Quantitative Finance and Risk Management

A Physicist's Approach

Jan W Dash

• Publisher: WSPC
• Year: 2016
• ISBN:
  9789814571258
• Edition: 2
• Topic: Business
• Subtopic: Finance
• Index: Business

Written by a physicist with extensive experience as a risk/finance quant, this book treats a wide variety of topics. Presenting the theory and practice of quantitative finance and risk, it delves into the "how to" and "what it's like" aspects not covered in textbooks or papers. A "Technical Index" indicates the mathematical level for each chapter.

This second edition includes some new, expanded, and wide-ranging considerations for risk management: Climate Change and its long-term systemic risk; Markets in Crisis and the Reggeon Field Theory; " Smart Monte Carlo " and American Monte Carlo; Trend Risk — time scales and risk, the Macro–Micro model, singular spectrum analysis; credit risk: counterparty risk and issuer risk; stressed correlations — new techniques; and Psychology and option models.

Solid risk management topics from the first edition and valid today are included: standard/advanced theory and practice in fixed income, equities, and FX; quantitative finance and risk management — traditional/exotic derivatives, fat tails, advanced stressed VAR, model risk, numerical techniques, deals/portfolios, systems, data, economic capital, and a function toolkit; risk lab — the nuts and bolts of risk management from the desk to the enterprise; case studies of deals; Feynman path integrals, Green functions, and options; and "Life as a Quant" — communication issues, sociology, stories, and advice.

PART I: INTRODUCTION, OVERVIEW, AND EXERCISE

1. Introduction / Outline; Note for 2^nd Edition; Unresolved Problems

Who/ How/What, “Tech. Index”, Messages, Personal Note

1. For Whom is This Book Written?

This book is primarily for PhD scientists and engineers who want to learn about quantitative finance, and for finance graduate students¹. Practicing “quants” and academic research workers will find topics of interest. There are even essays with no equations for non-technical managers.

2. How Can This Book Benefit You?

This book will enable you to gain an understanding of practical and theoretical quantitative finance and risk management.

3. What is In This Book?

The book is a combination of a practical “how it’s done” book, a textbook, and a research book. It contains techniques and results for quantitative problems with which I have dealt in the trenches for many years as a quant on Wall Street. Each topic is treated as a unit, sometimes drilling way down. Related topics are presented in parallel, because that is how the real world works. An informal style is used to convey a picture of reality. There are even some stories.

4. What is the “Tech. Index”? What Technical Background is Needed?

The “Tech. Index” for each chapter is a relative index for this book lying between 1-10 and indicating technical or mathematical sophistication. The average index is 5. An index 1-3 requires almost no math, while 8-10 assumes a PhD. No background in finance is assumed, but some would definitely be helpful.

5. How Should You Read This Book? What is in the Footnotes?

You can choose topics that interest you. Chapters are self-contained. The footnotes add depth and interesting commentary.

6. Message to Non-Technical Managers

Parts of this book will help you get a better understanding of quantitative issues. Important chapters have discussions of systems, models, and data. Skip sections with equations (maybe read chapters with the Tech. Index up to 3).

7. Message to Students

You will learn quantitative techniques better if you work through derivations on your own, including performing calculations, programming and reflection. The mathematician George Polya gave some good advice: “The best way to learn anything is to discover it by yourself”. Bon voyage.

8. Message to PhD Scientists and Engineers

While the presentation is aimed at being self-contained, financial products are extensive. Reading a finance textbook in parallel would be a good idea.

9. Message to Professors

Part of the book can be used in an advanced MS or PhD finance course (Tech. Index up to 8)², or for MBAs (Tech. Index up to 5). Topics you may find of interest include: (1) Feynman path integrals and Green functions for options, (2) The Macro-Micro trend-risk model with explicit time scales connecting to both macroeconomics and finance, (3) Optimally stressed correlation matrices, (4) Stressed VAR, (5) Smart Monte Carlo, (6) Market crisis modeling, (7) Psychology and options models, (8) Climate-Change Risk.

10. A Personal Note

This book is largely based on my own work and/or first-hand experience. It is in part retrospective, looking back over trails traversed and sometimes blazed. Some results are in my 1988-89 CNRS preprints when I was on leave from the CNRS as the head of the Quantitative Analysis Group at Merrill Lynch, in my 1993 SIAM Conference talk, and in my CIFEr tutorials. Footnotes entitled “History” contain dates when my calculations were done over the years, along with recollections and stories³.

Summary Outline: Book Contents

The book consists of seven divisions.

I. Qualitative Overview of Risk

A qualitative overview of risk is presented, plus an instructive and amusing exercise emphasizing communication.

II. Risk Lab for Derivatives (Nuts and Bolts of Risk Management)

The “Risk Lab” first examines equity and FX options, including skew. Then interest rate curves, swaps, bonds, caps, and swaptions are discussed. Practical risk management including portfolio aggregation is discussed, along with static and time-dependent scenario analyses.

This is standard textbook material, and directly relevant for basic quantitative work.

III. Exotics, Deals, and Case Studies

Topics include barriers, double barriers, hybrids, average options, the Viacom CVR, DECs, contingent caps, yield-curve options, reloads, index-amortizing swaps, and various other exotics and products.

By now, this is mostly standard material. The techniques presented in the case studies are generally useful, and would be applicable in other situations.

IV. Quantitative Risk Management

Topics include optimally stressed positive-definite correlation matrices, fat-tail volatility, Plain/Stressed/Enhanced VAR, CVAR uncertainty, credit issuer and counterparty risk, model issues and quality assurance, systems issues and strategic computing, data issues, the Wishart Theorem, economic capital, and unused-limits risk. This is the largest of the six divisions of the book.

Much of this material is standard, although there are various improvements and innovations.

V. Path Integrals, Green Functions, and Options

Feynman path integrals provide an explicit and straightforward method for evaluating financial products, e.g. options. The simplicity of the path integral technique avoids mathematical obscurity. My original applications of path integrals and Green functions to options are presented, including pedagogical examples, mean-reverting Gaussian dynamics, memory effects, multiple variables, and two related straightforward proofs of Girsanov’s theorem. Consistency with the stochastic equations is emphasized. Numerical aspects are treated, including the Castresana-Hogan path-integral discretization. Critical exponents and the nonlinear-diffusion Reggeon Field Theory RFT are discussed. Recent empirical connections of the RFT with markets in crises are presented.

The results by now are all known. The presentation is not standard.

VI. Trend Risk and The Macro-Micro Model

Trend risk is the fourth generic risk (separate from volatility risk, correlation risk, and jump risk). The problem is “sliding into the mud”, not covered by the cost of doing business, as in the transition into a recession. The Macro-Micro model has built-in trend risk. Initially, as developed with A. Beilis, it originated through an examination of models capable of reproducing yield-curve dynamical behavior – in a word, producing yield-curve movements that look like real data. The real feature of this model is that it has time scales with different dynamic behavior. The model contains separate mechanisms for long-term and short-term behaviors of rates. The model is connected in principle with macroeconomics through quasi-random quasi-equilibrium paths, and it is connected with financial models through strong mean-reverting dynamics for fluctuations through trading. Applications of the Macro-Micro model to the FX and equities markets are also presented, along with recent formal developments. Option pricing and no-arbitrage in the Macro-Micro framework are discussed. Finally a “function toolkit”, possibly useful for business cycles and/or trading, is presented.

This material is not standard but should be.

Note for the 2^nd Edition (2015)

A lot of water has passed under the bridge since the 1^st edition, first printed in 2004, including a financial crisis and increased emphasis on risk management. The material however continues to be relevant; I use it regularly (even items I thought were peripheral). The added material for the 2^nd edition is largely new and hopefully will be of interest^4,5.

Climate Change Risk Management – NEW TOPIC

Climate change risk management is the most significant addition to the 2^nd edition of this book. Climate change with its global warming temperature trend presents increasing serious risks to business, the economy, finance, and society in general. I believe that the ensemble of increasingly serious climate impacts can potentially destabilize the inherently unstable worldwide financial and economic systems into deep crisis.

I propose a formal structure for climate risk management, and also emphasize positive opportunities occasioned by mitigating climate change. I also propose two climate risk metrics: “Climate Change Value at Risk” and a “Climate Change Reward-to-Risk Ratio”. I discuss a negative ethically based discount rate for valuation of future climate impacts, if we do not act sufficiently responsibly on climate mitigation. I also give a survey of climate issues (science, impacts, mitigation/adaptation, contrarians).

I believe that we must be optimistic on working out a solution to the climate problem. There is no other choice.

Evaluation – Where do we stand? What about the future?

The current generation of quants and risk analysts set up a basically sound quantitative finance and risk management structure since the late 1980’s, starting from basically no quantitative structure. This has required an immense effort, also including many people across many disciplines. Still, my opinion is that risk management of finance is essentially still in an adolescent state, because our risk procedures are only effective at times when there are no really big risks.

Unsolved Problems in Finance and Risk Management

Here is a short list of what I believe are important basic unsolved problems. Advances will require increased understanding of ...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Contents
• Acknowledgments
• PART I: INTRODUCTION, OVERVIEW, AND EXERCISE
• PART II: RISK LAB (NUTS AND BOLTS OF RISK MANAGEMENT)
• PART III: EXOTICS, DEALS, AND CASE STUDIES
• PART IV: QUANTITATIVE RISK MANAGEMENT
• PART V: PATH INTEGRALS, GREEN FUNCTIONS, AND OPTIONS
• PART VI: THE MACRO-MICRO MODEL
• PART VII: CLIMATE CHANGE RISK MANAGEMENT
• INDEX: CH. 1 – CH. 52
• INDEX: CLIMATE CHANGE RISK MANAGEMENT, CH. 53