Reader-Friendly Paths for Learning Stochastic Calculus in Finance
Summary
The document recommends a staged set of resources for someone beginning stochastic calculus with applications to quantitative finance. It suggests first learning binomial trees, Wiener processes, Itô’s lemma, and Black–Scholes–Merton in the context of an introductory derivatives text. For deeper study, it names Shreve’s books, while noting that independent learners may find them demanding, and points to an elementary finance-focused alternative.
Other suggested texts cover foundational probability and solved exercises, or a broader range of advanced mathematical methods for financial markets. The answer also mentions university lecture notes connecting stochastic differential equations with partial differential equations. These recommendations are based partly on the respondent’s experience and partly on reputation or a contents-page review; the best choice depends on the learner’s mathematical preparation and preferred balance of exposition and formalism.
Key ideas
- An introductory derivatives text can present stochastic calculus concepts in an applied financial context.
- Shreve’s books are recommended for thorough treatment, though they may be challenging for self-study.
- An elementary finance-focused text and a probability book with solved exercises may suit beginners.
- Advanced mathematical finance texts and university notes offer further topics after the basics.
- Choose a resource based on prior probability, statistics, and mathematical background.
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Full text
# Stochastic Calculus in Quantitative analysis # Stochastic Calculus in Quantitative analysis I am an aspiring quant that would like to get a head start learning stochastic calculus, which books FROM EXPERIENCE are the most reader friendly? ## Answer by Jacob Amos (score 8) https://quant.stackexchange.com/a/11099 For a basic introduction, the three chapters in Hull's Options, Futures, and Other Derivatives on Binomial Trees, Wiener Processes and Ito's Lemma, and The Black-Scholes-Merton Model helped me start to understand the basic concepts within a broader context. After that, Shreve's two books seems to be pretty popular (see here and here). He explains things pretty thoroughly in my opinion and his writing is pretty clear, which I like. For someone starting out wanting to learn on their own, though, I've heard his books can be a bit tough to wade through. If you find that to be the case, check out Mikosch's Elementary Stochastic Calculus With Finance in View. Another one that might be helpful is Basic Stochastic Processes by Brzezniak and Zastawniak. It reviews basic probability and other fundamentals, and has solved exercises, which could be really nice for someone starting off and learning on their own. And then another one I've seen mentioned is Mathematical Methods for Financial Markets. I haven't read it personally, but judging from the Table of Contents it seems to cover a good breadth of advanced topics if that's more of interest to you. Which one you go with kind of depends on your experience, what math/stats you've taken, your personal preferences for style and writing/math balance so to speak. But hopefully this gives you enough to get your started :) (Oh, and I also came across this page from an NYU class on partial differential equations for finance. It has PDF lecture notes that might be helpful, depending on what you're looking for. Specifically, the Lecture 1 notes start off with a discussion of the "Links between stochastic differential equations and PDE.")
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