Stochastic Calculus

[MisterPickle]

I'll have to check out Hoek, looks promising. After getting into these texts and seeing what the course material looks like for some MFE programs, the only other book I wish I had read before this is John Hull's "Options, Futures, and other Derivatives." The entire first half does a complete breakdown of all the financial products and strategies, then gets into the serious math later in the book. Shreve is essentially a math text with financial highlights.

 

[rajanS]

shreve's book is good. but you need more than just basic probability. Perhaps a book in 'introduction to probability models' by ross is a good supplement to shreve's book. Otherwise, shreve's book is a hard to read book. I can't imagine going over martingales before covering markov chains

 

[rajanS]

i don't understand why many books use different notations for the same concept. Stochastic calculus should all follow some standard notation. I have seen strike prices referred to as x, k or E many times and it gets rather frustrating. When will fin math follow a universal notation?

 

[rajanS]

I'll have to check out Hoek, looks promising. After getting into these texts and seeing what the course material looks like for some MFE programs, the only other book I wish I had read before this is John Hull's "Options, Futures, and other Derivatives." The entire first half does a complete breakdown of all the financial products and strategies, then gets into the serious math later in the book. Shreve is essentially a math text with financial highlights.

Hoeke's book is 109 dollars...urggg

 

[Steven]

Why Shreve's is such a good book is because it has an excellent balance between theory and examples (and very gentle explanation). If anyone has any experience in trying to read those treatises in the most abstract branch in mathematics, with utter abstractness and conciseness, you will love the book of Shreve's even more. Of course those treatises are probably meant for experts, but it is hard to imagine anyone wants to learn the theory without examples...

Besides, a lot of the results in abstract math is counter-intuitive, anyone who claims he/she can understand the theory without examples is likely to be overconfident or even delusional.

 

[Tsotne]

Why Shreve's is such a good book is because it has an excellent balance between theory and examples (and very gentle explanation). If anyone has any experience in trying to read those treatises in the most abstract branch in mathematics, with utter abstractness and conciseness, you will love the book of Shreve's even more. Of course those treatises are probably meant for experts, but it is hard to imagine anyone wants to learn the theory without examples...

Besides, a lot of the results in abstract math is counter-intuitive, anyone who claims he/she can understand the theory without examples is likely to be overconfident or even delusional.

I completely agree. Shreve has really a good balance between theory and examples. A bit hard though. Even professors are spending considerable time to get an overall intuition author embedded in explaining topics. 2nd Vol (Continuous time models) is more difficult. It's right as you said, this book is for experts, however even for stochastic calculus students like us, it's hard to begin learning this book unless you devote full time on this subject. For example, while having to study numerous important subjects at the university, it'll be a bit tough to keep up with this subject. If you have lighter schedule and softer subjects then it's good chance to start Shreve.

 

[Huan Dao]

Hoeke's book is 109 dollars...urggg

Does your local university have a library, you could try apply for a membership and borrow books from there, I don't have to spend a cent to read those books from the Master Reading List.

 

[Tsotne]

Does your local university have a library, you could try apply for a membership and borrow books from there, I don't have to spend a cent to read those books from the Master Reading List.

There can be some city libraries which provide members with different books in various subjects. Membership costs relatively low in most cases. But there are some books which is strongly suggested to "hold" after finishing studies. Shreve is such kind of book. When you need a quick referral you take it and read about the specific topic.

 

[Kenny L]

I used these book when I first started on stochastic calculus:

Oksendal's Stochastic Differential Equation;
Aggoun & Elliott's Measure Theory and Filtering

 

[DoubleTrouble]

I think Shreve's book is an excellent book on the application of Stochastic Calculus in Finance but not a very good book in Stochastic Calculus.

What I like about Vol.2 is that it's easy to read and not to heavy on the mathematics. Gives great understanding!

 

[bubblegum]

I cant believe what I am hearing, Shreve's book is about as easy as you are going to find for Stochastics in continuous time for finance. Its the first book I would recommend to anyone who wanted to delve into this fascinating subject (well read vol 1 first). Ive got Bjork's book as well, its good but not nearly as easy to read as Shreve. To be honest if you can not understand or read Shreve then what's the point, its super simple in the way he explains everything, and yes there is a huge amount of hand waving throughout the book, but it is exactly this that make it easy to read.

Personally I find Wilmott's books unbearable/unreadable, I can't stand Hull as its just so vague on the maths side of things and I don't like Baxter and Rennie for the same reason (i.e lets write a book about something thats quite simple and try and make it even simpler by missing out all the maths!). There is some rigour in Shreve's book but nothing compared to some of the other books out there. Try readying P. Protter - Stochastic differential equations and integration first off, your be lost after a few pages, try reading Rodger and Williams - Difussions, Martingales and Markov processes, your'll be lost after the first sentence!

Ive got Risk-Neutral Valuation by N. Bingham as well and that is also not as easy to read as Shreve, Ive also got Financial modelling with jump processes by P Tankov, and yes, they have successfully made a subject thats quite simple appear difficult.

Now I would not recommend Shreve's earlier books, i.e. the ones he did with Karatzas, but In my view (and it is just my view) Shreve's Vol 1 and Vol 2 are the easiest introduction to financial mathematics you will ever find. And yes they are easy and only to undergraduate level, to be a Quant a far deeper understanding than what's covered in those books would be needed.

Oh, and Oksendal's book is only good if you are comfortable with measure theory and functional analysis, otherwise the proofs and exercises will be tough going. Hes also very notion heavy with the Tex editor, i.e lets put a subscript under and subscript under a subscript, and makes some vague summation over some vague domain. Its like in Oksendal's book he just states the m.g.f for multi-dimensional Gaussian processes and lets you scratch your head a bit, where as Shreve will very simply derive it so its easy to understand, simple!

 

[DoubleTrouble]

To be honest if you can not understand or read Shreve then what's the point, its super simple in the way he explains everything

Well, everybody is at different stages of the education. I agree with you but it all depends on which background you have so try and be a bit more humble perhaps?

Also agree with you on Hull. I actually believe his vagueness makes it harder to understand.

 

[bubblegum]

Well, everybody is at different stages of the education. I agree with you but it all depends on which background you have so try and be a bit more humble perhaps?

Ok, I was being a bit harsh, my comments are only in regard to people who have done or are doing an undergrad degree in Maths, I could see that if someone who was doing computer sciences or business studies might find it tough going.

Also agree with you on Hull. I actually believe his vagueness makes it harder to understand.

You took the words right out of mouth, I could not agree with you more, I find Hull an absolute nightmare to read, although my friend who is studying business studies and economics swears by Hull's book!

 

[snipez]

Oh, and Oksendal's book is only good if you are comfortable with measure theory and functional analysis, otherwise the proofs and exercises will be tough going. Hes also very notion heavy with the Tex editor, i.e lets put a subscript under and subscript under a subscript, and makes some vague summation over some vague domain. Its like in Oksendal's book he just states the m.g.f for multi-dimensional Gaussian processes and lets you scratch your head a bit, where as Shreve will very simply derive it so its easy to understand, simple!

Huh, there is no functional analysis in Oksendal's text. Sure you're often working over Banach Spaces (ha I just used that term so I can still pretend like I still remember functional analysis but it's actually just a complete normed linear space right? so not that exciting I guess) or the like, but you don't actually have to do any functional analysis (e.g. prove the open mapping theorem or the hahn-banach theorem, to give 2 very basic examples).

As for notation, that's just something you deal with. Anyone who has studied a bit of PDE theory knows that notation is a nightmare. In any case it's not hard to figure out and you either adapt to it or come up with your own set of notation.

Most of the concentrated measure theory terminology appears early on when he talks about basic probability theory, which is only to be expected. But that doesn't mean you need to be an expert in the subject to read Oksendal. Assuming you've taken a basic real analysis course, reading the first chapter of Big Rudin will at least get you up to speed on the basic ideas used.

In any case, I think some of the NYU Math Finance lecture notes are pretty good. But for problems, both Shreve and Oksendal have plenty of good exercises.

 

[bubblegum]

Huh, there is no functional analysis in Oksendal's text.

The proofs are developed mostly in terms of classical functional analysis - square integrable real functions, geometry of real Hilbert spaces etc. Ok true you dont really need much more than the basics to get by but it still makes it harder than Shreve for the beginner to read, which is what this thread is all about.

 

[quotes]

Alison Etheridge's
A Course in Financial Calculus
is a strong recommend
It has explanations,
and very rigorous proofs,
also deep concepts,
yet unsolvable exercises,
plus many typos.

If you are bored by Shreve, try Alison. It will give you some challenge and thinking.
If you feel it is still too simple, try any of Marc Yor's books, and you will consider a quit.

In terms of easy reading, I believe Joshi's book is better than Wilmott's.