JWD
Senior Member
Posts: 1306
Joined: Mar 2005
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Wed Mar 16, 05 02:22 PM
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Here is an excerpt (Chapter 1) so forum users can get an overview picture of my book.
1. Introduction and Outline
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 graduate students in finance programs (see footnote 1). Practicing quantitative analysts (“quants”) and 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 over fifteen 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 Finance Background is Needed?
The “Tech. Index” for each chapter is a relative index for this book lying between 1-10 and indicating mathematical sophistication. The average index is 5. An index 1-3 requires almost no math, while 8-10 requires a PhD and maybe more. 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 commentary; they are useful sidebars.
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 (or 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 could be used in a PhD finance course (Tech. Index up to 8), 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 model with explicit time scales connecting to both macroeconomics and finance, (3) Optimally stressed correlation matrices, (4) Enhanced/Stressed VAR.
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 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 (see footnote 2).
Summary Outline: Book Contents
The book consists of six 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 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 are briefly discussed. The results by now are all known. The presentation is not standard.
VI. The Macro-Micro Model (A Research Topic)
The Macro-Micro model, developed initially with A. Beilis, 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 model contains separate mechanisms for long-term and short-term behaviors of rates, with explicit time scales. 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 due to trading. Further 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. I believe that these topics will form a fruitful area for further research and collaborations.
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Footnotes for Chapter 1:
1. History: The book is an outgrowth of my tutorial on Risk Management given annually for five successive years (1996-2000) at the Conference on Intelligence in Financial Engineering (CIFEr), organized jointly by the IEEE and IAFE. The attendees comprised roughly 50% quantitative analysts holding jobs in finance and 50% PhD scientists or engineers interested in quantitative finance.
2. History: To translate dates, my positions were VP Manager at Merrill Lynch (1987-89); Director at Eurobrokers (1989-90), Director at Fuji Capital Markets Corp. (1990-93), VP at Citibank (1993), and Director at Smith Barney/Salomon Smith Barney/Citigroup (1993-2003). I managed PhD Quantitative Analysis Groups at Merrill, FCMC, and at SB/SSB/Citigroup through various mergers.
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Edited: Sat Sep 22, 07 at 01:03 PM by JWD
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