the relevance of learning advanced stochastic calculus

[vkaul]

I am confused by the books out there for stochastic calculus. I started with Baxter and then moved on to Shreve-2 for finance. But I am wondering how useful it is to read even more advanced books like karatzas shreve and rogers, williams. It will take a huge amount of time( more than one year) to even understand these books that too with extreme dedication. Is it that useful for any job in Wall Street. I know it is useful for academia.

 

[chaoticrambler]

If you can solve with total confidence the problems on stochastic calculus in "Heard on the street" and Mark Joshi's interview book, you should be good to go. In interviews, the questions focus on basics. I think a lot of people struggle answering basic questions but have spent too much time on black scholes. E.g. solving a stochastic integral by first principles could be a question that can be asked. People who have just crammed up the ITO formula won't have a clue.

 

[bigbadwolf]

But I am wondering how useful it is to read even more advanced books like karatzas shreve and rogers, williams.

From a quant finance point of view, they're an utter waste of time (though lovingly written books and indispensable to specialists in stochastic theory; I have both myself).

 

[chaoticrambler]

From a quant finance point of view, they're an utter waste of time (though lovingly written books and indispensable to specialists in stochastic theory; I have both myself).

What about Oksendal ? Like the first 5 chapters + some later material on diffusions ?

 

[daleholborow]

From a quant finance point of view, they're an utter waste of time (though lovingly written books and indispensable to specialists in stochastic theory; I have both myself).

Do you mind if i ask why they are an utter waste of time? Do you consider them out of date, superceded, too theoretical, not theoretical enough...etc etc?

I have a copy of shreve, but its been sadly neglected and laying at the bottom of my collection, but looking through it again now, it does look clean and clear, so presumably its a question of content, rather than presentation/delivery?

 

[bigbadwolf]

Do you mind if i ask why they are an utter waste of time? Do you consider them out of date, superceded, too theoretical, not theoretical enough...etc etc?

I have a copy of shreve, but its been sadly neglected and laying at the bottom of my collection, but looking through it again now, it does look clean and clear, so presumably its a question of content, rather than presentation/delivery?

No, Karatzas and Shreve and Rogers and Williams are neither out of date nor have they been superceded (as far as I know). But for one in quant finance, or an FE student, they go way too far, assume too much of a background, and are just too theoretical. Or in other words, one will not enhance one's market rate by going through them. These are monographs designed for specialists in stochastic theory. Karatzas and Shreve's Methods of Mathematical Finance is a sequel to their abstruse Brownian Motion and Stochastic Calculus. I'm not clear on who exactly they're targeting. Maybe math grad students whose speciality is stochastic theory/probability and who crave a rigorous introduction to stochastic finance because that's the way they've been trained?

Vols 1 and 2 of Shreve should suffice (or equivalents such as Elliott and Kopp's Mathematics of Financial Markets or Bingham and Kiesel's Risk-Neutral Valuation).

In my humble opinion, for someone in finance his understanding of probability and stochastic should be heuristic and not axiomatic (in the sense of definition-lemma-theorem-corollary). Just as an engineer knows how to use PDEs without necessarily worrying about existence and uniqueness conditions and exactly what conditions a PDE theorem needs for its proof.

 

[Bastian Gross]

I emphasize to learn stochastic analysis and calculus.
There are a lot of books in that issue, so I've additionally recommend a book by Fred Espen Benth ("Option Theory with Stochastic Analysis") and several papers for the rest.

 

[quantstart]

This is a problem I am having too. I have Vols 1 and 2 of Shreve and am wondering whether I should just concentrate on Crack and the questions in there. Where do people see their time being optimally spent in terms of a first career in Quant?