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How to Be a Quantitative Ecologist is comprised of two equal parts on mathematics and statistics with emphasis on quantitative skills. A major component of this guide is computer implementation techniques, accompanied by computer practicals using the language R.

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

Ecological research is becoming increasingly quantitative, yet students often opt out of courses in mathematics and statistics, unwittingly limiting their ability to carry out research in the future. This textbook provides a practical introduction to quantitative ecology for students and practitioners who have realised that they need this opportunity. The text is addressed to readers who haven't used mathematics since school, who were perhaps more confused than enlightened by their undergraduate lectures in statistics and who have never used a computer for much more than word processing and data entry. From this starting point, it slowly but surely instils an understanding of mathematics, statistics and programming, sufficient for initiating research in ecology. The book's practical value is enhanced by extensive use of biological examples and the computer language R for graphics, programming and data analysis. Key Features: Provides a complete introduction to mathematics statistics and computing for ecologists. Presents a wealth of ecological examples demonstrating the applied relevance of abstract mathematical concepts, showing how a little technique can go a long way in answering interesting ecological questions. Covers elementary topics, including the rules of algebra, logarithms, geometry, calculus, descriptive statistics, probability, hypothesis testing and linear regression. Explores more advanced topics including fractals, non-linear dynamical systems, likelihood and Bayesian estimation, generalised linear, mixed and additive models, and multivariate statistics. R boxes provide step-by-step recipes for implementing the graphical and numerical techniques outlined in each section. How to be a Quantitative Ecologist provides a comprehensive introduction to mathematics, statistics and computing and is the ideal textbook for late undergraduate and postgraduate courses in environmental biology. \"With a book like this, there is no excuse for people to be afraid of maths, and to be ignorant of what it can do.\" -Professor Tim Benton, Faculty of Biological Sciences, University of Leeds, UK

Industrial metals can be distinguished as ferrous or non‐ferrous metals in relation to their iron content. They are defined as ‘industrial’ to address their end use and distinguish them from precious metals. Unlike most commodities, where several exchanges challenge each other to attract liquidity, base metals trading concentrate on the London Metal Exchange (LME). The history of the LME goes together with that of the base‐metals market. This chapter starts with a brief history of the LME. It provides an overview of each metal's characteristics, consumption data and industry uses. The chapter explains how crucial China is in today's metals markets. It gives an introduction to base‐metals volatility trading and analysis. The chapter focuses on the specific features of metals options from the point of view of the trader rather than that of the risk manager or the quantitative analyst.

Quantitative analysts are better known as quants. They perform a vital role in most capital market organisations but are often regarded as quite different by virtue of their personalities and interactions with other business functions. This chapter unveils some of the mystery that surrounds the quants. A quant uses his or her skills to develop mathematical calculations. He provides yield information, prices a single trade, calculates risk measures, analyses competitor's product, and so on. Banks employ quants for supporting a trading desk, market risk control, counterparty risk control, research, client advisory, competition analysis, and defence. Their position in relation to IT staff depends on the type of interaction desired. The two groups can work independently, collaboratively or somewhere in between. Some quants aid the traders with pricing and risk management while others are involved in the control function helping to quantify market and counterparty risk exposures.

This chapter describes a perspective view from a Tier 1 Company. It discusses an article by Owain Self, Executive Director, European Algorithmic Trading at UBS. Owain highlights the important considerations when developing and supporting a credible algorithmic trading tool and what it takes to maintain that credibility in a constantly changing market. There are three areas to draw from – the traders, the quantitative analysts, and the technology developers – and it is essential to create a balance between these three groups. Technology obviously plays an essential part in a process so dominated by performance and a considerable investment has to be made. The latest generation of technology is essential and legacy systems are to be avoided – particularly when constant development and improvement plays such an integral role in the product's success. The chapter also discusses factors determining the success of an algorithmic trading product.

In this chapter we make our high level case for a new organization called “cybersecurity risk management.” We outline what such an organization would look like in terms of high‐level charter as well as its sub‐organizations and personnel. These include: quantitative risk analysts (QRAs), analytics technology, program management, and training and development. We also touch on a concern around the topic of corporate audit and the role audit should and should not play in the furthering of quantitative approaches within the enterprise. Last, we conclude with a broader call to action in terms of the overall security ecosystem, and highligh the concern for the “Big One” in terms of compound breach.