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What book should I start with in order to learn about the mathematics behind financial (derivatives I think!) trading that would be used in HF's & IB's (Not sure whether there would be a difference).

I have a strong background in mathematics particularly with regard to measure theory, probability theory and stochastic calculus having studied Rana, Kai-Lee Chung & Oksendals famous texts on these subjects. I also have a strong knowledge of partial differential equations. (Not sure what other areas of mathematics would be useful?)

I am looking for the most concise and quickest way to teach myself about the core mathematics and ideas behind quantative finance.

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  • $\begingroup$ ...or lecture notes $\endgroup$ – Permian Aug 5 '14 at 18:13
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I would consider:

  1. Wilmott, P., Paul Wilmott on Quantitative Finance 3 Volume Set
  2. Hull, J. C., Options, Futures and Other Derivatives
  3. Baxter, M. & Rennie, A., Financial Calculus: An Introduction to Derivative Pricing
  4. McNeil, A. et al, Quantitative Risk Management: Concepts, Techniques and Tools
  5. Brigo, D. & Mercurio, F., Interest Rate Models - Theory and Practice

for $\mathbb{Q}$-type introductory reading. On the $\mathbb{P}$-side, it depends what you're looking for - volatility trading, interest rates, $\Delta1$, cash products, risk management, market models, numerical techniques, data-driven techniques etc.

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  • $\begingroup$ What about equity derivatives? Interest rate products? $\endgroup$ – Permian Aug 5 '14 at 18:36
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    $\begingroup$ For interest rates... Rebonato has two books - Modern Pricing of Interest-Rate Derivatives and Interest-Rate Option Models. I would also look at Pelsser's Efficient Methods for Valuing Interest Rate and James & Webber's Interest Rate Modelling. $\endgroup$ – madilyn Aug 5 '14 at 18:50
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    $\begingroup$ Equity options are probably the most thoroughly-covered among financial engineering texts so I think the 4 books I've recommended cover most of the introductory reading that you need. In addition to that, perhaps you could take a look at Rebonato's Volatility and Correlation, and Sinclair's two books. $\endgroup$ – madilyn Aug 5 '14 at 18:53
  • $\begingroup$ how about credit trading? $\endgroup$ – athos Aug 6 '14 at 7:24
  • $\begingroup$ Im really not sure what I would like most, so may be interested. $\endgroup$ – Permian Aug 6 '14 at 10:42
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Introductory: "Introduction to the Mathematics of Financial Derivatives"; Salih Neftci

More mathematical: "Stochastic Calculus for Finance I and II"; Steven Shreve

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  • $\begingroup$ Is stochastic calculus for finance I really worth reading? Looks pretty discrete $\endgroup$ – Permian Aug 7 '14 at 14:22
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    $\begingroup$ Stoch Calc I can be useful. Some interesting foundational material. Yes its largely discrete. But it could be skipped if you are already familiar with Oksendal et al. $\endgroup$ – jupiter Aug 8 '14 at 4:38
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I would suggest to start with one of the coursera course, Mathematical Methods for Quantitative Finance. It's an introductory course on mathematical concepts that can be applied in finance.

Books: 1) A Primer for Mathematics of Financial Engineering. 2) Paul Wilmott on Quantitative Finance.

Also, check out this article on Quantnet: Master Reading list for Financial Engineering Students

I hope this helps you.

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