500 daily returns. Secondly, we present out-of-sample hedging results on S\&P 500 vanilla options as well as a trading strategy based on theoretical prices, which we compare to simpler models including the classical Black-Scholes delta-hedging approach.
  • A Model for Queue Position Valuation in a Limit Order Book
  • Portfolio Risk Assessment using Copula Models abstract In the paper, we use and investigate copulas models to represent multivariate dependence in financial time series. We propose the algorithm of risk measure computation using copula models. Using the optimal mean-$CVaR$ portfolio we compute portfolio's Profit and Loss series and corresponded risk measures curves. Value-at-risk and Conditional-Value-at-risk curves were simulated by three copula models: full Gaussian, Student's $t$ and regular vine copula. These risk curves are lower than historical values of the risk measures curve. All three models have superior prediction ability than a usual empirical method. Further directions of research are described.
  • Model for Constructing an Options Portfolio with a Certain Payoff Function abstract The portfolio optimization problem is a basic problem of financial analysis. In the study, an optimization model for constructing an options portfolio with a certain payoff function has been proposed. The model is formulated as an integer linear programming problem and includes an objective payoff function and a system of constraints. In order to demonstrate the performance of the proposed model, we have constructed the portfolio on the European call and put options of Taiwan Futures Exchange. The optimum solution was obtained using the MATLAB software. Our approach is quite general and has the potential to design options portfolios on financial markets.
  • Active Loan Trading
  • Bayesian Realized-GARCH Models for Financial Tail Risk Forecasting Incorporating Two-sided Weibull Distribution abstract The realized GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed in the realized GARCH framework. Further, sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. An adaptive Bayesian Markov Chain Monte Carlo method is developed and employed for estimation and forecasting, whose properties are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH, GARCH with two-sided Weibull distribution and realized GARCH models, tail risk forecasting results across 7 market index return series and 2 individual assets clearly favor the realized GARCH models incorporating two-sided Weibull distribution, especially models employing the sub-sampled realized variance and sub-sampled realized range, over a six year period that includes the global financial crisis.
  • Option Pricing with Delayed Information abstract We propose a model to study the effects of delayed information on option pricing. We first talk about the absence of arbitrage in our model, and then discuss super replication with delayed information in a binomial model, notably, we present a closed form formula for the price of convex contingent claims. Also, we address the convergence problem as the time-step and delay length tend to zero and introduce analogous results in the continuous time framework. Finally, we explore how delayed information exaggerates the volatility smile.
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