Looking for derivatives book

[pauly]

Hi All,

I am new to this website and will not know even a fraction of what most people on this site know. However, I was hoping some of you may be able to give me some sound advice. Recently as part of my job, I have became exposed to the accounting for derivatives. I get the accounting ok since I am an accountant, but I do not get the math or valuation behind derivatives. I am not very good at math and it is a long long time since I did any such stuff at high school. I was hoping some of you may be able to recommend some books that would be a good starter for me to understand the math and valuation of derivatives. I looked through the recommended reading posts, but want to make sure that whatever I am recommended will be basic enough for me. It seemed that even some of the "primer" books on these posts were probably for people that have some idea what they are talking about. I can't stress enough, I am not as smart as you guys!

Any help would be very very much appreciated.

Thank you,

Pauly G

 

[Andy Nguyen]

The books in the 'Master Reading List' section generally assume you have a firm grasp of college level mathematics - multivariate calculus, linear algebra, calculus based probability, and differential equations to name a few.

What's the highest level of mathematics you have studied?

 

[Andy Nguyen]

It depends on the derivatives. Is it bond, stock option, credit, or something exotic?
You can get John Hull for a general review of the derivatives. If the product you do is simple enough, you can get by with it. Otherwise there are books specializing on each derivatives.
Most evaluation is simple and can be done via vanilla spreadsheets. Others would require 3rd party products or models from the quants.

 

[pauly]

Thanks Andy. Initially I want to understand the math behind the valuation of relatively plain vanilla instruments, Forwards, futures, options, interest rate swaps, bonds, and then when I feel I have a solid grasp of that maybe start to move on.

Again, any advice is very much appreciated.

 

[pauly]

Thanks Sanket.

I did some basic algebra and calculus at high school years and years ago but have forgotten it all. Is there a book you would recommend that would be worthwhile readhing so that I can learn the basics?

Thanks again for your help.

 

[Sanket Patel]

I'm not too familiar with the myriad of calculus books in print, but I, myself, used James Stewart's Calculus: Early Transcendentals and Morris Kline's Calculus: An Intuitive and Physical Approach.

As for linear algebra, I think you'd be in good hands with Gilbert Strang's Introduction to Linear Algebra. For ordinary differential equations, I think Boyce and DiPrima's Elementary Differential Equations with Boundary Value Problems is a good pick.

You may want to message bigbadwolf - he knows his way around books and perhaps may be able to recommend better titles.

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[Stefan Zota]

Thanks Sanket.

I did some basic algebra and calculus at high school years and years ago but have forgotten it all. Is there a book you would recommend that would be worthwhile readhing so that I can learn the basics?

Thanks again for your help.

For Calculus, try Stefanica's Math Primer book.
For Linear Algebra, Strang's book can be a good starting point.
For Probability and Stochastic Calculus, Shreve's book is the reference.

Last 2 books are more theoretical, but still required.

 

[doug reich]

I think Stefanica may be a little much for someone who insists on his lack of math sophistication. Shreve may also be a stretch, but I haven't thought of it from this perspective.

 

[pauly]

I think Stefanica may be a little much for someone who insists on his lack of math sophistication. Shreve may also be a stretch, but I haven't thought of it from this perspective.

Thanks Doug, do you know of any alternative text books that you would recommend as a starting point?

Thank you.

 

[Sanket Patel]

You could take a look at some of the Schaum's books. But you have to keep in mind, they're mostly outline/review type books which pick and choose the "key" topics. They're inevitably bound to leave out certain topics.

For a derivatives book, I think Hull's Options, Futures, and Other Derivatives may be a good place to start. It is pretty low key when it comes to math.

 

[bigbadwolf]

Thanks Doug, do you know of any alternative text books that you would recommend as a starting point?

What exactly is you current math skill set? Can you solve a quadratic? Can you prove the Pythagorean theorem? Can you differentiate an implicit function? Can you integrate by parts? For someone who's saying he's forgotten his basic algebra, I wouldn't recommend Stefanica or Shreve.

Furthermore, if your current math knowledge and skills really are as abysmal as you suggest, you'll probably need a couple of years, maybe more, to get to a stage where you can tackle the books above. It's not so much that there's a vast amount of material to be learnt -- there isn't from a mathematician's point of view -- but rather the issue of getting gradually into a mathematical frame of mind (something the quant responders to your posts are taking for granted).

 

[pauly]

Thank you bigbadwolf, that helps a lot, and confirms my suspicions, i.e., I am not yet smart enough to even read the books that you guys think of as easy!! I think I could solve a basic quadratic equation, but could not prove the Pythagorean theorem, could not differentiate an implicit function and could not integrate by parts.

I apologize if I am wasting your time, I realize that my math skills are non-existent in comparison to the people on here, although I still intend on making an effort to get smarter on this.

If you do know of any really simple math books that cover the areas you feel are necessary to understand the math behind derivatives then I would appreciate your recommendations. If not, no problem.

Thanks again for your help.

 

[bigbadwolf]

Thank you bigbadwolf, that helps a lot, and confirms my suspicions, i.e., I am not yet smart enough to even read the books that you guys think of as easy!! I think I could solve a basic quadratic equation, but could not prove the Pythagorean theorem, could not differentiate an implicit function and could not integrate by parts.

Start by buying Simmons' "Pre-Calculus Mathematics in a Nutshell," now published by Barnes and Noble, I think. You have to know everything in this slim book forwards and backwards before you start calculus. This should be your primary reference. Unfortunately it is too terse to serve as a text (he seems to think 60 minutes is all should take to explain trig). You will need to buy supplementary texts with copious problem sets and then endure the drudgery of working through those problems so that you acquire speed and competence. This is what math is about: problem-solving with agility and speed. The areas you need will be algebra, analytic geometry, and trigonometry. Additional topics on functions, on permutations and combinations, and on elementary probability will come in handy later. You're a grown man, you can find books on these topics for yourself, but in general look for books that were published sixty or eighty years ago in used bookshops: they have loads of drill-type problems, which is what you need at the moment. Realistically speaking, allow yourself anywhere between one to two years for this pre-calc mathematics. And then another year at least for basic calc. It's not that the content is inherently daunting; it's that acquiring the mathematical frame of mind -- something we take for granted on this forum -- takes time. After this two-to-three year period, you'll be equipped for Stefanica or Willmott.

 

[pauly]

Thanks bigbadwolf, very helpful and much appreciated.

 

[tobias elbert]

I'd say Neftci's 'Introduction to the Mathematics of Financial Derivatives' is a good to read and easy to understand introduction:

Amazon.com: Introduction to the Mathematics of Financial Derivatives (Academic Press Advanced Finance): Salih N. Neftci: Books

It also covers calculus to the extent needed to understand the topics within the book. It's thus fairly self-contained. IMHO the best introductory text on quant finance out there for people coming from a NONscientific background and there is probably no chance of finding an easier treatment of the subject.

 

[alfredo]

for beginner

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For advanced topics, one book less known but better i think than hull'book

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[DoFX]

Start by buying Simmons' "Pre-Calculus Mathematics in a Nutshell," now published by Barnes and Noble, I think. You have to know everything in this slim book forwards and backwards before you start calculus. This should be your primary reference. Unfortunately it is too terse to serve as a text (he seems to think 60 minutes is all should take to explain trig). You will need to buy supplementary texts with copious problem sets and then endure the drudgery of working through those problems so that you acquire speed and competence. This is what math is about: problem-solving with agility and speed. The areas you need will be algebra, analytic geometry, and trigonometry. Additional topics on functions, on permutations and combinations, and on elementary probability will come in handy later. You're a grown man, you can find books on these topics for yourself, but in general look for books that were published sixty or eighty years ago in used bookshops: they have loads of drill-type problems, which is what you need at the moment. Realistically speaking, allow yourself anywhere between one to two years for this pre-calc mathematics. And then another year at least for basic calc. It's not that the content is inherently daunting; it's that acquiring the mathematical frame of mind -- something we take for granted on this forum -- takes time. After this two-to-three year period, you'll be equipped for Stefanica or Willmott.

I know this is an old post but wanted to thank you for this great outline. I found it helpful in filling some gaps in my math foundations. Buying and studying Simmons in detail was one of the most effective and rewarding learning experiences I've had.

Would you be able to provide some guidance on covering calculus? Would like to learn the subject as effectively as possible. I was thinking of using Lang's "A First Course in Calculus" (Springer, fifth edition). Seems to be a solid middle ground between the more "fluff" calculus books (e.g. Stewart) and books that are perhaps too advanced for a first rigorous touch on calculus (e.g. Apostol/Spivak). Do you have any recommendations for covering calculus within this frame?

 

[Ken Abbott]

Figlewski's "Financial Options" book taught me all I needed to know. It provides intuition, not equations.

 

[bigbadwolf]

Would you be able to provide some guidance on covering calculus? Would like to learn the subject as effectively as possible. I was thinking of using Lang's "A First Course in Calculus" (Springer, fifth edition). Seems to be a solid middle ground between the more "fluff" calculus books (e.g. Stewart) and books that are perhaps too advanced for a first rigorous touch on calculus (e.g. Apostol/Spivak). Do you have any recommendations for covering calculus within this frame?

Don't know your level -- are you approaching calc for the first time or want a quick revision? Lang's book is fine. I also like "Beginning Calculus" published by Schaum's (assuming you're learning it for the first time). Apostol's two volumes on calculus (not his analysis book) are also good. Probably the ideal combination is a book that just covers the ideas, with brief sketches of proofs or plausible arguments and a heavier book that is full of problems. Lang is probably okay for the overview. Apostol for the problems. I also like Strang's treatment of calculus but don't remember if his book has loads of drill-type problems.

 

[DoFX]

Don't know your level -- are you approaching calc for the first time or want a quick revision? Lang's book is fine. I also like "Beginning Calculus" published by Schaum's (assuming you're learning it for the first time). Apostol's two volumes on calculus (not his analysis book) are also good. Probably the ideal combination is a book that just covers the ideas, with brief sketches of proofs or plausible arguments and a heavier book that is full of problems. Lang is probably okay for the overview. Apostol for the problems. I also like Strang's treatment of calculus but don't remember if his book has loads of drill-type problems.

Thank you - very helpful.

Current level: Beginner. I understand the basic concepts of differentiation, the rules of derivatives etc. But no prior knowledge of integral calculus or multivariable calculus.

I take it your advice is still valid for such knowledge level?