The financial market has been an area of increased research interest for mathematicians and statisticians. Some of the main research areas are on the log returns of assets (shares, bond, foreign exchange, option) and the volatility which is the variation in the log returns. The volatility is widely studied because of its applications in trading financial instruments which are, used for forecasting prices and measuring the risk of financial assets. In this work, a process of trading activities is considered. It is assumed that at a random time-point a parameter change in the trading process occurs, indicating changed trading behavior. It is important to be able to state that such a change has occurred quickly and accurately, which will help the investor to make a decision either to buy or sell financial assets. To effectively make this decision a financial model is developed using the family of Autoregressive Conditional Heteroskedastic (ARCH) and stopping rule is created which signal alarms as soon as return on financial asset goes beyond or below some threshold. The work ends with a model that can be applied to real data.
A complete guide to day trading stocks, options, or futures,plus companion workbook This valuable guide is a complete day trading course (with acompanion workbook) that walks novice traders through all the daytrading opportunities. The Day Trader´s Course is packed with basictechnical skill, proven winning strategies, and essentialbackground. Lewis Borsellino reveals when to buy and when to sell,and shows readers how to identify when ´´it´s over´´ for a particularstock, option, or future. Drawing from his considerable experience,he identifies the rules that every trader should follow.
Market Risk Analysis is the most comprehensive, rigorous and detailed resource available on market risk analysis. Written as a series of four interlinked volumes each title is self-contained, although numerous cross-references to other volumes enable readers to obtain further background knowledge and information about financial applications. Volume I: Quantitative Methods in Finance covers the essential mathematical and financial background for subsequent volumes. Although many readers will already be familiar with this material, few competing texts contain such a complete and pedagogical exposition of all the basic quantitative concepts required for market risk analysis. There are six comprehensive chapters covering all the calculus, linear algebra, probability and statistics, numerical methods and portfolio mathematics that are necessary for market risk analysis. This is an ideal background text for a Masters course in finance. Volume II: Practical Financial Econometrics provides a detailed understanding of financial econometrics, with applications to asset pricing and fund management as well as to market risk analysis. It covers equity factor models, including a detailed analysis of the Barra model and tracking error, principal component analysis, volatility and correlation, GARCH, cointegration, copulas, Markov switching, quantile regression, discrete choice models, non-linear regression, forecasting and model evaluation. Volume III: Pricing, Hedging and Trading Financial Instruments has five very long chapters on the pricing, hedging and trading of bonds and swaps, futures and forwards, options and volatility as well detailed descriptions of mapping portfolios of these financial instruments to their risk factors. There are numerous examples, all coded in interactive Excel spreadsheets, including many pricing formulae for exotic options but excluding the calibration of stochastic volatility models, for which Matlab code is provided. The chapters on options and volatility together constitute 50% of the book, the slightly longer chapter on volatility concentrating on the dynamic properties the two volatility surfaces the implied and the local volatility surfaces that accompany an option pricing model, with particular reference to hedging. Volume IV: Value at Risk Models builds on the three previous volumes to provide by far the most comprehensive and detailed treatment of market VaR models that is currently available in any textbook. The exposition starts at an elementary level but, as in all the other volumes, the pedagogical approach accompanied by numerous interactive Excel spreadsheets allows readers to experience the application of parametric linear, historical simulation and Monte Carlo VaR models to increasingly complex portfolios. Starting with simple positions, after a few chapters we apply value-at-risk models to interest rate sensitive portfolios, large international securities portfolios, commodity futures, path dependent options and much else. This rigorous treatment includes many new results and applications to regulatory and economic capital allocation, measurement of VaR model risk and stress testing.
Written for traders with a basic knowledge of trends and technical analysis, Practical Trend Analysis introduces advanced analytical tools for recognizing how risks evolve as trends proceed. Readers will learn how to use trend prediction to manage market risks far more effectively. Michael C. Thomsett provides insights on technical signals such as candlestick reversals, price gaps, and movement through resistance or support; distinguishing between strong and weak trends; objectively evaluating the health of a stock´s current price levels, trading breadth, and technical condition; and anticipating plateaus, slowdowns, or price reversals. He presents detailed coverage of trendlines and channel lines; patterns and confirmations of both reversals and continuations; broadening and narrowing trends, price jumps; and trends based on volume, moving averages, and momentum. Practical Trend Analysis will enable traders, both amateur and professional, to go far beyond mere trend ´´following.´´ Michael C. Thomsett is a market expert, author, speaker, and coach. His many books include Stock Market Math, Candlestick Charting, and The Mathematics of Options.
Brownian Motion Calculus Ubbo Wiersema Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver of the irregular behaviour of financial quantities. That exposition is based on the easily understood discrete random walk. Thereafter the gains from trading in a random environment are formulated in a discrete-time setting. The continuous-time equivalent requires a new concept, the ItM stochastic integral. Its construction is explained step by step, using the so-called norm of a random process (its magnitude), of which a motivated exposition is given in an Annex. The next topic is ItM´s formula for evaluating stochastic integrals; it is the random process counter part of the well known Taylor formula for functions in ordinary calculus. Many examples are given. These ingredients are then used to formulate some well established models for the evolution of stock prices and interest rates, so-called stochastic differential equations, together with their solution methods. Once all that is in place, two methodologies for option valuation are presented. One uses the concept of a change of probability and the Girsanov transformation, which is at the core of financial mathematics. As this technique is often perceived as a magic trick, particular care has been taken to make the explanation elementary and to show numerous applications. The final chapter discusses how computations can be made more convenient by a suitable choice of the so-called numeraire. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website www.wiley.com/go/brownianmotioncalculus.