Which book is best for my self-study of stochastic calculus?

Hi everybody,

I have a master's in statistics. It has been almost a decade but my knowledge of probability had (once) gone as far as the following concepts : the probability triple, the monotone and dominated convergence theorems, martingales, and very vaguely the radon-nikodym derivative (you get the idea). Probably need a few weeks of quiet study to review all these and get back up to speed.

Anyway, I am now aiming to make a career switch from being a buy-side macro economist to a buy-side quant, and I think learning about stochastic calculus would be helpful (avoided that course back in the day because the professor was a known disaster). My aim is NOT to become so acquainted with the subject so I could begin dong Phd research on the topic. Just want to be solidly grounded enough to be an effective and efficient quant.

Need a book for self-study and I have narrowed down my list to the these two. Which one would you think is better for me? Or would there be a 3rd better option I am not aware of? My goal is to get as much out of a book as quickly as possible, to the point that I am totally comfortable with the key concepts, how they have come about, and how they are applied in finance. Your advice is much appreciated, thank you so much!

1. Shreve: Stochastic Calculus and Finance
2. Michael Steele: Stochastic Calculus and Financial Applications
 

Daniel Duffy

C++ author, trainer
So..? OP is asking about a book for stochastic calculus
Depends how you define stochastic calculus.
Because you will only half understand stochastic calculus by studying theoretical SDEs. It is too one-sided; besides most SDEs don't have analytic solutions.

Ideally, you need to learn Measure Theory and Lebesgue Integration as foundation. How in earth will you understand Girsanov and Radon-Nikodym otherwise?
 
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Depends how you define stochastic calculus.
Because you will only half understand stochastic calculus by studying theoretical SDEs. It is too one-sided; besides most SDEs don't have analytic solutions.

Ideally, you need to learn Measure Theory and Lebesgue Integration as foundation. How in earth will you understand Girsanov and Radon-Nikodym otherwise?
This is what makes Shreve's volume 2 great, he packages the necessary measure theoretic results into the first two chapters so that one is able to understand results such as the ones you mention. Of course, his treatment is surface level, but nonetheless it is sufficient to understand the motivation behind results like that of Girsanov.

Learning stochastic calculus does not require you to learn numerical methods for SDEs. The main ingredients, e.g. brownian motion and martingales, stochastic integration, Itos lemma, Girsanov and Feynman-Kac, SDEs, in my opinion have nothing to do with numerical methods at the surface. Where numerical methods make sense is in a second course -- a first course in stochastic calculus should focus on the (pure) mathematics, and this is exactly what Shreve volume 2 does.
 

Daniel Duffy

C++ author, trainer
This is what makes Shreve's volume 2 great, he packages the necessary measure theoretic results into the first two chapters so that one is able to understand results such as the ones you mention. Of course, his treatment is surface level, but nonetheless it is sufficient to understand the motivation behind results like that of Girsanov.

Learning stochastic calculus does not require you to learn numerical methods for SDEs. The main ingredients, e.g. brownian motion and martingales, stochastic integration, Itos lemma, Girsanov and Feynman-Kac, SDEs, in my opinion have nothing to do with numerical methods at the surface. Where numerical methods make sense is in a second course -- a first course in stochastic calculus should focus on the (pure) mathematics, and this is exactly what Shreve volume 2 does.
That's why I prefer Glasserman .. he integrates the two approaches.
Horses for courses.
 
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