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Illustrates how R may be used successfully to solve problems in quantitative finance Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R provides R recipes for asset allocation and portfolio optimization problems. It begins by introducing all the necessary probabilistic and statistical foundations, before moving on to topics related to asset allocation and portfolio optimization with R codes illustrated for various examples. This clear and concise book covers financial engineering, using R in data analysis, and univariate, bivariate, and multivariate data analysis. It examines probabilistic calculus for modeling financial engineering—walking the reader through building an effective financial model from the Geometric Brownian Motion (GBM) Model via probabilistic calculus, while also covering Ito Calculus. Classical mathematical models in financial engineering and modern portfolio theory are discussed—along with the Two Mutual Fund Theorem and The Sharpe Ratio. The book also looks at R as a calculator and using R in data analysis in financial engineering. Additionally, it covers asset allocation using R, financial risk modeling and portfolio optimization using R, global and local optimal values, locating functional maxima and minima, and portfolio optimization by performance analytics in CRAN. * Covers optimization methodologies in probabilistic calculus for financial engineering * Answers the question: What does a \"Random Walk\" Financial Theory look like? * Covers the GBM Model and the Random Walk Model * Examines modern theories of portfolio optimization, including The Markowitz Model of Modern Portfolio Theory (MPT), The Black-Litterman Model, and The Black-Scholes Option Pricing Model Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R s an ideal reference for professionals and students in economics, econometrics, and finance, as well as for financial investment quants and financial engineers.

Illustrates how R may be used successfully to solve problems in quantitative finance Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R provides R recipes for asset allocation and portfolio optimization problems. It begins by introducing all the necessary probabilistic and statistical foundations, before moving on to topics related to asset allocation and portfolio optimization with R codes illustrated for various examples. This clear and concise book covers financial engineering, using R in data analysis, and univariate, bivariate, and multivariate data analysis. It examines probabilistic calculus for modeling financial engineering-walking the reader through building an effective financial model from GBM via probabilistic calculus, while also covering Ito Calculus. Classical mathematical models in financial engineering and modern portfolio theory are discussed-along with the Two Mutual Fund Theorem and The Sharpe Ratio. The book also looks at R as a calculator and using R in data analysis in financial engineering. Additionally, it covers asset allocation using R, financial risk modeling and portfolio optimization using R, global and local optimal values, locating functional maxima and minima, and portfolio optimization by performance analytics in CRAN. Covers optimization methodologies in probabilistic calculus for financial engineering Answers the question: What does a \"Random Walk\" Financial Theory look like? Covers The Geometric Brownian Motion (GBM) Model and the Random Walk Model Examines modern theories of portfolio optimization, including The Markowitz Model of Modern Portfolio Theory (MPT), The Black-Litterman Model, and The Black-Scholes Option Pricing Model Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R is an ideal reference for professionals and students in economics, econometrics, and finance, as well as for financial investment quants and financial engineers.

Financial engineering is defined as the application of mathematical methods to the solution of problems in finance. The recent financial crisis raised many challenges for financial engineers: not only were financially engineered products such as collateralized debt obligations and credit default swaps implicated in causing the crisis, but the risk management techniques developed by financial engineers appeared to fail when they were most desperately needed. This book is the first in a series describing research by a multidisciplinary team of economists, mathematicians and control theorists exploring new research directions in financial engineering. It is broadly divided into three parts. The first part of the book reviews recent developments of real options; an application of the theory of financial options to capital investments with the emphasis on flexibility. Topics covered include the technique of variational inequalities, the use of forward and backward stochastic differential equations and the application of a real option approach to a consumption and portfolio selection problem. The second part of the book presents new topics, including simultaneous control of dividend payments and risk management, risk measures and non-linear probability models and a survey of recent studies on market microstructure. The last part of the volume proposes a new perspective. The availability and success of mathematical tools has attracted many talented people to the financial services industry. This examination of the way in which they are approaching current and future challenges will be of interest to all those working in the field of financial engineering.

Intro -- Title Page -- Copyright -- Dedication -- Preface -- About the Companion Website -- Chapter 1: Introduction to Financial Engineering -- 1.1 What Is Financial Engineering? -- 1.2 The Meaning of the Title of This Book -- 1.3 The Continuing Challenge in Financial Engineering -- 1.4 \"Financial Engineering 101\": Modern Portfolio Theory -- 1.5 Asset Class Assumptions Modeling -- 1.6 Some Typical Examples of Proprietary Investment Funds -- 1.7 The Dow Jones Industrial Average (DJIA) and Inflation -- 1.8 Some Less Commendable Stock Investment Approaches -- 1.9 Developing Tools for Financial Engineering Analysis -- Review Questions -- Chapter 2: Probabilistic Calculus for Modeling Financial Engineering -- 2.1 Introduction to Financial Engineering -- 2.2 Mathematical Modeling in Financial Engineering -- 2.3 Building an Effective Financial Model from GBM via Probabilistic Calculus -- 2.4 A Continuous Financial Model Using Probabilistic Calculus: Stochastic Calculus, Ito Calculus -- 2.5 A Numerical Study of the Geometric Brownian Motion (GBM) Model and the Random Walk Model Using R -- Review Questions and Exercises -- Chapter 3: Classical Mathematical Models in Financial Engineering and Modern Portfolio Theory -- 3.1 An Introduction to the Cost of Money in the Financial Market -- 3.2 Modern Theories of Portfolio Optimization -- 3.3 The Black-Litterman Model -- 3.4 The Black-Scholes Option Pricing Model -- 3.5 The Black-Litterman Model -- 3.6 The Black-Litterman Model -- 3.7 The Black-Scholes Option Pricing Model -- 3.8 Some Worked Examples -- Review Questions and Exercises -- Solutions to Exercise 3: The Black-Scholes Equation -- Chapter 4: Data Analysis Using R Programming -- 4.1 Data and Data Processing -- Review Questions for Section 4.1 -- 4.2 Beginning R -- Review Questions for Section 4.2 -- 4.3 R as a Calculator.

This book is the culmination of three years of research effort on a multidisciplinary project in which physicists, mathematicians, computer scientists and social scientists worked together to arrive at a unifying picture of complex networks. The contributed chapters form a reference for the various problems in data analysis visualization and modeling of complex networks.

Students and professionals intending to work in any area of finance must master not only advanced concepts and mathematical models but also learn how to implement these models computationally. This comprehensive text, first published in 2002, combines the theory and mathematics behind financial engineering with an emphasis on computation, in keeping with the way financial engineering is practised in capital markets. Unlike most books on investments, financial engineering, or derivative securities, the book starts from very basic ideas in finance and gradually builds up the theory. It offers a thorough grounding in the subject for MBAs in finance, students of engineering and sciences who are pursuing a career in finance, researchers in computational finance, system analysts, and financial engineers. Along with the theory, the author presents numerous algorithms for pricing, risk management, and portfolio management. The emphasis is on pricing financial and derivative securities: bonds, options, futures, forwards, interest rate derivatives, mortgage-backed securities, bonds with embedded options, and more.

01 02 Barrier options are a class of highly path-dependent exotic options which present particular challenges to practitioners in all areas of the financial industry. They are traded heavily as stand-alone contracts in the Foreign Exchange (FX) options market, their trading volume being second only to that of vanilla options. The FX options industry has correspondingly shown great innovation in this class of products and in the models that are used to value and risk-manage them. FX structured products commonly include barrier features, and in order to analyse the effects that these features have on the overall structured product, it is essential first to understand how individual barrier options work and behave. FX Barrier Options takes a quantitative approach to barrier options in FX environments. Its primary perspectives are those of quantitative analysts, both in the front office and in control functions. It presents and explains concepts in a highly intuitive manner throughout, to allow quantitatively minded traders, structurers, marketers, salespeople and software engineers to acquire a more rigorous analytical understanding of these products. The book derives, demonstrates and analyses a wide range of models, modelling techniques and numerical algorithms that can be used for constructing valuation models and risk-management methods. Discussions focus on the practical realities of the market and demonstrate the behaviour of models based on real and recent market data across a range of currency pairs. It furthermore offers a clear description of the history and evolution of the different types of barrier options, and elucidates a great deal of industry nomenclature and jargon. 19 02 There are no other books which focus on the topic of barrier options, despite it being a topic of great interest to many market practitioners, especially in FX The FX derivatives market is huge – the largest derivatives market in the world, and there is always interest in new materials on pricing of financial instruments in this space. This book provides a thorough treatment of a very under published aspect of FX – barrier options Through his work as a practitioner and trainer, the author is well placed to describe the latest best practice as well as historic approaches clearly with a balance of words, diagrams, graphs, mathematics and programming code. - The first book to analyse FX barrier options, an important and commonly traded class of exotic option, frequently traded (but not always understood) on the largest derivatives market in the world – FX 04 02 Preface Foreword Glossary of Mathematical Notation Contract Types 1 Meet the Products 1.1 Spot 1.1.1 Dollars per euro or euros per dollar? 1.1.2 Big figures and small figures 1.1.3 The value of Foreign 1.1.4 Converting between Domestic and Foreign 1.2 Forwards 1.2.1 The FX forward market 1.2.2 A formula for the forward rate 1.2.3 Payoff a forward contract 1.2.4 Valuation of a forward contract 1.3 Vanilla options 1.3.1 Put-Call Parity 1.4 Barrier-contingent vanilla options 1.5 Barrier-contingent payments 1.6 Rebates 1.7 Knock-in-knock-out (KIKO) options 1.8 Types of barriers 1.9 Structured products 1.10 Specifying the contract 1.11 Quantitative truisms 1.11.1 Foreign exchange symmetry and inversion 1.11.2 Knock-out plus knock-in equals no-barrier contract 1.11.3 Put-call parity 1.12 Jargon-buster 2 Living in a Black-Scholes World 2.1 The Black-Scholes model equation for spot price 2.2 The process for ln S 2.3 The Black-Scholes equation for option pricing 2.3.1 The lagless approach 2.3.2 Derivation of the Black-Scholes PDE 2.3.3 Black-Scholes model | hedging assumptions 2.3.4 Interpretation of the Black-Scholes PDE 2.4 Solving the Black-Scholes PDE 2.5 Payments 2.6 Forwards 2.7 Vanilla options 2.7.1 Transformation of the Black-Scholes PDE 2.7.2 Solution of the diffusion equation for vanilla options 2.7.3 The vanilla option pricing formulae 2.7.4 Price quotation styles 2.7.5 Valuation behaviour 2.8 Black-Scholes pricing of barrier-contingent vanilla options 2.8.1 Knock-outs 2.8.2 Knock-ins 2.8.3 Quotation methods 2.8.4 Valuation behaviour 2.9 Black-Scholes pricing of barrier-contingent payments 2.9.1 Payment in Domestic 2.9.2 Payment in Foreign 2.9.3 Quotation methods 2.9.4 Valuation behaviour 2.10 Discrete barrier options 2.11 Window barrier options 2.12 Black-Scholes numerical valuation methods 3 Black-Scholes Risk Management 3.1 Spot risk 3.1.1 Local spot risk analysis 3.1.2 Delta 3.1.3 Gamma 3.1.4 Results for spot Greeks 3.1.5 Non-local spot risk analysis 3.2 Volatility risk 3.2.1 Local volatility risk analysis 3.2.2 Non-local volatility risk 3.3 Interest rate risk 3.4 Theta 3.5 Barrier over-hedging 3.6 Co-Greeks 4 Smile Pricing 4.1 The shortcomings of the Black-Scholes model 4.2 Black-Scholes with term structure (BSTS) 4.3 The implied volatility surface 4.4 The FX vanilla option market 4.4.1 At-the-money volatility 4.4.2 Risk reversal 4.4.3 Buttery 4.4.4 The role of the Black-Scholes model in the FX vanilla options market 4.5 Theoretical Value (TV) 4.5.1 Conventions for extracting market data for TV calculations 4.5.2 Example broker quote request 4.6 Modelling market implied volatilities 4.7 The probability density function 4.8 Three things we want from a model 4.9 The local volatility (LV) model 4.9.1 It's the smile dynamics, stupid 4.10 Five things we want from a model 4.11 Stochastic volatility (SV) models 4.11.1 SABR model 4.11.2 Heston model 4.12 Mixed local/stochastic volatility (lsv) models 4.12.1 Term structure of volatility of volatility 4.13 Other models and methods 4.13.1 Uncertain Volatility (UV) models 4.13.2 Jump-diffusion models 4.13.3 Vanna-volga methods 5 Smile Risk Management 5.1 Black-Scholes with term structure 5.2 Local volatility model 5.3 Spot risk under smile models 5.4 Theta risk under smile models 5.5 Mixed local/stochastic volatility models 5.6 Static hedging 5.7 Managing risk across businesses 6 Numerical Methods 6.1 Finite-difference (FD) methods 6.1.1 Grid geometry 6.1.2 Finite-difference schemes 6.2 Monte Carlo (MC) methods 6.2.1 Monte Carlo schedules 6.2.2 Monte Carlo algorithms 6.2.3 Variance reduction 6.2.4 The Brownian Bridge 6.2.5 Early termination 6.3 Calculating Greeks 6.3.1 Bumped Greeks 6.3.2 Greeks from finite-difference calculations 6.3.3 Greeks from Monte Carlo 7 Further Topics 7.1 Managed currencies 7.2 Stochastic interest rates (SIR) 7.3 Real-world pricing 7.3.1 Bid-offer spreads 7.3.2 Rules-based pricing methods 7.4 Regulation and market abuse A Derivation of the Black-Scholes Pricing Equations for Vanilla Options B Normal and lognormal probability distributions B.1 Normal distribution B.2 Lognormal distribution C Derivation of the local volatility function C.1 Derivation in terms of call prices C.2 Local volatility from implied volatility C.3 Working in moneyness space C.4 Working in log space C.5 Specialization to BSTS D Calibration of mixed local/stochastic volatility (LSV) models E Derivation of Fokker-Planck equation for the local volatility model 08 02 'FX Barrier Options are the subject of more in-depth study by practitioners than almost any other class of exotic options and yet they have been given relatively short shrift in the literature until now. Zareer Dadachanji's book brilliantly fills this gap. Readers are led gently but thoroughly from the basics to the state of the art with ample discussion throughout (and full mathematical details supplied in appendices). Highly recommended for beginners and experts alike.' — Ben Nasatyr, Head of FX Quantitative Analysis, Citigroup 'Zareer Dadachanji's book on FX barrier options is clear, precise, and a pleasure to read. The derivations are as simple as possible while remaining correct, and the book displays a judicious blend of theory, modelling and practice. Students and practitioners will learn a lot (and not just about FX barrier options), and will do so with pleasure.' — Riccardo Rebonato, Global Head of Rates and FX Analytics, PIMCO, and Visiting Lecturer, Mathematical Finance, Oxford University 'The market in FX barrier options has grown from a niche to the most liquid exotics market in the world, requiring models that are both very sophisticated and computationally efficient. The first of its kind, Dr Dadachanji's treatise is exclusively dedicated to the subject. The book requires few prerequisites but quickly builds to the state of the art in a clear and comprehensive manner. Undoubtedly it will be an indispensable companion to anyone involved in the subject or interested in learning it.' — Vladimir Piterbarg, Head of Quantitative Analytics at Rokos Family Office 'This is the book I wish I'd had when I started my career as an FX quant – an insider's view of FX barrier option modelling from both a theoretical and practical perspective. It builds from the basic market set-up through to the latest techniques in an FX quant's toolkit.' — Mark Jex, FX Quant in investment banks for 20 years, and pioneer of the mixed local/ stochastic volatility model 'As one who understands financial engineering from the trader's perspective as well as from the quant's, Zareer Dadachanji has written a very valuable book on FX barrier options. Requiring very little pre-requisite financial knowledge, it guides readers through the plethora of quantitative concepts, techniques and practical issues associated with these products. And it is an enjoyable read to boot.' — Simon Hards, Global Head of FX Trading at Credit Suisse 31 02 The first book to analyse FX barrier options, frequently traded (but not always understood) on the largest derivatives market in the world – FX 13 02 Zareer Dadachanji is a quantitative analysis consultant with nearly two decades of corporate experience, mostly in financial quantitative modelling across a range of asset classes. He has spent 14 years working as a front-office quant at banks and hedge funds, including NatWest/RBS, Credit Suisse and latterly Standard C