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New book - A Linear Algebra Primer for Financial Engineering - Dan Stefanica

dstefan

Baruch MFE Director
Joined
5/19/06
Messages
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We are happy to announce that the book ``A Linear Algebra Primer for Financial Engineering" by Dan Stefanica was published on July 15.

This book covers numerical linear algebra methods required for financial engineering applications, and includes the mathematical underpinnings for many methods used in practice. Many of these applications, complete with pseudocodes, are included in the book, which is appropriate for self-study. It is the second book in the Financial Engineering Advanced Background series, after ``A Primer for the Mathematics of Financial Engineering".

The book can be ordered from http://www.fepress.org/nla-primer for $49.60, a 20% discount off the $62 list price, for all orders placed before August 1, 2014.
All orders from http://www.fepress.org/nla-primer will be signed and personalized by the author.

________________________________________________________________________

Title: A Linear Algebra Primer for Financial Engineering
Author: Dan Stefanica
Softcover: 338 pages
Publisher: Financial Engineering Press
FE Press page and sample sections: http://www.fepress.org/nla-primer
Table of Contents: attached
FE Press Price: $49.60 (List Price: $62)
Amazon US: http://tinyurl.com/nsoryr8
Amazon UK: http://tinyurl.com/nvpo67m
Also available on amazon.de amazon.fr amazon.it amazon.es

Financial Applications
• The Arrow—Debreu one period market model
• One period index options arbitrage
• Covariance and correlation matrix estimation from time series data
• Ordinary least squares for implied volatility computation
• Minimum variance portfolios and maximum return portfolios
• Value at Risk and portfolio VaR

Linear Algebra Topics
• LU and Cholesky decompositions and linear solvers
• Optimal solvers for tridiagonal symmetric positive matrices
• Ordinary least squares and linear regression
• Linear Transformation Property
• Efficient cubic spline interpolation
• Multivariate normal random variables
________________________________________________________________________

About the Author
Dan Stefanica
has been the Director of the Financial Engineering Masters Program at Baruch College, City University of New York, since its inception in 2002. He teaches graduate courses on numerical methods for financial engineering, as well as pre-program courses on advanced calculus and numerical linear algebra with financial applications. His research spans numerical analysis, graph theory, and geophysical fluid dynamics.
 

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  • nla_primer-toc.pdf
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The publishers site has several sample sections. I would take a look at these before buying the book. It is not a book that will appeal to everyone.

My background is computer science. I was not a math major. I found Dr. Stefanica's "Primer" difficult, even for mathematical topics that I already knew (like Legrangian multipliers). I took a look at the section on linear regression for this book, also a topic I know from a graduate class and found it similarly obscure (although I understood it). This is not a book that would work for me, for "self-study" unless I had already taken a class in the topic. Those who are math majors or who have done graduate work in math will probably like the book more. If you like the "Primer" you will probably like this book. I bought the primer and sold it on Amazon since I didn't find it much help in my studies.
 
The publishers site has several sample sections. I would take a look at these before buying the book. It is not a book that will appeal to everyone.

The book requires prior knowledge of linear algebra at undergraduate level, which may then be enough for self-studying the book.

The topics on the publisher website may be more advanced or niche topics. I attached here the pdf for Chapter 1 which covers basic concepts and some financial applications on these concepts and is a good example of the spirit in which the book is written.
 

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  • ch1-nla_primer.PDF
    225.5 KB · Views: 842
From the first chapter, I would recommend an intermediate level of mathematical "maturity" before using this book for self study. For newbies to Linear Algebra, I would suggest you work through a good introductory text in Linear Algebra, then pace through Strang's Linear Algebra text. It also jumps into Financial Engineering applications straight off the bat, which for newbies to finance like myself is daunting.

Having completed Strang's text I think I'll sink my teeth into this textbook and give a more informative review.
 
From the first chapter, I would recommend an intermediate level of mathematical "maturity" before using this book for self study. For newbies to Linear Algebra, I would suggest you work through a good introductory text in Linear Algebra, then pace through Strang's Linear Algebra text. It also jumps into Financial Engineering applications straight off the bat, which for newbies to finance like myself is daunting.

Having completed Strang's text I think I'll sink my teeth into this textbook and give a more informative review.

Very good comment - the NLA Primer is not a linear algebra textbook and assumes the reader has taken a linear algebra course in the past. It includes topics that will be useful for financial engineering studies, and presents them in a different way than linear algebra books usually do.

The emphasis is on topics with financial engineering applications, and on those applications, beginning from the first chapter.
 
A Solutions Manual should be available in late November or early December 2014.
 
This is just another book among a million written for financial engineering! Is it a new book? Yes, it is but the contents are nothing more than a repetitive stuffs we have seen for the last 30 years. Every good quant out there can write a book like this one, so can i! But i don't write because i'd be feeling like a parot blahblah...the same old boring stuffs!

Have a look at this line again
"Financial Applications The Arrow—Debreu one period market model..."

The real financial market is NOT a Arrow-Debreu, and what this book offers are NOT practical applications!

I'd urge the author to write something for real. Yes, for real!!! Even one page for real things! I would appreciate that effort!
 
We are happy to announce that the book ``A Linear Algebra Primer for Financial Engineering" by Dan Stefanica was published on July 15.

This book covers numerical linear algebra methods required for financial engineering applications, and includes the mathematical underpinnings for many methods used in practice. Many of these applications, complete with pseudocodes, are included in the book, which is appropriate for self-study. It is the second book in the Financial Engineering Advanced Background series, after ``A Primer for the Mathematics of Financial Engineering".

The book can be ordered from http://www.fepress.org/nla-primer for $49.60, a 20% discount off the $62 list price, for all orders placed before August 1, 2014.
All orders from http://www.fepress.org/nla-primer will be signed and personalized by the author.

________________________________________________________________________

Title: A Linear Algebra Primer for Financial Engineering
Author: Dan Stefanica
Softcover: 338 pages
Publisher: Financial Engineering Press
FE Press page and sample sections: http://www.fepress.org/nla-primer
Table of Contents: attached
FE Press Price: $49.60 (List Price: $62)
Amazon US: http://tinyurl.com/nsoryr8
Amazon UK: http://tinyurl.com/nvpo67m
Also available on amazon.de amazon.fr amazon.it amazon.es

Financial Applications
• The Arrow—Debreu one period market model
• One period index options arbitrage
• Covariance and correlation matrix estimation from time series data
• Ordinary least squares for implied volatility computation
• Minimum variance portfolios and maximum return portfolios
• Value at Risk and portfolio VaR

Linear Algebra Topics
• LU and Cholesky decompositions and linear solvers
• Optimal solvers for tridiagonal symmetric positive matrices
• Ordinary least squares and linear regression
• Linear Transformation Property
• Efficient cubic spline interpolation
• Multivariate normal random variables
________________________________________________________________________

About the Author
Dan Stefanica
has been the Director of the Financial Engineering Masters Program at Baruch College, City University of New York, since its inception in 2002. He teaches graduate courses on numerical methods for financial engineering, as well as pre-program courses on advanced calculus and numerical linear algebra with financial applications. His research spans numerical analysis, graph theory, and geophysical fluid dynamics.

Here i express my dislike the use of the term "Financial Engineering" is that: Finance is not a Science and the financial markets are the right places for traders, regulators, arbitrageurs, and absolutely not for engineers, especially those with knowledge of with graph theory, geophysical fluid dynamics. Market derivatives prices are not Formula 1 engines to which engineers can design or even upgrade. Traders often use daily tools as simple as cubic polynomials plus their powerful intuition in making prices, this strongly implies that the book being marketed here has no roles whatsoever in financial markets. This book is a curse of curses to financial markets.

I would be a damn fool of fools to buy this book!
 
I'd urge to write something for real. Yes, for real!!! Even one page for real things! I would appreciate that effort!

what topics should it include ? IMO your comments are valid

Here i express my dislike the use of the term "Financial Engineering" is that: Finance is not a Science and the financial markets are the right places for traders, regulators, arbitrageurs, and absolutely not for engineers, especially those with knowledge of with graph theory, geophysical fluid dynamics. Market derivatives prices are not Formula 1 engines to which engineers can design or even upgrade. Traders often use daily tools as simple as cubic polynomials plus their powerful intuition in making prices
a trader friend of mine would agree with you 100 percent
 
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"Traders often use daily tools as simple as cubic polynomials plus their powerful intuition in making prices,"

No fear of arbitrage with them cubics?
 
Insulting as this message is, it requires an answer.

Firstly, the book serves a very clear purpose: it contains the material we would like the students accepted in the Baruch MFE Program to know before they come to the Numerical Linear Algebra summer refresher seminar. As the book is now available, they can read it ahead of time, so the NLA seminar is more in depth and shorter, allowing for room for a statistics summer refresher seminar.

I'd urge the author to write something for real. Yes, for real!!! Even one page for real things! I would appreciate that effort!

Had you looked at the link above where sample sections are posted (http://www.fepress.org/nla-primer/ see also attached), a section is on implied volatility computation using least squares, which is a subtle problem, and describes the current method used by Bloomberg. Not something you would find in the vast majority of books.

To paraphrase, ``I would appreciate" the effort to look into the information posted before posting an opinion.

Have a look at this line again
"Financial Applications The Arrow—Debreu one period market model..."

The real financial market is NOT a Arrow-Debreu, and what this book offers are NOT practical applications!

A section in the book describes how a one period market model can be constructed for S&P options. That could lead to finding arbitrage opportunities, by refining the method.

But again, the opinion was posted based on the Table of Contents, not the actual content of the book.

I would be a damn fool of fools to buy this book!

This is a common thread in other posts: https://www.quantnet.com/threads/new-book-advanced-quantitative-finance-with-c.17775/#post-137890
 

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  • ch8-implied_vol_least_squares.pdf
    95.8 KB · Views: 297
Had you looked at the link above where sample sections are posted (http://www.fepress.org/nla-primer/ see also attached), a section is on implied volatility computation using least squares, which is a subtle problem, and describes the current method used by Bloomberg. Not something you would find in the vast majority of books.

A section in the book describes how a one period market model can be constructed for S&P options. That could lead to finding arbitrage opportunities, by refining the method.

So what?! In my opinion, still nothing is new! Nonsignificant contribution whatsoever. As simple as "...finding arbitrage opportunities,..." you are saying that with the tech provided in your book one can confidently predict the next market crash if he wishes to?!
 
So what?! In my opinion, still nothing is new! Nonsignificant contribution whatsoever. As simple as "...finding arbitrage opportunities,..." you are saying that with the tech provided in your book one can confidently predict the next market crash if he wishes to?!

You don't know what you're talking about. The book is a text, not a research monograph. And there's no claim of predicting the next crash. What is your point?
 
You don't know what you're talking about. The book is a text, not a research monograph. And there's no claim of predicting the next crash. What is your point?

You don't know what you'd read because you read with your mind closed.

Finanical market is real. Derivattives markets are real. Arbitrage opportunities are real. Three market crashes in three decades were real. Making prices and writing options are real activities. Writing such a book like this one full of hypothetical markets, arbitrage opportunities, etc... is definitely a way of making money from ignorant students. Again, buying such a book is absolutely a waste of money. Give students a real taste of reality.

To get some real sense of reality, you'd better read articles written by Alie Ayache, and people with similar views. After this if you're still against my view, i won't waste my time further on you and your lot of old bureaucratic closed minded bunch in this forum.

Let me give young students some questions and advices: Who make derivatives prices and with what tools? Answer: traders, NOT quants, and with tools as simple tools as Excel spreadsheets and VBA codes. Have a look at SPX option prices here http://www.marketwatch.com/investing/index/spx/options
If you cannot tell how these prices are made, you must know that derivatives prices are NOT made or engineered by
"...numerical linear algebra methods required for financial engineering applications, and includes the mathematical underpinnings for many methods used in practice..."

This book, a text or not, is considered irrelevant to what is considered a real thing. It is NOT worth for students to learn from.

And that is my $1 mil point to you, mr "bigbadwolf".
 
Which books would you recommend to learn about the real world?

Hi pingu,

A question asked is a smart question! Thanks for asking a smart question. I don't have a particular book(s) to refer you to, but i can direct you to where to find the right source of readings. Let me begin the real world, to traders and speculators, it is a market place where they exchange financial contracts, write and trade new financial derivatives. Most of these people donot possess knowledge of stochastic calculus and they need to, and they don't live in an artificial world that is so-called the risk-neutral world by academics/financial engineers. Stocks are traded in stock markets, futures in the futures exchange markets, options in their own markets. With futures, two parties agree to exchange an underlying asset (corn, wheat, oil, etc...) for a predetermined price at a certain maturity. Does such a simple contract require "linear algebra" or "financial engineering"? Of course not. Same goes for vanillas. Now we also trade options on futures, derivatives on derivatives. This is source of complexity of the real world which is indefinite and infinte, and by no means can be confined in a hypothetical world - the risk-neutral world which is constructed on many unreal assumptions.

So here are my recommendations: (1) stay away from those books/papers that include terms like "financial engineering" because they wrongly imply, even suggest, that financial derivatives prices are mathematically made and financially engineered; (2) stay away from books/papers that embrace a belief that we live in a risk neutral world where market prices are all risk-neutral; lastly (3) mathematics is just a tool, just like a computer or excel spreadsheet, and can only be used to compute, not make prices for derivatives. Traders make prices, mathematics don't!

Go and search for articles/papers that promote a sensible realistic approach that doesnot allow you to make false/stupid assumptions, nonsensical models, etc... These sort of articles/papers are not often found the mainstream published journals and books because most of their editors still embrace the old conventional approach - the risk neutral approach.
 
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