ESSENTIAL MATHEMATICS FOR MARKET RISK MANAGEMENT

There are many textbooks available on the subject of financial risk management, however relatively few of these develop and emphasize the mathematical story behind this subject. In short, there isn't an obvious mathematical risk management equivalent to the plethora of mathematical pricing textbooks mentioned that exist. Simon Hubbert plugs this gap for both financial mathematics students and practitioners.  The book is self-contained and takes the reader on a mathematical journey from the early ideas of risk quantification up to the sophisticated models and approaches of the present day, linking and highlighting the milestones along the way. The book opens with an introduction to the kinds of problems that a typical financial risk manager will face both on a day-to-day basis (e.g. monitoring the performance of a financial portfolio) and also in the form of long term projects (e.g. developing a model for the volatility of a financial asset). The book is divided into four parts: Part 1. The Mathematical Toolbox. This consists of three self-contained mathematical chapters covering applied linear algebra, probability theory and mathematical optimization. These chapters are designed to capture the essential mathematical tools that are needed to explore many common risk management problems. Part 2. Mathematical Risk Management: Basic Theory. This consists of  five chapters which chart the historical development of risk management as a mathematical subject. The story opens with an investigation of the so-called risk free world where the growth of a financial investment is completely predictable. We then take the plunge into the world of risky financial assets and pose the following fundamental question: What is the relationship between the risk and potential reward of holding a portfolio of risky financial assets? Readers will then be shown how to derive a mathematical solution to this problem that dates back to the 1950s and the pioneering work of Harry Markowitz. Simon will then show how this solution inspired a surge of academic interest into the quantifcation of risk. The section will close by asking How should a financial institution cater for the possibility that its trading portfolio could suffer a huge loss? This question received a great deal of attention in the 1990s when regulatory bodies established guidelines regarding how much capital a bank ought to put aside in order to cope with adverse movements in the financial markets. There are, as we shall see, many ways of answering this question but by far the most popular is the concept of computing the so-called Value at Risk (VaR) for the portfolio. Part 3. Statistical Toolbox. In order to investigate some of the more recent pioneering developments in modern risk management it is necessary that readers become acquainted with a certain amount of statistical theory. The third section of the book consists of 5 chapters which are designed to supply the reader the right amount of statistical background. Part 4. Mathematical Risk Management: Advanced Theory. The book closes by looking at more advanced topics.  To begin with the focus is on derivative products, which, at the simplest level, can be viewed as non-linear mathematical functions of an underlying financial variable . The difficult mathematical challenge is to find a precise form of this non-linear function. Simon will show how to derive the pricing formula for one of the simplest examples and also investigate how VaR can be measured for a non-linear portfolio, i.e., one that contains derivative products. The reader will then be shown how to put the statistical tools to work and provide a scientific investigation into the properties of the loss random variable of a typical random variable. Another chapter is dedicated to designing mathematical models for volatility and a further chapter delivers a theoretical description of the extreme losses. In the final chapter

Everything you need to know in order to manage risk effectively within your organization You cannot afford to ignore the explosion in mathematical finance in your quest to remain competitive. This exciting branch of mathematics has very direct practical implications: when a new model is tested and implemented it can have an immediate impact on the financial environment. With risk management top of the agenda for many organizations, this book is essential reading for getting to grips with the mathematical story behind the subject of financial risk management. It will take you on a journey--from the early ideas of risk quantification up to today's sophisticated models and approaches to business risk management. To help you investigate the most up-to-date, pioneering developments in modern risk management, the book presents statistical theories and shows you how to put statistical tools into action to investigate areas such as the design of mathematical models for financial volatility or calculating the value at risk for an investment portfolio. Respected academic author Simon Hubbert is the youngest director of a financial engineering program in the U.K. He brings his industry experience to his practical approach to risk analysis Captures the essential mathematical tools needed to explore many common risk management problems Website with model simulations and source code enables you to put models of risk management into practice Plunges into the world of high-risk finance and examines the crucial relationship between the risk and the potential reward of holding a portfolio of risky financial assets This book is your one-stop-shop for effective risk management.