Analytical Finance is a comprehensive introduction to the financial engineering of equity and interest rate instruments for financial markets. Developed from notes from the author’s many years in quantitative risk management and modeling roles, and then for the Financial Engineering course at Mälardalen University, it provides exhaustive coverage of vanilla and exotic mathematical finance applications for trading and risk management, combining rigorous theory with real market application. Coverage includes: • Date arithmetic’s, quote types of interest rate instruments • The interbank market and reference rates, including negative rates• Valuation and modeling of IR instruments; bonds, FRN, FRA, forwards, futures, swaps, CDS, caps/floors and others • Bootstrapping and how to create interest rate curves from prices of traded instruments• Risk measures of IR instruments• Option Adjusted Spread and embedded options• The term structure equation, martingale measures and stochastic processes of interest rates; Vasicek, Ho-Lee, Hull-While, CIR• Numerical models; Black-Derman-Toy and forward induction using Arrow-Debreu prices and Newton–Raphson in 2 dimension• The Heath-Jarrow-Morton framework• Forward measures and general option pricing models• Black log-normal and, normal model for derivatives, market models and managing exotics instruments• Pricing before and after the financial crisis, collateral discounting, multiple curve framework, cheapest-to-deliver curves, CVA, DVA and FVA
Detailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry. This volume focuses solely on equity derivatives problems, beginning with basic problems in derivatives securities before moving on to more advanced applications, including the construction of volatility surfaces to price exotic options. By providing a methodology for solving theoretical and practical problems, whilst explaining the limitations of financial models, this book helps readers to develop the skills they need to advance their careers. The text covers a wide range of derivatives pricing, such as European, American, Asian, Barrier and other exotic options. Extensive appendices provide a summary of important formulae from calculus, theory of probability, and differential equations, for the convenience of readers. As Volume II of the four-volume Problems and Solutions in Mathematical Finance series, this book provides clear explanation of the mathematics behind equity derivatives, in order to help readers gain a deeper understanding of their mechanics and a firmer grasp of the calculations. Review the fundamentals of equity derivatives Work through problems from basic securities to advanced exotics pricing Examine numerical methods and detailed derivations of closed-form solutions Utilise formulae for probability, differential equations, and more Mathematical finance relies on mathematical models, numerical methods, computational algorithms and simulations to make trading, hedging, and investment decisions. For the practitioners and graduate students of quantitative finance, Problems and Solutions in Mathematical Finance Volume II provides essential guidance principally towards the subject of equity derivatives.
This book provides an introduction to the valuation of financial instruments on equity markets. Written from the perspective of trading, risk management and quantitative research functions and written by a practitioner with many years’ experience in markets and in academia, it provides a valuable learning tool for students and new entrants to these markets. Coverage includes: ·Trading and sources of risk, including credit and counterparty risk, market and model risks, settlement and Herstatt risks. ·Numerical methods including discrete-time methods, finite different methods, binomial models and Monte Carlo simulations. ·Probability theory and stochastic processes from the financial modeling perspective, including probability spaces, sigma algebras, measures and filtrations. ·Continuous time models such as Black-Scholes-Merton; Delta-hedging and Delta-Gamma-hedging; general diffusion models and how to solve Partial Differential Equation using the Feynmann-Kac representation. ·The trading, structuring and hedging several kinds of exotic options, including: Binary/Digital options; Barrier options; Lookbacks; Asian options; Chooses; Forward options; Ratchets; Compounded options; Basket options; Exchange and Currency-linked options; Pay later options and Quantos. ·A detailed explanation of how to construct synthetic instruments and strategies for different market conditions, discussing more than 30 different option strategies. With source code for many of the models featured in the book provided and extensive examples and illustrations throughout, this book provides a comprehensive introduction to this topic and will prove an invaluable learning tool and reference for anyone studying or working in this field.
This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the book has real-world applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. It is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering.
Volume 1 of 'The Strategic Analysis of Financial Markets,' — Framework, is premised on the belief that markets can be understood only by dropping the assumptions of rationality and efficient markets in their extreme forms, and showing that markets still have an inherent order and inherent logic. But that order results primarily from the 'predictable irrationality' of investors, as well as from people's uncoordinated attempts to profit. The market patterns that result do not rely on rationality or efficiency.A framework is developed for understanding financial markets using a combination of psychology, statistics, game and gambling analysis, market history and the author's experience. It expresses analytically how professional investors and traders think about markets — as games in which other participants employ inferior, partially predictable strategies. Those strategies' interactions can be toxic and lead to booms, bubbles, busts and crashes, or can be less dramatic, leading to various patterns that are mistakenly called 'market inefficiencies' and 'stylized facts.'A logical case is constructed, starting from two foundations, the psychology of human decision making and the 'Fundamental Laws of Gambling.' Applying the Fundamental Laws to trading leads to the idea of 'gambling rationality' (grationality), replacing the efficient market's concept of 'rationality.' By classifying things that are likely to have semi-predictable price impacts (price 'distorters'), one can identify, explore through data analysis, and create winning trading ideas and systems. A structured way of doing all this is proposed: the six-step 'Strategic Analysis of Market Method.' Examples are given in this and Volume 2.Volume 2 of 'The Strategic Analysis of Financial Markets' — Trading System Analytics, continues the development of Volume 1 by introducing tools and techniques for developing trading systems and by illustrating them using real markets. The difference between these two Volumes and the rest of the literature is its rigor. It describes trading as a form of gambling that when properly executed, is quite logical, and is well known to professional gamblers and analytical traders.But even those elites might be surprised at the extent to which quantitative methods have been justified and applied, including a life cycle theory of trading systems. Apart from a few sections that develop background material, Volume 2 creates from scratch a trading system for Eurodollar futures using principles of the Strategic Analysis of Markets Method (SAMM), a principled, step-by-step approach to developing profitable trading systems. It has an entire Chapter on mechanical methods for testing and improvement of trading systems, which transcends the rather unstructured and unsatisfactory 'backtesting' literature. It presents a breakout trend following system developed using factor models. It also presents a specific pairs trading system, and discusses its life cycle from an early, highly profitable period to its eventual demise. Recent developments in momentum trading and suggestions on improvements are also discussed.
Written by leading market risk academic, Professor Carol Alexander, Practical Financial Econometrics forms part two of the Market Risk Analysis four volume set. It introduces the econometric techniques that are commonly applied to finance with a critical and selective exposition, emphasising the areas of econometrics, such as GARCH, cointegration and copulas that are required for resolving problems in market risk analysis. The book covers material for a one-semester graduate course in applied financial econometrics in a very pedagogical fashion as each time a concept is introduced an empirical example is given, and whenever possible this is illustrated with an Excel spreadsheet. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM. Empirical examples and case studies specific to this volume include: Factor analysis with orthogonal regressions and using principal component factors; Estimation of symmetric and asymmetric, normal and Student t GARCH and E-GARCH parameters; Normal, Student t, Gumbel, Clayton, normal mixture copula densities, and simulations from these copulas with application to VaR and portfolio optimization; Principal component analysis of yield curves with applications to portfolio immunization and asset/liability management; Simulation of normal mixture and Markov switching GARCH returns; Cointegration based index tracking and pairs trading, with error correction and impulse response modelling; Markov switching regression models (Eviews code); GARCH term structure forecasting with volatility targeting; Non-linear quantile regressions with applications to hedging.
A number of methodologies have been employed to provide decision making solutions globalized markets. Hidden Markov Models in Finance offers the first systematic application of these methods to specialized financial problems: option pricing, credit risk modeling, volatility estimation and more. The book provides tools for sorting through turbulence, volatility, emotion, chaotic events – the random "noise" of financial markets – to analyze core components.
