Arbitrage Theory In Continuous Time

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1. adamentAug 2022
   If you come from a pure math theory first background I would advise starting out with Björks “Arbitrage theory in continuous time”, I personally found the lack of rigor and superfluous examples in Hull frustrating and found Björk much more approachable then you can look into Hull for real life practicalities like daycount conventions, etc. If you want to go into complex derivatives pricing I would advise looking at the Andersen and Piterbarg trilogy.
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2. pvitzJan 2021
   Someone with a strong math background should cut Wilmott and go directly to Shreve: Stochastic Calculus for Finance II (or Björk: Arbitrage Theory in Continuous Time).
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3. GrustafDec 2020
   If you need to understand derivatives then start with Hull: Options, Futures and Other Derivatives. Then read Björk: Arbitrage Theory in Continuous Time. Both excellent books in their own ways.

   But it depends completely on what kind of finance you’ll be doing!

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4. veyronOct 2011
   You need to be a little more specific regarding your interests and background. If you are interested in theory, there are plenty of books discussing specific models. However, most practical or buzzword (e.g. HFT) books are rubbish (think about it: if you have a profitable operation, why would you write a book? Unless, like me, you have a screw loose :P )

   If you want some practical discussions, "Trading and Exchanges" by Larry Harris is a bit dated, but nothing comes close. Most of the descriptions are still valid today (even if some of the mechanics have changed)

   If you want something more along the lines of what a financial engineer would know:

   - "Options, Futures, and other Derivatives" by John Hull (goes over basic models without delving too deeply into theoretical math aspects)

   - "Stochastic Calculus for Finance II" by Steve Shreve (goes over the basic stuff but has enough stats to keep a grad student happy)

   - "Monte Carlo Methods in Financial Engineering" by Paul Glasserman (much more practical, and goes over subtleties of monte carlo simulation and other stuff like low discrepancy sampling)

   - "Modelling Fixed Income Securities and Interest Rate Options" by Robert Jarrow (walks through how to perform certain simulations, covers lots of little details most theoretical books skip)

   If you want something more theoretical:

   - "Introduction to Stochastic Calculus Applied to Finance" by Lamberton and Lapeyre (Nice little intro)

   - "Arbitrage Theory in Continuous Time" by Tomas Bjork (Slower discussion, larger breadth)

   - "Brownian Motion and Stochastic Calculus" and "Methods of Mathematical Finance" by Karatzas and Shreve (Solid theoretical foundation, for the more mathematically inclined)

   There was a good non-measure theoretic discussion of financial models but the name escapes me ATM.

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5. iterationxJun 2010
   Arbitrage Theory in Continuous Time (Oxford Finance Series) http://www.amazon.com/gp/product/0199271267/ref=oss_product
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6. potiuperJan 2021
   > Björk: Arbitrage Theory in Continuous Time

   is standard graduate stochastic calculus course material. An undergrad degree in math usually specializes in a certain track: algebra or analysis. The analysis background would be a closer fit as the material is focused on the continuous applications (not HFT) and likely have covered the introductory measure and probability theory material. The finance portion focuses on the arbitrage-risk neutral model that is at least a semester worth a material.

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