O objetivo desta dissertação é desenvolver um modelo de gestão de risco de liquidez que flexibilize as principais simplificações geralmente realizadas pelas instituições financeiras na aplicação de testes de estresse para gerenciamento do risco de liquidez. Assim, esta pesquisa consiste em estimar um fluxo de caixa unificado de uma instituição sob diferentes cenários econômicos, testando se as volatilidades implícitas das opções são um bom indicador de mudanças significativas no mercado de capitais brasileiro, como quebras de correlações históricas e avaliando o efeito da utilização de um deslocamento não paralelo da Estrutura a Termo da Taxa de Juros na aplicação de um teste de estresse. Para alcançar os objetivos propostos, desenvolveu-se uma pesquisa exploratória através do método de estudo de casos. Para isto, este trabalho utilizou um modelo de análise fatorial para avaliar os movimentos da estrutura a termo da taxa de juros brasileira, além de uma ferramenta prática para capturar as informações fornecidas pela volatilidade implícita e uma matriz de correlação entre as variáveis do cenário econômico utilizado para o teste de estresse. Concluiu-se que: i) a realização de um ajuste no cenário econômico em função da matriz de correlação de suas variáveis contribui para a coerência desse teste com seu contexto econômico, sensibilizando significativamente os valores dos fluxos de caixa futuros das instituições financeiras; ii) os resultados da análise fatorial indicam que a aplicação de um deslocamento não paralelo da ETTJ tem pouca importância prática para a melhoria da coerência dos testes de estresse, em função da grande concentração de poder explicativo da sua variabilidade em torno do fator nível e do baixo poder explicativo dos fatores inclinação e curvatura, principalmente nos vértices iniciais; iii) a volatilidade implícita pode ser utilizada como um proxy da volatilidade futura, apesar das suas limitações. Com a aplicação do modelo em uma instituição financeira, foi sugerido um grid de decisão a ser utilizado no gerenciamento do risco de liquidez. / The aim of this dissertation is to develop a framework for liquidity risk management that relaxes the main simplifications made by financial institutions when using stress tests to manage their liquidity risk. This research consists of an estimatate of a financial institution cash flow under different scenarios, testing if option´s implied volatilities are a good proxy for significant future changes in the brazilian capital market (like historical correlations shifts) and evaluating the use of a non-parallel yield curve shift for the stress test process. To reach the desired objectives, it was developed an exploratory research through the study case method. This work, therefore, uses a factor analysis model to evaluate the Brazilian yield curve term structure movements, a practical tool to capture the information provided by implied volatility and a correlation matrix among the scenario variables used for stress testing. The conclusions were: i) the correlation adjusted scenario adds coherence to the stress test process; ii) a non-parallel yield curve shift adds little coherence, because most of its variance can be explained by the factor level and only a few can be explained by the factors slope and curvature; iii) the option´s implied volatility can be used as a proxy for the future volatility. After the use of this model in a financial instituition cash flow, a decision grid was developed to be used in the liquidity risk management.

O objetivo desta dissertação é desenvolver um modelo de gestão de risco de liquidez que flexibilize as principais simplificações geralmente realizadas pelas instituições financeiras na aplicação de testes de estresse para gerenciamento do risco de liquidez. Assim, esta pesquisa consiste em estimar um fluxo de caixa unificado de uma instituição sob diferentes cenários econômicos, testando se as volatilidades implícitas das opções são um bom indicador de mudanças significativas no mercado de capitais brasileiro, como quebras de correlações históricas e avaliando o efeito da utilização de um deslocamento não paralelo da Estrutura a Termo da Taxa de Juros na aplicação de um teste de estresse. Para alcançar os objetivos propostos, desenvolveu-se uma pesquisa exploratória através do método de estudo de casos. Para isto, este trabalho utilizou um modelo de análise fatorial para avaliar os movimentos da estrutura a termo da taxa de juros brasileira, além de uma ferramenta prática para capturar as informações fornecidas pela volatilidade implícita e uma matriz de correlação entre as variáveis do cenário econômico utilizado para o teste de estresse. Concluiu-se que: i) a realização de um ajuste no cenário econômico em função da matriz de correlação de suas variáveis contribui para a coerência desse teste com seu contexto econômico, sensibilizando significativamente os valores dos fluxos de caixa futuros das instituições financeiras; ii) os resultados da análise fatorial indicam que a aplicação de um deslocamento não paralelo da ETTJ tem pouca importância prática para a melhoria da coerência dos testes de estresse, em função da grande concentração de poder explicativo da sua variabilidade em torno do fator nível e do baixo poder explicativo dos fatores inclinação e curvatura, principalmente nos vértices iniciais; iii) a volatilidade implícita pode ser utilizada como um proxy da volatilidade futura, apesar das suas limitações. Com a aplicação do modelo em uma instituição financeira, foi sugerido um grid de decisão a ser utilizado no gerenciamento do risco de liquidez. / The aim of this dissertation is to develop a framework for liquidity risk management that relaxes the main simplifications made by financial institutions when using stress tests to manage their liquidity risk. This research consists of an estimatate of a financial institution cash flow under different scenarios, testing if option´s implied volatilities are a good proxy for significant future changes in the brazilian capital market (like historical correlations shifts) and evaluating the use of a non-parallel yield curve shift for the stress test process. To reach the desired objectives, it was developed an exploratory research through the study case method. This work, therefore, uses a factor analysis model to evaluate the Brazilian yield curve term structure movements, a practical tool to capture the information provided by implied volatility and a correlation matrix among the scenario variables used for stress testing. The conclusions were: i) the correlation adjusted scenario adds coherence to the stress test process; ii) a non-parallel yield curve shift adds little coherence, because most of its variance can be explained by the factor level and only a few can be explained by the factors slope and curvature; iii) the option´s implied volatility can be used as a proxy for the future volatility. After the use of this model in a financial instituition cash flow, a decision grid was developed to be used in the liquidity risk management.

Diploma thesis focuses on liquidity risk management of commercial banks in the Czech banking market in 2002-2015. This main goal is achieved through a comprehensive analysis within a framework that uses several different methods. A theoretical framework for bank liquidity management is drawn up for a theoretical evaluation, summary of the current literature and a summary of the regulatory framework including the newly introduced Basel III requirements and indicators is put together. The research part is focused on assessing the development and current state of liquidity of Czech banks by analyzing of liquidity ratios and regression analysis of panel data. The level of liquidity and the size of the liquid pillow is judged to be sufficient and stable from the results of the individual analyses. The net position of Czech banks on the interbank market on an international scale also reflects a good level of liquidity. The major determinants of Czech bank liquidity in the period under review were mainly capital adequacy, bank size, loan portfolio quality, growth rate of GDP and interest rates.

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Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In modern theory of finance, the so-called First and Second Fundamental Theorems of Asset Pricing play an important role in pricing options with no-arbitrage. These theorems gives a necessary and sufficient conditions for a market to have no-arbitrage and for a market to be complete. An early version of the First Fundamental Theorem of Asset Pricing was proven by Harrison and Kreps [30] in the case of a finite probability space. A more general version was proven by Harrison and Pliska [31] in the case of a finite probability space and discrete time. In the case of continuous time, Delbaen and Schachermayer [19] introduced a more general concept of no-arbitrage called "No-Free Lunch With Vanishing Risk" (NFLVR), and showed that for a locally-bounded semimartingale price process NFLVR is essentially equivalent to the existence of an equivalent local martingale measure. The goal of this thesis is to review the theory of arbitrage pricing and the extension of this theory to include liquidity risk. At the current time, liquidity risk is a key challenge faced by investors. Consequently there is a need to develop more realistic pricing models that include liquidity risk. We present an approach to liquidity risk by Çetin, Jarrow and Protter [10]. In to this approach the liquidity risk is embedded into the classical theory of arbitrage pricing by having investors act as price takers, and assuming the existence of a supply curve where prices depend on trade size. This framework assumes that the quantity impact on the price transacted is momentary. Using trading strategies that are both continuous and of finite variation allows one to avoid liquidity costs. Therefore, the First and Second Fundamental Theorems of Asset Pricing and the Black-Scholes model can be extended. / AFRIKAANSE OPSOMMING: In moderne finansiële teorie speel die sogenaamde Eerste en Tweede Fundamentele Stellings van Bateprysbepaling ’n belangrike rol in die prysbepaling van opsies in arbitrage-vrye markte. Hierdie stellings gee nodig en voldoende voorwaardes vir ’n mark om vry van arbitrage te wees, en om volledig te wees. ’n Vroeë weergawe van die Eerste Fundamentele Stelling was deur Harrison en Kreps [30] bewys in die geval van ’n eindige waarskynlikheidsruimte. ’n Meer algemene weergawe was daarna gepubliseer deur Harrison en Pliska [31] in die geval van ’n eindige waarskynlikheidsruimte en diskrete tyd. In die geval van kontinue tyd het Delbaen en Schachermayer [19] ’n meer algemene konsep van arbitragevryheid ingelei, naamlik “No–Free–Lunch–With–Vanishing–Risk" (NFLVR), en aangetoon dat vir lokaalbegrensde semimartingaalprysprosesse NFLVR min of meer ekwivalent is aan die bestaan van ’n lokaal martingaalmaat. Die doel van hierdie tesis is om ’n oorsig te gee van beide klassieke arbitrageprysteorie, en ’n uitbreiding daarvan wat likideit in ag neem. Hedendaags is likiditeitsrisiko ’n vooraanstaande uitdaging wat beleggers die hoof moet bied. Gevolglik is dit noodsaaklik om meer realistiese modelle van prysbepaling wat ook likiditeitsrisiko insluit te ontwikkel. Ons bespreek die benadering van Çetin, Jarrow en Protter [10], waar likiditeitsrisiko in die klassieke arbitrageprysteorie ingesluit word deur die bestaan van ’n aanbodkromme aan te neem, waar pryse afhanklik is van handelsgrootte. In hierdie raamwerk word aangeneem dat die impak op die transaksieprys slegs tydelik is. Deur gebruik te maak van handelingsstrategië wat beide kontinu en van eindige variasie is, is dit dan moontlik om likiditeitskoste te vermy. Die Eerste en Tweede Fundamentele Stellings van Bateprysbepaling en die Black–Scholes model kan dus uitgebrei word om likiditeitsrisiko in te sluit.

This thesis investigates systematic liquidity risk and short-term stock price reaction to large one-day price changes. We study 642 constituents of the FTSALL share index over the period from 1st July 1992 to 29th June 2007. We show that the US evidence of a priced systematic liquidity risk of Pastor and Stambaugh (2003) and Liu (2006) is not country-specific. Particularly, systematic liquidity risk is priced in the London Stock Exchange when Amihud's (2002) illiquidity ratio is used as a liquidity proxy. Given the importance of systematic liquidity risk in the asset pricing literature, we are interested in testing whether the different levels of systematic liquidity risk across stocks can explain the anomaly following large one-day price changes. Specifically, we expect that the stocks with high sensitivity to the fluctuations in aggregate market liquidity to be more affected by price shocks. We find that most liquid stocks react efficiently to price shocks, while the reactions of the least liquid stocks support the uncertain information hypothesis. However, we show that time-varying risk is more important than systematic liquidity risk in explaining the price reaction of stocks in different liquidity portfolios. Indeed, the time varying risk explains nearly all of the documented overreaction and underreaction following large one-day price changes. Our evidence suggests that the observed anomalies following large one-day price shocks are caused by the pricing errors arising from the use of static asset pricing models. In particular, the conditional asset pricing model of Harris et al. (2007), which allow both risk and return to vary systematically over time, explain most of the observed anomalies. This evidence supports the Brown et al. (1988) findings that both risk and return increase in a systematic fashion following price shocks.

Syfte: Syftet är att undersöka om det finns ett samband mellan aktiers likviditet och avkastning. Metod: Vår studie består av en kvantitativ metod där vi med hjälp av databasen Eikon från Thomson Reuters samlat in finansiella data. Vi har sedan med hjälp av Excel sammanställt och gjort beräkningar och slutligen gjort korrelationstester i statistikprogrammet SPSS. Resultat och slutsats: Studien skiljer sig från tidigare forskningsresultat då ingen signifikant likviditetspremie kan fastställas vid årlig ombalansering av portföljerna. När portföljerna behåller samma aktier under hela tidsperioden (6 år) finner vi däremot att den minst likvida portföljen genererar betydligt högre avkastning jämfört med den mest likvida portföljen. Bidrag: Studiens teoretiska bidrag stärker tidigare forskningsresultat om att beta inte är ett komplett riskmått vad gäller illikvida aktier. Ingen likviditetspremie uppkommer då innehavsperioden är ett år men då vår innehavsperiod istället är sex år finner vi stora skillnader mellan vår minst respektive mest likvida portfölj. Studiens praktiska bidrag riktar sig till investerare och företagsledare. Investerare kan vid längre tidsperioder nyttja LM12 som en investeringsstrategi för att skapa en överavkastning och företagsledare kan undersöka nyttan med att öka likviditeten i företagets aktier för att sänka företagets WACC och därmed öka värdet på företaget.  Förslag till vidare forskning: För att studera aktielikviditeten vidare skulle andra innehavsperioder (längre än ett år) för portföljerna kunna undersökas. Att undersöka längre tidsperioder för studien hade också varit intressant för att undersöka hur likviditetspremien varierar över tid. / Aim: The aim is to examine if there is a relationship between the liquidity and return of common stocks.  Method: This study consists of quantitative research method in which we have collected financial data using the Eikon database from Thomson Reuters. We then compiled and made calculations using Excel and finally made correlation tests in the statistics program SPSS. Result and conclusion: The results from this study differs from previous research results since no significant liquidity premium could be determined while using annual rebalancing of the portfolios. When the portfolios held the same stocks for the entire period (6 years), we found that the least liquid portfolio generated significantly higher returns compared to the most liquid portfolio.  Contribution of the thesis: The study's theoretical contribution strengthens previous research results in that beta is not a complete risk measure in terms of illiquid shares. No liquidity premium arises when the holding period is one year, but when our holding period is instead six years, we find great differences between our least and most liquid portfolio. The practical contribution of the study is aimed at investors and business leaders. Investors can use LM12 as an investment strategy to create an excess return during long holding periods, and business leaders can examine the benefits of increasing the liquidity of the company's common stock to lower the company's WACC and hence increase the value of the company. Suggestion for future research: In order to study the liquidity premium further, other holding periods (longer than one year) for the portfolios could be investigated. Investigating longer time periods for the study would also be interesting to investigate how the liquidity premium varies over time.

Ce travail de thèse aborde deux sujets : (i) L'utilisation d'une nouvelle méthode numérique pour l'évaluation des options sur un panier d'actifs, (ii) Le risque de liquidité, la modélisation du carnet d'ordres et la microstructure de marché. Premier thème : Un algorithme glouton et ses applications pour résoudre des équations aux dérivées partielles. L'exemple typique en finance est l'évaluation d'une option sur un panier d'actifs, laquelle peut être obtenue en résolvant l'EDP de Black-Scholes ayant comme dimension le nombre d'actifs considérés. Nous proposons d'étudier un algorithme qui a été proposé et étudié récemment dans [ACKM06, BLM09] pour résoudre des problèmes en grande dimension et essayer de contourner la malédiction de la dimension. L'idée est de représenter la solution comme une somme de produits tensoriels et de calculer itérativement les termes de cette somme en utilisant un algorithme glouton. La résolution des EDP en grande dimension est fortement liée à la représentation des fonctions en grande dimension. Dans le Chapitre 1, nous décrivons différentes approches pour représenter des fonctions en grande dimension et nous introduisons les problèmes en grande dimension en finance qui sont traités dans ce travail de thèse. La méthode sélectionnée dans ce manuscrit est une méthode d'approximation non-linéaire appelée Proper Generalized Decomposition (PGD). Le Chapitre 2 montre l'application de cette méthode pour l'approximation de la solution d'une EDP linéaire (le problème de Poisson) et pour l'approximation d'une fonction de carré intégrable par une somme des produits tensoriels. Un étude numérique de ce dernier problème est présenté dans le Chapitre 3. Le problème de Poisson et celui de l'approximation d'une fonction de carré intégrable serviront de base dans le Chapitre 4 pour résoudre l'équation de Black-Scholes en utilisant l'approche PGD. Dans des exemples numériques, nous avons obtenu des résultats jusqu'en dimension 10. Outre l'approximation de la solution de l'équation de Black-Scholes, nous proposons une méthode de réduction de variance des méthodes Monte Carlo classiques pour évaluer des options financières. Second thème : Risque de liquidité, modélisation du carnet d'ordres, microstructure de marché. Le risque de liquidité et la microstructure de marché sont devenus des sujets très importants dans les mathématiques financières. La dérégulation des marchés financiers et la compétition entre eux pour attirer plus d'investisseurs constituent une des raisons possibles. Dans ce travail, nous étudions comment utiliser cette information pour exécuter de façon optimale la vente ou l'achat des ordres. Les ordres peuvent seulement être placés dans une grille des prix. A chaque instant, le nombre d'ordres en attente d'achat (ou vente) pour chaque prix est enregistré. Dans [AFS10], Alfonsi, Fruth et Schied ont proposé un modèle simple du carnet d'ordres. Dans ce modèle, il est possible de trouver explicitement la stratégie optimale pour acheter (ou vendre) une quantité donnée d'actions avant une maturité. L'idée est de diviser l'ordre d'achat (ou de vente) dans d'autres ordres plus petits afin de trouver l'équilibre entre l'acquisition des nouveaux ordres et leur prix. Ce travail de thèse se concentre sur une extension du modèle du carnet d'ordres introduit par Alfonsi, Fruth et Schied. Ici, l'originalité est de permettre à la profondeur du carnet d'ordres de dépendre du temps, ce qui représente une nouvelle caractéristique du carnet d'ordres qui a été illustré par [JJ88, GM92, HH95, KW96]. Dans ce cadre, nous résolvons le problème de l'exécution optimale pour des stratégies discrètes et continues. Ceci nous donne, en particulier, des conditions suffisantes pour exclure les manipulations des prix au sens de Huberman et Stanzl [HS04] ou de Transaction-Triggered Price Manipulation (voir Alfonsi, Schied et Slynko) / This work is organized in two themes : (i) A novel numerical method to price options on manyassets, (ii) The liquidity risk, the limit order book modeling and the market microstructure.First theme : Greedy algorithms and applications for solving partial differential equations in high dimension Many problems of interest for various applications (material sciences, finance, etc) involve high-dimensional partial differential equations (PDEs). The typical example in finance is the pricing of a basket option, which can be obtained by solving the Black-Scholes PDE with dimension the number of underlying assets. We propose to investigate an algorithm which has been recently proposed and analyzed in [ACKM06, BLM09] to solve such problems and try to circumvent the curse of dimensionality. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum using a greedy algorithm. The resolution of high dimensional partial differential equations is highly related to the representation of high dimensional functions. In Chapter 1, we describe various linear approaches existing in literature to represent high dimensional functions and we introduce the high dimensional problems in finance that we will address in this work. The method studied in this manuscript is a non-linear approximation method called the Proper Generalized Decomposition. Chapter 2 shows the application of this method to approximate the so-lution of a linear PDE (the Poisson problem) and also to approximate a square integrable function by a sum of tensor products. A numerical study of this last problem is presented in Chapter 3. The Poisson problem and the approximation of a square integrable function will serve as basis in Chapter 4for solving the Black-Scholes equation using the PGD approach. In numerical experiments, we obtain results for up to 10 underlyings. Second theme : Liquidity risk, limit order book modeling and market microstructure. Liquidity risk and market microstructure have become in the past years an important topic in mathematical finance. One possible reason is the deregulation of markets and the competition between them to try to attract as many investors as possible. Thus, quotation rules are changing and, in general, more information is available. In particular, it is possible to know at each time the awaiting orders on some stocks and to have a record of all the past transactions. In this work we study how to use this information to optimally execute buy or sell orders, which is linked to the traders' behaviour that want to minimize their trading cost. In [AFS10], Alfonsi, Fruth and Schied have proposed a simple LOB model. In this model, it is possible to explicitly derive the optimal strategy for buying (or selling) a given amount of shares before a given deadline. Basically, one has to split the large buy (or sell) order into smaller ones in order to find the best trade-off between attracting new orders and the price of the orders. Here, we focus on an extension of the Limit Order Book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied. The additional feature is a time-varying LOB depth that represents a new feature of the LOB highlighted in [JJ88, GM92, HH95, KW96]. We solve the optimal execution problem in this framework for both discrete and continuous time strategies. This gives in particular sufficient conditions to exclude Price Manipulations in the sense of Huberman and Stanzl [HS04] or Transaction-Triggered Price Manipulations (see Alfonsi, Schied and Slynko). The seconditions give interesting qualitative insights on how market makers may create price manipulations

當保險契約被發行時，保險公司必須被要求盡可能的具備承擔未來不可知的風險的能力。本文將死亡風險、利率風險、脫退風險以及流動性風險引入，並針對生死合險契約進行盈餘分析。在此以 Vasicek (1977) 所提出之隨機利率模型、根據被保險人理性行為作為基礎之脫退模型以及引入簡化後的 Longstaff、Mithal與Nies (2005)流動性風險債券價格來描述各種風險。根據上述模型假設下計算保費及準備金，遂以蒙地卡羅模擬法量化源於各種風險之盈餘。最後，本文計算保險公司之盈餘對各風險參數之敏感度分析，並計算各期破產與發生流動性問題之可能性。 / Once insurance contracts are issued, the insurers should be capable to deal with the unknown conditions in the future as possible. In this paper, we analyze the impact of mortality, interest rate, surrender and liquidity risks on the surplus of endowment contract. We model the interest rate risk by Vasicek model, the surrender rate based on the rational behavior of policyholders and introduce the discounted price of zero coupon bonds as the liquidity risk. Under such assumptions, we compute the premium and reserve, demonstrate the simulated insurance surplus, and finally exhibit the statistics of the surplus from different sources. The simulated results show the sensitivity of the surplus to the parameters of the risks. At the same time, we also show the probabilities of insolvency and illiquidity of the insurer before the maturity date of the contract due to the fluctuating surrender rate and liquidity risk resulting from the stochastic interest rate.