Showing posts with label mathematical finance. Show all posts
Showing posts with label mathematical finance. Show all posts

9/26/2012

Market Risk Analysis Review

Market Risk Analysis
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This is a very good introduction on the subject of portfolio management. I bought these books as a mathematical engineer because I want to write my thesis about stock options. Everything is clearly explained, they even explain a lot of the easy mathematics you need to succeed in the world of finance. Every book contains a cd which is very handy if you want to calculate an option's price in a minute or something.
In my opinion there is not enough said in the book about options, but then again, it is a book to learn the basics. If you want to become a succesfull options trader, you do need more literature on the forecasting of volatility surfaces and backtesting of technical indicators etc.

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Market Risk Analysis is the most comprehensive, rigorous and detailed resource available on market risk analysis. Written as a series of four interlinked volumes each title is self-contained, although numerous cross-references to other volumes enable readers to obtain further background knowledge and information about financial applications.
Volume I: Quantitative Methods in Finance covers the essential mathematical and financial background for subsequent volumes. Although many readers will already be familiar with this material, few competing texts contain such a complete and pedagogical exposition of all the basic quantitative concepts required for market risk analysis. There are six comprehensive chapters covering all the calculus, linear algebra, probability and statistics, numerical methods and portfolio mathematics that are necessary for market risk analysis. This is an ideal background text for a Masters course in finance.
Volume II: Practical Financial Econometrics provides a detailed understanding of financial econometrics, with applications to asset pricing and fund management as well as to market risk analysis. It covers equity factor models, including a detailed analysis of the Barra model and tracking error, principal component analysis, volatility and correlation, GARCH, cointegration, copulas, Markov switching, quantile regression, discrete choice models, non-linear regression, forecasting and model evaluation.
Volume III: Pricing, Hedging and Trading Financial Instruments has five very long chapters on the pricing, hedging and trading of bonds and swaps, futures and forwards, options and volatility as well detailed descriptions of mapping portfolios of these financial instruments to their risk factors. There are numerous examples, all coded in interactive Excel spreadsheets, including many pricing formulae for exotic options but excluding the calibration of stochastic volatility models, for which Matlab code is provided. The chapters on options and volatility together constitute 50% of the book, the slightly longer chapter on volatility concentrating on the dynamic properties the two volatility surfaces the implied and the local volatility surfaces that accompany an option pricing model, with particular reference to hedging.
Volume IV: Value at Risk Models builds on the three previous volumes to provide by far the most comprehensive and detailed treatment of market VaR models that is currently available in any textbook. The exposition starts at an elementary level but, as in all the other volumes, the pedagogical approach accompanied by numerous interactive Excel spreadsheets allows readers to experience the application of parametric linear, historical simulation and Monte Carlo VaR models to increasingly complex portfolios. Starting with simple positions, after a few chapters we apply value-at-risk models to interest rate sensitive portfolios, large international securities portfolios, commodity futures, path dependent options and much else. This rigorous treatment includes many new results and applications to regulatory and economic capital allocation, measurement of VaR model risk and stress testing.

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2/11/2012

Interest Rate Modeling: Theory and Practice (Chapman & Hall/CRC Financial Mathematics Series) Review

Interest Rate Modeling: Theory and Practice (Chapman and Hall/CRC Financial Mathematics Series)
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This is the book which I chose to keep for a comprehensive IR modeling textbook after reading many. Quite good since it introduces you all basic IR modeling issues almost step by step with a further learning direction for smiles.As the title says, the book also dips some industry practice.

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Containing many results that are new or exist only in recent research articles, Interest Rate Modeling: Theory and Practice portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods.The text begins with the mathematical foundations, including Ito's calculus and the martingale representation theorem. It then introduces bonds and bond yields, followed by the Heath-Jarrow-Morton (HJM) model, which is the framework for no-arbitrage pricing models. The next chapter focuses on when the HJM model implies a Markovian short-rate model and discusses the construction and calibration of short-rate lattice models. In the chapter on the LIBOR market model, the author presents the simplest yet most robust formula for swaption pricing in the literature. He goes on to address model calibration, an important aspect of model applications in the markets; industrial issues; and the class of affine term structure models for interest rates.Taking a top-down approach, Interest Rate Modeling provides readers with a clear picture of this important subject by not overwhelming them with too many specific models. The text captures the interdisciplinary nature of the field and shows readers what it takes to be a competent quant in today's market.This book can be adopted for instructional use. For this purpose, a solutions manual is available for qualifying instructors.

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12/17/2011

Interest Rate Modeling. Volume 3: Products and Risk Management Review

Interest Rate Modeling. Volume 3: Products and Risk Management
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I have read the vol 1 and vol 3. This review is for vol 3 only. After reading vol 1 (pls refer to my review for Vol 1) I was very impressed with the theoretical coverage and numerical tips, given by the authors who are probably the best quants on the street. Having this in mind I was expecting the same excitement and detail coverage for a wide range of vol products in vol 3. Now I have briefly finished reading vol 3, I have to say my feeling of vol 3 is mixed. I love the theortical treatment very well, the mapping in chap 16, the spread options in chap 17, the different improvements of regression in chap 18, the bermudans in 19, etc. The good thing is the subject is talked in detail with proofs and some implementation tips, and it is hard to find such material in other quant books. However, I feel something is missing. Some real trade examples maybe would fill some blanks. Just how to vega hedge a perticular CLE in real life, for example? I know there is no simple answer but would love to see how the big banks are doing it. I was expecting the authors discuss the hedging strategy for various type of vol products, 1 by 1, in detail, but I was a bit disappointed. Another pity I feel is the lack of discussion of forward vol and certain 2nd-order derivative profiles for the callables. Such as negative volga for accretor callables, I think every vol trader on the street knows this is ugly, however the authors didn't talk about it. Maybe the focus of this book is mainly about pricing models but not hedging/managing a vol book. Well, there are really too many things to cover I guess so can't expect a perfect book. Overall I would still highly recommend this book for quants and vol traders.

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Table of contents for all three volumes (full details at andersen-piterbarg-book.com)Volume I. Foundations and Vanilla Models Part I. Foundations
Introduction toArbitrage Pricing Theory
Finite Difference Methods
Monte Carlo Methods
Fundamentals of Interest Rate Modelling
Fixed Income Instruments
Part II. Vanilla Models
Yield Curve Construction and Risk Management
Vanilla Models with Local Volatility
Vanilla Models with Stochastic Volatility I
Vanilla Models with Stochastic Volatility II
Volume II. Term Structure Models Part III. Term Structure Models
One-Factor Short Rate Models I
One-Factor Short Rate Models II
Multi-Factor Short Rate Models
The Quasi-Gaussian Model with Local and Stochastic Volatility
The Libor Market Model I
The Libor Market Model II
Volume III. Products and Risk Management Part IV. Products
Single-Rate Vanilla Derivatives
Multi-Rate Vanilla Derivatives
Callable Libor Exotics
Bermudan Swaptions
TARNs, Volatility Swaps, and Other Derivatives
Out-of-Model Adjustments
Part V. Risk management
Fundamentals of Risk Management
Payoff Smoothing and Related Methods
Pathwise Differentiation
Importance Sampling and Control Variates
Vegas in Libor Market Models
Appendix
Markovian Projection


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12/10/2011

Interest Rate Modeling. Volume 1: Foundations and Vanilla Models Review

Interest Rate Modeling. Volume 1: Foundations and Vanilla Models
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About me: I am a trader in rates volatility and have a MS degree in MFE. I have only read the vol 1 of the 3 books so I am only reviewing the vol 1.
The book is more or less seperated into 2 parts: chap 1 to 5 are introductory materials for required math and numerical methods, and chap 6 to 9 are where things gets bit more technical and interesting. To me, if you want to get something out of this book you got to be comfortable with quants stuff, some basics like "Continuous time finance 2" from Shreve is required before you start this book. I found the material in chap6 to 9 interesting and instructive. There are many books about local and stochastic vols but I have yet to find any book that covered the material from head to toe like this book. The style of the writing is theory/proof/remark/example, and the derivations of the proof and formula is not too hard to follow, as long as you have the background as I mentioned before. The author also covered some important results from recent papers in the field, and talked about implementation challenges in numerical methods, which is very detail and I think it provides some coverage of the gap from theory to implementation. I'd love to read more about the details of what the banks used in their desks but I guess the authors would not expose what they really used at their work.
Overall this is a good book for quants. For traders I think vol 1 could be too technical and not much use because it does not cover the pricing and hedging of specific vol products, which is supposed to be in vol 3.

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Table of contents for all three volumes (full details at andersen-piterbarg-book.com)Volume I. Foundations and Vanilla Models Part I. Foundations
Introduction toArbitrage Pricing Theory
Finite Difference Methods
Monte Carlo Methods
Fundamentals of Interest Rate Modelling
Fixed Income Instruments
Part II. Vanilla Models
Yield Curve Construction and Risk Management
Vanilla Models with Local Volatility
Vanilla Models with Stochastic Volatility I
Vanilla Models with Stochastic Volatility II
Volume II. Term Structure Models Part III. Term Structure Models
One-Factor Short Rate Models I
One-Factor Short Rate Models II
Multi-Factor Short Rate Models
The Quasi-Gaussian Model with Local and Stochastic Volatility
The Libor Market Model I
The Libor Market Model II
Volume III. Products and Risk Management Part IV. Products
Single-Rate Vanilla Derivatives
Multi-Rate Vanilla Derivatives
Callable Libor Exotics
Bermudan Swaptions
TARNs, Volatility Swaps, and Other Derivatives
Out-of-Model Adjustments
Part V. Risk management
Fundamentals of Risk Management
Payoff Smoothing and Related Methods
Pathwise Differentiation
Importance Sampling and Control Variates
Vegas in Libor Market Models
Appendix
Markovian Projection


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12/09/2011

Interest Rate Modeling. Volume 2: Term Structure Models Review

Interest Rate Modeling. Volume 2: Term Structure Models
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I really find "Interest Rate Modeling" by Leif Andersen and Vladimir Piterbarg not only the best practical guide on interest rates derivatives modeling but also one of the best books on quantitative finance, in general. It is no wonder that many quants supporting asset classes other than interest rates derivatives bought this book as well. It is not only rigorous to ensure good understanding and giving the big picture but also very practical showing what would work in practice and what not, and how (using what tools) it can be achieved. Other books sometimes go on describing in details models that no one would ever use in practice just for the sake of completeness, or never discuss implementation details, which are the most important if the model is to be applied in practice (not mentioning curves building, Greeks and Risk Management). I am sure that every trading desk has already got a few copies of this book for reference: before it was a sharp need for a comprehensive interest rate derivatives book in practice like that. It is comprehensive because it methodologically covers all the components for successful understanding, development, and application of interest rates modeling in practice: mathematical and financial background (with tractable proofs and very useful references), the detailed description of traded interest rate derivatives, various practically applicable models (from basic to the most sophisticated) and numerical methods in a very systematic and consistent approach. I really recommend this book to everyone interested in quantitative finance: equally to academics (including students in financial engineering, mathematical finance etc) and practitioners.

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Table of contents for all three volumes (full details at andersen-piterbarg-book.com)Volume I. Foundations and Vanilla Models Part I. Foundations
Introduction toArbitrage Pricing Theory
Finite Difference Methods
Monte Carlo Methods
Fundamentals of Interest Rate Modelling
Fixed Income Instruments
Part II. Vanilla Models
Yield Curve Construction and Risk Management
Vanilla Models with Local Volatility
Vanilla Models with Stochastic Volatility I
Vanilla Models with Stochastic Volatility II
Volume II. Term Structure Models Part III. Term Structure Models
One-Factor Short Rate Models I
One-Factor Short Rate Models II
Multi-Factor Short Rate Models
The Quasi-Gaussian Model with Local and Stochastic Volatility
The Libor Market Model I
The Libor Market Model II
Volume III. Products and Risk Management Part IV. Products
Single-Rate Vanilla Derivatives
Multi-Rate Vanilla Derivatives
Callable Libor Exotics
Bermudan Swaptions
TARNs, Volatility Swaps, and Other Derivatives
Out-of-Model Adjustments
Part V. Risk management
Fundamentals of Risk Management
Payoff Smoothing and Related Methods
Pathwise Differentiation
Importance Sampling and Control Variates
Vegas in Libor Market Models
Appendix
Markovian Projection


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