Dan Stefanica's A Primer for the Mathematics of Financial Engineering

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A book based on material taught in the Advanced Calculus refresher course to the incoming students of the Financial Engineering MS Program at Baruch College has been published recently.

Title: A Primer for the Mathematics of Financial Engineering
Author: Dan Stefanica (http://www.quantnet.org/wiki/Dan_Stefanica)
Softcover: 302 pages
Publisher: Financial Engineering Press
ISBN-13: 978-0979757600
ISBN-10: 0979757606
Price: USD 55

The author of the book has been the Director of the Baruch MFE program since its inception in 2002.

More details about the book, as well as sample sections, are available here (http://www.fepress.org/store/index.php?main_page=product_info&products_id=180)

You can pre-order the book at www.fepress.org (http://www.fepress.org/) by following the link on the front page; using the coupon code 4938e34fc1 by May 15 provides a 20% discount. All purchases from FEPress.org will be signed by the author.

You can also order directly on Amazon by clicking on the link below.

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The book was written primarily for the benefit of prospective students for financial engineering or mathematical finance programs. Building a solid base for further study is of tremendous importance. This book contains core concepts important for a successful learning experience in financial engineering graduate programs, and its study should pay dividends right away.

Mathematical topics (selected):
numerical integration methods
Lagrange multipliers
convergence of Taylor series expansions
finite difference approximations
Stirling's formula
polar coordinates transformations
Newton's method for higher dimensional problemsFinancial topics (selected):
bond duration and convexity
Put-Call parity
Black-Scholes formula
numerical estimation of the Greeks
implied volatility
bootstrapping for finding interest rate curvesEvery chapter contains both mathematical topics and financial applications, and concludes with exercises that are a mix of mathematical and financial questions.
Many of these exercises are, in fact, questions that are frequently asked in interviews for quantitative jobs in financial institutions, and some are constructed in a sequential fashion, building upon each other, as is often the case at interviews.

Complete solutions to most of the exercises will be posted at FE Book - Quantnet.org - Financial Engineering Forum (http://www.quantnet.org/forum/forumdisplay.php?f=88)

[Dmytro]

look forward to getting - and using! - this book.
congratulations on such a great accomplishment.

[Aditya Chitral]

congratulations !!

is indian or international edition for this book available?

[VladimirBunicu]

look forward to getting - and using! - this book.
congratulations on such a great accomplishment.

Dmytro, I believe you can also get your copy signed by the author ;)
Now I can see where the financial math class' handouts are coming from...

Congratulations, professor Stefanica! =D>

[bigbadwolf]

Ordered a copy from Amazon ($42).

[charlesdwright]

Ordered a copy from Amazon ($42).


Are there any used ones on there yet? :D

Congratulations, Prof. Dan.

[sandeep]

Congratulations, Prof. Stefanica!!

[Rachit]

Congratulations Professor Dan! =D> =D> =D>
May we see more books in the future..!!

[Christian]

Congrats! Now what are you going to do with all this free time of yours, Professor??

[dstefan]

congratulations !!

is indian or international edition for this book available?

There will be no such editions, unfortunately.

[rmeenaks]

Hi,

I just bought your book from Amazon. Any chance you can send me the lecture notes/power point slides/etc for this book?

Thanks,

Ram

[dstefan]

There are no lecture notes, slides, or other additional materials for the book.

However, solutions to all the problems will be posted on QuantNet:
FE Book - Quantnet.org - Financial Engineering Forum (http://www.quantnet.org/forum/forumdisplay.php?f=88)

[bigbadwolf]

Okay, I now have the book in my hands. My first impression (albeit superficial) is that it's what I expected it to be: a one-stop shop for all the pre-req math one needs for an MFE program. I particularly like the way the math has been interwoven with applications to finance (bond pricing, Black-Scholes formula, and in particular, the Black-Scholes PDE).

The one quibble I have is that the discussion of probability is skimpy. For teaching non-measure-theoretic-probability, I'd use Meester's "A Natural Introduction to Probability," published by Birkhauser (or Ross's book, "A First Course in Probability," cited in the references provided in DS's book). For measure-theoretic probability, I'd use the Capinski and Kopp book (also cited by DS), and/or relevant sections in Shreve's second volume.

For applied math in general, and numerical solutions to PDEs specifically, I'd refer to Gilbert Strang's recently published, "Computational Science and Engineering." And before I forget, his book on calculus is a one-stop shop for all the basic calc (short of ODEs and PDEs) a quant is likely to need (Strang is a master pedagogue).

[Andy]

I know those who order from fepress.org and choose pick up option will get to see the author and get a signed copy of the book. Would those who choose to buy from Financial Engineering Press (www.fepress.org) and pay for shipping will get a signed copy also?

A signed copy is always more valuable and personable I suppose.

[Yuriy]

Andy, it is not always the case with signed copies. I have one book signed by the author (he seems to sign all his books), but that does not make the book any more valuable.

What makes the book more valuable for me is that I know the author personally. But in the case when I know the author personally, a signed copy is twice as valuable.

[alain]

Andy, I have a funny story about signed copies (BTW, I got my signed copy yesterday. Thanks Prof. Stefanica).

I had the pleasure to meet Dr. Sidney Harmam from Harman/Kardon fame once and he said that all his books are signed. By whom? By Sidney Harman :)

[Andy]

The only signed copy I ever had is from my PhD adviser - Prof. Melvin Nathanson, a number theorist. He gave me his Amazon.com: Additive Number Theory: Inverse Problems and the Geometry of Sumsets (Graduate Texts in Mathematics): Melvyn B. Nathanson: Books (http://www.amazon.com/Additive-Number-Theory-Problems-Mathematics/dp/0387946551/)
It's one of the graduate textbook in addictive number theory.

It's super sweet that he gave me a copy as a gift. So I'm looking forward to getting a signed copy from Prof. Stefanica.
Somewhere down the road, I would be able to tell my son: "Daddy knows the author of this book".

[bigbadwolf]

The only signed copy I ever had is from my PhD adviser - Prof. Melvin Nathanson, a number theorist.

You were a budding number theorist? My respect for you soars into the stratosphere. Incidentally, I also have the Nathanson book (I believe it was one of a pair he wrote for Springer GTM; I think I also have the other one). Number theory is the queen of mathematics (Gauss). Quant math is a joke: pedestrian and prosaic.

(The above is all off-topic)

[Andy]

Number theory is definitely a wonderful subject. The problem set are very elementary and accessible to most undergraduates. To solve it is a different story.
I learned Latex, used C++ while working on the postage stamp problem (http://mathworld.wolfram.com/PostageStampProblem.html) with my advisor.
I met Terrence Tao (Field Medal in 2006) and Ben Green during many conferences, attended workshops that study his papers, attend NYU, Columbia weekly number theory seminars. We studied Tao-Green paper before it was published. It was the highlight of my school years then.

But again, I realize that writing a paper, let alone a book is a tremendous undertaking. I'm amazed at how fast some people publish papers. It seems like my adviser just wrote another paper every other week over BBQ.

So all the kudos to Prof. Stefanica for publishing his first book. It is not easy but it will definitely help those who want to prepare for an MFE program. We went through most of the material in his book during one refresher course. It's a lot to learn/do (math theory -> financial application -> implementation in C++) in 2 weeks.

Having this in advance would half the pain and double the joy.

[bigbadwolf]

attend NYU, Columbia weekly number theory seminars.

Then you probably knew Armand Brumer (at Fordham) and Ken Kramer (at Queens).

(Again off-topic)

[dstefan]

Okay, I now have the book in my hands. My first impression (albeit superficial) is that it's what I expected it to be: a one-stop shop for all the pre-req math one needs for an MFE program. I particularly like the way the math has been interwoven with applications to finance (bond pricing, Black-Scholes formula, and in particular, the Black-Scholes PDE).

Thanks :)

Interesting which finance topics you preferred. The sections on the ATM approximation formulas were most fun to write.

The one quibble I have is that the discussion of probability is skimpy. For teaching non-measure-theoretic-probability, I'd use Meester's "A Natural Introduction to Probability," published by Birkhauser (or Ross's book, "A First Course in Probability," cited in the references provided in DS's book). For measure-theoretic probability, I'd use the Capinski and Kopp book (also cited by DS), and/or relevant sections in Shreve's second volume.

We intend to write a short series of books containing most of the math background required when beginning graduate studies in financial engineering:

Numerical Linear Algebra Methods for Financial Engineering Applications

A Probability Primer for Mathematical Finance

Differential Equations with Numerical Methods for Financial Engineering

The format and level of depth and coverage of each one of those books should be similar to those from the Math Primer book. I only covered the minimal amount of probability (and did so briefly while still making things comprehensible) required to present the Black-Scholes formula. A very rigorous and complete treatment of probability with emphasis on topics with financial applications will be given by my colleague, Professor Elena Kosygina, in the Probability Primer book.

[dstefan]

I know those who order from fepress.org and choose pick up option will get to see the author and get a signed copy of the book. Would those who choose to buy from Financial Engineering Press (http://www.fepress.org) and pay for shipping get a signed copy also?

Very good idea, I will do so.

[rmeenaks]

When are the other books coming out? I really like this primer book....Hits every topic I wanted to see...

Great Job and Keep it coming,

Ram

[Andy]

I just got my signed copy yesterday from Prof. Stefanica and am going through the chapters now.
Who wants to be the first reviewer of the book on Amazon?

[Pravit]

Some of you who got the book when it just came out must have had some time to read it by now. What are your impressions? I'm thinking of getting this book soon too (before April 30 :) ) but I'd like to hear some feedback from readers first. I'll be attending the math finance program at Toronto this fall and want to get started on my review as soon as the semester ends :)

[Andy]

I just skimmed through the book and I can say that the materials have been updated, expanded and better organized than when I learned it in 2006.

You should know the calculus level 1,2,3 fairly well. The old calculus concepts we all study in college is now presented in a financial framework so it's refreshing. I really like the homework and the financial application part.

I think I got to refresh my rusty calculus memory and C++ by doing the math exercise and financial applications in the book. There are bond pricers, black scholes, greeks, etc. It's a good way to combine all the relevant skills.

The bottom line is that the materials in this book and the sequential Linear Algebra refresher have helped tremendously to prepare for the rigorousness of the program. If I didn't take the refresher, I would have thought calculus refresher is a waste of time being a math grad. I'm glad I took the refresher. The amount I learned in this is sizable and the knowledge is non-trivial.

On the other hand, for people who are not in the Baruch program or can't take the refresher, the price of the book is outweighed by the value you gain from it.

From the point of view of someone who will begin an MFE program soon, it's a no brainner especially if your program does not offer refresher courses. If you want to jump start your MFE study and gain an edge over your fellow students, this is a good way to spend the summer doing.
There are couples of exercises in the book that I was asked during my internship interviews.
Last but not least, you should get the book because my name is mentioned in it.

[quirkfee]

I am attending the CMU MSCF program starting fall of this year. Although the program offers a refresher course, I ordered a copy of this book anyway because it seems like a great desk reference to have. Looking forward to receiving it soon! :)

[Pravit]

Yep, I think I'll get it too, $44 is quite a reasonable price, compared to the ridiculous prices American textbook manufacturers charge these days...

Quirkfree, it was a hard decision for me to turn down CMU :) I was looking on their Countdown website to see what textbooks they use for the math review, but it seems they only mentioned some probability textbooks. I feel pretty comfortable with my probability, but I could def. use some review on Taylor series and that sort of thing, so hopefully Dr. Stefanica's book will be helpful to me.

[dstefan]

I feel pretty comfortable with my probability, but I could def. use some review on Taylor series and that sort of thing, so hopefully Dr. Stefanica's book will be helpful to me.

I do hope the book will be useful - it was written to serve as a quick (but thorough) math refresher for people enrolling in financial engineering programs, with emphasis on financial applications. And good luck in your studies!

[Pravit]

Thanks Dr. Stefanica! I look forward to reading your book.

[satyag]

I know those who order from fepress.org and choose pick up option will get to see the author and get a signed copy of the book. Would those who choose to buy from Financial Engineering Press (http://www.fepress.org) and pay for shipping will get a signed copy also?

A signed copy is always more valuable and personable I suppose.

Where do you have to go for store pickup ?

[dstefan]

Where do you have to go for store pickup ?

Midtown Manhattan.

[satyag]

Midtown Manhattan.
I just ordered one at fepress.org for in store pickup. But there is no mention of address anywhere. Could you give me the address ?

[Bridgett]

a much discussed book... anticipating to read it and benefit from it myself... :)

[Andy]

The discount coupon is now extended through May 15

[Bridgett]

The discount coupon is now extended through May 15

... to accommodate the popular demand!!! =D>

[Andy]

Somebody posted a review on Amazon ;)

[Pravit]

I've gone through chapters 0 and 1 and so far I really like the book. It's been giving me a good review of stuff I should know and already taught me some stuff I didn't know, like linear recursion, finding closed formulas for sums, and big-O and little-O notation. I enjoyed doing the exercises in chapter 1 about options - I knew what call and put options were in theory, but doing the exercises gave me a better intuitive feeling of how they work. I'm doing the bits about numerical integration now. Look forward to working through the rest of this book over the summer!

[bobbychopra]

Trying to get the book today and putting the appropriate coupon code, but it says "This coupon has expired"

Any ideas whats wrong? Coupon code I tried is 4938e34fc1 as listed. Thanks in advance!

[dstefan]

The coupon is working properly now.

[bobbychopra]

Thanks Prof!

Also, I chose the "Pick Up From Store" option. I know you mentioned the store was in Midtown Manhattan, but where exactly? Or is it the Baruch Book Store?

I wasn't too sure. Could someone please help regarding where I can pick up the book?

[Sanket Patel]

Dr Stefanica,

Where will additional solutions be posted? I've read the first few chapters and worked majority of those problems. I must say, so far, the book has been great.

[dstefan]

The plan is to start posting the solutions around June 1st and complete them by June 15. I will generate a pdf file with all solutions as well.

Ideally, each problem will be in its own thread, which will be open for comments and alternative solutions beginning June 15.

But then again, beginning in June 2007 I kept thinking the book will be out ``next month"... ;)

[MidasCFA]

can't wait to get my hands on the book too. i'm sure it will help jumpstart:) my graduate studies at rutgers MSMF this coming fall.

[Andy]

Just saw Dominic's review of Dan Stefanica's book on his blog. You can read this piece and other interesting writing at Quant Careers Blog by Dominic (http://www.wilmott.com/blogs/dcfc/)

I've just been looking through a copy of Dan Stefanica's book, "A Primer for the Mathematics of Financial Engineering" Here (http://www.amazon.com/Primer-Mathematics-Financial-Engineering/dp/0979757606/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1211112873&sr=8-1)
It's well written and covers much that a quant should know.
That is in fact, why I regard it as such a scary book. There are parts of the mathematics that I remember first doing when I was a teenager. I like to think I have some ability at maths, but no one ever called me a child prodigy. Stefanica runs the Baruch Masters in Financial Engineering, which is distinctly one of the better MFE programmes. And before you email me to ask, we never ever give out an ordered list of programs.

Apparently, people apply to serious MFE programs not knowing the chain rule in calculus. Obviously you'd expect a bit of background noise in applications from those who think quantitative finance is some form of extreme accountancy, or who mistake it for an MBA. But I am told that such holes exist in people who have passed numerate degrees from universities you will have heard of. This book will cover a lot of the maths you need to be clear on if you are going to survive any sort of masters degree in financial engineering, or the CQF. So the first bit of utility you gain from it, is helping you work out whether this line of work is for you. You can make your way in this line of work without being a PhD, but you cannot prosper if PDEs are forever beyond you. The maths are put in a financial context, which helps, since most people in this field are porting across from a different discipline. Being focused in financial maths, you do not use time on types of mathematics not used in QF. But of course you should not kid yourself that this book will get you all the maths you need to know. It's will help you get up to speed if time is pressing.

Aside from the calculus applied to variants on solving Black Scholes model, deriving greeks, there is a basic introduction to finite difference methods. He doesn't even try to do this in C++, which is a wise choice, else the target reader would just get lost.
At $42.50 it is cheaper than many finance books, which is nice, and makes it something of a bargain. If you're starting a finance masters this year, you ought to take a look.

[LTCM]

Not to be rude, but is this seriously all the math needed to start an MFE?

You can learn everything in this book during your first two years of undergrad.

[LTCM]

that being said, I it is obviously still a good review to have on hand, as opposed to 6-7 textbooks.

[dstefan]

Not to be rude, but is this seriously all the math needed to start an MFE?

No, it is not. A more complete review of the math needed to start an MFE would include Linear Algebra, Probability, and Differential Equations, and maybe statistics and a some other subjects, too. We have plans to, eventually, write similar texts in those areas, too.

As you pointed out, the Primer is a very good text to refresh calculus (and learn some finance in the process, too). You learn topics that will turn out to be really useful when studying in an MFE and see their financial applications right away.

[pauly]

No, it is not. A more complete review of the math needed to start an MFE would include Linear Algebra, Probability, and Differential Equations, and maybe statistics and a some other subjects, too. We have plans to, eventually, write similar texts in those areas, too.

As you pointed out, the Primer is a very good text to refresh calculus (and learn some finance in the process, too). You learn topics that will turn out to be really useful when studying in an MFE and see their financial applications right away.

Hi dstefan,

I have no idea about financial engineering and I have not looked at basic math for several years. My career has recently taken me into the derivatives world, and I find it difficult because I do not have a sound understanding of the math that is needed to understand how to value derivatives. Would your book be good for someone like me or is there a certain amount of assumed knowledge that I would need to have before starting your book? If that is the case, do you have any other books you would recommend for me?

Any help is very much appreciated.

[dstefan]

Hi pauly,

The knowledge assumed by the book is at the level of Calculus 1 and 2. In my opinion, the book could be used for self study. Sample sections are available at
A Primer for the Mathematics of Financial Engineering - $55.00 : Financial Engineering Press, Book store (http://www.fepress.org/store/index.php?main_page=product_info&products_id=180)

Dan