No description available.

Cette thèse explore théoriquement et empiriquement les implications de la dynamique jointe action/option sur divers problématiques liées au trading d’options. Dans un premier temps, nous commençons par l’étude de la dynamique jointe entre une option sur un stock et une option sur l’indice de marché. Le modèle CAPM fournit un cadre mathématique adéquat pour cette étude car il permet de modéliser la dynamique jointe d’un stock et son indice de marché. En passant aux prix d’options, nous montrons que le beta et la volatilité idiosyncratique, paramètres du modèle, permettent de caractériser la relation entre les surfaces de volatilité implicite du stock et de l’indice. Nous nous penchons alors sur l’estimation du paramètre beta sous la probabilité risque-neutre en utilisant les prix d’options. Cette mesure, appelée beta implicite, représente l’information contenue dans les prix d’options sur la réalisation du paramètre beta dans le futur.Pour cette raison, nous essayons de voir, si le beta implicite a un pouvoir prédictif du beta futur.En menant une étude empirique, nous concluons que le beta implicite n’améliore pas la capacité de prédiction en comparaison avec le beta historique qui est calculé à travers la régression linéaire des rendements du stock sur ceux de l’indice. Mieux encore, nous remarquons que l’oscillation du beta implicite autour du beta futur peut entraîner des opportunités d’arbitrage, et nous proposons une stratégie d’arbitrage qui permet de monétiser cet écart. D’un autre côté, nous montrons que l’estimateur du beta implicite pourrait être utilisé pour la couverture d’options sur le stock en utilisant des instruments sur l’indice, cette couverture concerne notamment le risque de volatilité et aussi le risque de delta. Dans la deuxième partie de notre travail, nous nous intéressons au problème de market making sur options. Dans cette étude, nous supposons que le modèle de dynamique du sous-jacent sous la probabilité risque-neutre pourrait être mal spécifié ce qui traduit un décalage entre la distribution implicite du sous-jacent et sa distribution historique.Dans un premier temps, nous considérons le cas d’un market maker risque neutre qui vise à maximiser l’espérance de sa richesse future. A travers l’utilisation d’une approche de contrôle optimal stochastique, nous déterminons les prix optimaux d’achat et de vente sur l’option et nous interprétons l’effet de présence d’inefficience de prix sur la stratégie optimale. Dans un deuxième temps, nous considérons que le market maker est averse au risque et essaie donc de réduire l’incertitude liée à son inventaire. En résolvant un problème d’optimisation basé sur un critère moyenne-variance, nous obtenons des approximations analytiques des prix optimaux d’achat et de vente. Nous montrons aussi les effets de l’inventaire et de l’inefficience du prix sur la stratégie optimale. Nous nous intéressons par la suite au market making d’options dans une dimension plus élevée. Ainsi, en suivant le même raisonnement, nous présentons un cadre pour le market making de deux options ayant des sous-jacents différents avec comme contrainte la réduction de variance liée au risque d’inventaire détenu par le market-maker. Nous déterminons dans ce cas la stratégie optimale et nous appuyons les résultats théoriques par des simulations numériques.Dans la dernière partie de notre travail, nous étudions la dynamique jointe entre la volatilité implicite à la monnaie et le sous jacent, et nous essayons d’établir le lien entre cette dynamique jointe et le skew implicite. Nous nous intéressons à un indicateur appelé "Skew Stickiness Ratio"qui a été introduit dans la littérature récente. Cet indicateur mesure la sensibilité de la volatilité implicite à la monnaie face aux mouvements du sous-jacent. Nous proposons une méthode qui permet d’estimer la valeur de cet indicateur sous la probabilité risque-neutre sans avoir besoin d’admettre des hypothèses sur la dynamique du sous-jacent. [...] / This thesis explores theoretically and empirically the implications of the stock/option joint dynamics on applications related to option trading. In the first part of the thesis, we look into the relations between stock options and index options under the risk-neutral measure. The Capital Asset Pricing Model offers an adequate mathematical framework for this study as it provides a modeling approach for the joint dynamics between the stock and the index. As we compute option prices according to this model, we find out that the beta and the idiosyncratic volatility of the stock, which are parameters of the model, characterize the relation between the implied volatility surface of the stock and the one of the index. For this reason, we focus on the estimation of the parameter beta under the risk-neutral measure through the use of option prices.This measure, that we call implied beta, is the information contained in option prices concerning the realization of the parameter beta in the future. Trying to use this additional information, we carry out an empirical study in order to investigate whether the implied beta has a predictive power of the forward realized beta. We conclude that the implied beta doesn’t perform better than the historical beta which is estimated using the linear regression of the stock’s returns onthe index returns. We conclude also that the oscillation of the implied beta around the forward realized beta can engender arbitrage opportunities, and we propose an arbitrage strategy which enables to monetize this difference. In addition, we show that the implied beta is useful to hedge stock options using instruments on the index. In the second part of our work, we consider the problem of option market making. We suppose that the model used to describe the dynamics of the underlying under the risk-neutral probability measure can be misspecified which means thatthe implied distribution of the underlying may be different from its historical one. We consider first the case of a risk neutral market maker who aims to maximize the expectation of her final wealth. Using a stochastic control approach, we determine the optimal bid and ask prices on the option and we interpret the effect of price inefficiency on the optimal strategy. Next to that, we suppose that the market maker is risk averse as she tries to minimize the variance of her finalwealth. We solve a mean-variance optimization problem and we provide analytic approximations for the optimal bid and ask prices. We show the effects of option inventory and price inefficiency on the optimal strategy. We try then to extrapolate the study to a higher dimension in order to see the effect of joint dynamics of the different underlyings on the optimal strategy. Thus, we study market making strategies on a pair of options having different underlyings with the aim to reduce the risk due to accumulated inventories in these two options. Through the resolution of the HJB equation associated to the new optimization problem, we determine the optimal strategy and we support our theoretical finding with numerical simulations. In the final part of the thesis, we study the joint dynamics of the at-the-money implied volatility and the spot process. We try to establish a relation between this joint dynamics and the implied skew through the use of a quantity called the Skew Stickiness Ratio which was introduced in the recent literature. The Skew Stickiness Ratio quantifies the effect of the log-return of the spot on the increment of theat-the-money volatility. We suggest a model-free approach for the estimation of the SSR (Skew Stickiness Ratio) under the risk-neutral measure, this approach doesn’t depend on hypothesis on the dynamics of the underlying. [...]

The purpose of this thesis is to analyze market making trading strategy and explore possibilities of using such strategy for intraday trading on the markets with the limit order book. In theoretical part we prove profitability of specified market making strategy under certain assumptions and moreover analyze effect of change of parameters on the performance of the strategy using one dimensional stochastic processes. Next the assumption of constant fair price is relaxed which leads to deterioration of profitability of these strategies. Because one dimensional stochastic processes do not capture price creation in the real world, we propose stochastic model of intraday trading in the next chapter. Advantage of this approach is that we can observe state of the limit order book during whole trading session and therefore better simulate conditions for test of the strategies. Although proposed model exhibit many phenomenons observed in empirical data like volatility clustering, in some situations it produces unrealistically high spread caused by the construction of the model, because arrivals of market and limit orders are modeled as independent processes. Another disadvantages are need of relatively extensive data for model calibration and high sensitivity of model to change of parameters. Lastly we test three different market making strategies under different choice of model parameters and show that expected profitability is positive in all cases.

This thesis considers three complications that arise from applying reinforcement learning to a real-world application. In the process of using reinforcement learning to build an adaptive electronic market-maker, we find the sparsity of data, the partial observability of the domain, and the multiple objectives of the agent to cause serious problems for existing reinforcement learning algorithms. We employ importance sampling (likelihood ratios) to achieve good performance in partially observable Markov decision processes with few data. Our importance sampling estimator requires no knowledge about the environment and places few restrictions on the method of collecting data. It can be used efficiently with reactive controllers, finite-state controllers, or policies with function approximation. We present theoretical analyses of the estimator and incorporate it into a reinforcement learning algorithm. Additionally, this method provides a complete return surface which can be used to balance multiple objectives dynamically. We demonstrate the need for multiple goals in a variety of applications and natural solutions based on our sampling method. The thesis concludes with example results from employing our algorithm to the domain of automated electronic market-making.

In this thesis we investigate some properties of market making and statistical arbitrage applied to High Frequency Trading (HFT). Using the Hamilton-Jacobi-Bellman(HJB) model developed by Guilbaud, Fabien and Pham, Huyen in 2012, we studied how market making works to obtain optimal strategy during limit order and market order. Also we develop the best investment strategy through Moving Average, Exponential Moving Average, Relative Strength Index, Sharpe Ratio.

Stock markets employ specialized traders, market-makers, designed to provide liquidity and volume to the market by constantly supplying both supply and demand. In this paper, we demonstrate a novel method for modeling the market as a dynamic system and a reinforcement learning algorithm that learns profitable market-making strategies when run on this model. The sequence of buys and sells for a particular stock, the order flow, we model as an Input-Output Hidden Markov Model fit to historical data. When combined with the dynamics of the order book, this creates a highly non-linear and difficult dynamic system. Our reinforcement learning algorithm, based on likelihood ratios, is run on this partially-observable environment. We demonstrate learning results for two separate real stocks.

We study the intraday behavior of bid-ask spreads for actively traded TAIEX option in Taiwan. A study of quality of price quotation offered by market makers is important because the market makers have the responsibilities to keep trading costs low and promote price discovery. Due to the observed wider price quotation from market makers, we find that market makers offer inefficient price quotations to fulfill their obligations under requirement of market making. Moreover, ways of quotation market makers choose, indeed, affect the price quotation of market makers. We also find foreign institutional investors (QFIIs) and market makers bear lower execution cost when they deal on TAIEX option market. Overall, despite the large trading volume and increasing liquidity in TAIEX option, our results suggest that market makers do not play an important role to the market liquidity of TAIEX option market as we thought previously. / We study the intraday behavior of bid-ask spreads for actively traded TAIEX option in Taiwan. A study of quality of price quotation offered by market makers is important because the market makers have the responsibilities to keep trading costs low and promote price discovery. Due to the observed wider price quotation from market makers, we find that market makers offer inefficient price quotations to fulfill their obligations under requirement of market making. Moreover, ways of quotation market makers choose, indeed, affect the price quotation of market makers. We also find foreign institutional investors (QFIIs) and market makers bear lower execution cost when they deal on TAIEX option market. Overall, despite the large trading volume and increasing liquidity in TAIEX option, our results suggest that market makers do not play an important role to the market liquidity of TAIEX option market as we thought previously.

During the last few years, market micro-structure research has been active in analysing the dependence of market efficiency on different market character­ istics. Make-take fees are one of those topics as they might modify the incen­ tives for participating agents, e.g. broker-dealers or market-makers. In this thesis, we propose a Hawkes process-based model that captures statistical differences arising from different fee regimes and we estimate the differences on limit order book data. We then use these estimates in an attempt to measure the execution quality from the perspective of a market-maker. We appropriate existing theoretical market frameworks, however, for the pur­ pose of hireling optimal market-making policies we apply a novel method of deep reinforcement learning. Our results suggest, firstly, that maker-taker exchanges provide better liquidity to the markets, and secondly, that deep reinforcement learning methods may be successfully applied to the domain of optimal market-making. JEL Classification Keywords Author's e-mail Supervisor's e-mail C32, C45, C61, C63 make-take fees, Hawkes process, limit order book, market-making, deep reinforcement learn­ ing kiselrastislavSgmail.com barunik@f sv.cuni.cz

Market making – the process of simultaneously and continuously providing buy and sell prices in a financial asset – is rather complicated to optimize. Applying reinforcement learning (RL) to infer optimal market making strategies is a relatively uncharted and novel research area. Most published articles in the field are notably opaque concerning most aspects, including precise methods, parameters, and results. This thesis attempts to explore and shed some light on the techniques, problem formulations, algorithms, and hyperparameters used to construct RL-derived strategies for market making. First, a simple probabilistic model of a limit order book is used to compare analytical and RL-derived strategies. Second, a market making agent is trained on a more complex Markov chain model of a limit order book using tabular Q-learning and deep reinforcement learning with double deep Q-learning. Results and strategies are analyzed, compared, and discussed. Finally, we propose some exciting extensions and directions for future work in this research field. / Likviditetsgarantering (eng. ”market making”) – processen att simultant och kontinuerligt kvotera köp- och säljpriser i en finansiell tillgång – är förhållandevis komplicerat att optimera. Att använda förstärkningsinlärning (eng. ”reinforcement learning”) för att härleda optimala strategier för likviditetsgarantering är ett relativt outrett och nytt forskningsområde. De flesta publicerade artiklarna inom området är anmärkningsvärt återhållsamma gällande detaljer om de tekniker, problemformuleringar, algoritmer och hyperparametrar som används för att framställa förstärkningsinlärningsbaserade strategier. I detta examensarbete så gör vi ett försök på att utforska och bringa klarhet över dessa punkter. Först används en rudimentär probabilistisk modell av en limitorderbok som underlag för att jämföra analytiska och förstärkningsinlärda strategier. Därefter brukas en mer sofistikerad Markovkedjemodell av en limitorderbok för att jämföra tabulära och djupa inlärningsmetoder. Till sist presenteras även spännande utökningar och direktiv för framtida arbeten inom området.

This thesis is among the first market microstructure studies of an index futures market with designated market makers in the academic literature. The purpose of this thesis is to investigate intraday patterns of key variables, the relative size of the components of the quoted bid-ask spread, and the order decisions of uninformed traders, in a continuous dealer market for index futures with market makers. Overall, our findings aim to contribute to a better understanding of the roles of market makers and public customers in price formation. Intraday patterns of financial market variables such as trade price, volume, trade size, quoted spreads, depth, and volatility separately for designated market makers and public customers are examined. The lack of relevant and appropriate data in futures markets, as evidenced by Hasbrouck (2003) and Kurov (2005), has inhibited the growth of market microstructure in futures markets. Individual orders, quotes, trader identification, and transactions from June 2003 to December 2004, for FTSEurofirst 80 and 100 index futures are used in the study. Inclusion of the parties to order execution distinguishes this data set from most other futures microstructure sources. As this thesis is the first known academic study of the extant market microstructure of the FTSEurofirst index futures, the institutional aspects of the trading process for the FTSEurofirst index futures are also explored. An alternative method for estimating three cost components as a proportion of the bid-ask spread is developed. A framework is developed for the order decision process of an uninformed trader for the first time in a futures market with market makers. The results of this thesis may have implications for other financial markets and the field of market microstructure.