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I am currently a student of a "normal" Finance program and would like to know some more things about quantitative finance in general and especially risk management.

When we derived formulas, such as the Black-Scholes formula, we didn't do it properly. For example, our professor simply gave us the result of Ito's formula, without explaining the background. You could say we applied things without even knowing the exact background. However, I would be very interested in those things, as they appear everywhere.

Does anyone have some book recommendations about those things? I don't need to completely understand every smallest piece of it, it would just be for my interest. I know it is difficult to find a book that perfectly suits my educational level. The book shouldn't be completely about one specific topic, but should still go into detail that I get an idea about it.

Examples for things we "learned", but never really learned:

  • Stochastic calculus, Ito's formula/integrals

  • How to get from the physical measure to the risk neutral measure, Girsanov's theorem

  • Non-standard option pricing: For example Jump diffusion model, Poisson processes

  • More advanced risk management

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  • $\begingroup$ Could anyone recommend books like "Quantitative risk management", "The Concepts and Practice of Mathematical Finance", "An Introduction to Quantitative Finance" $\endgroup$ – elemenope May 3 at 21:22
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    $\begingroup$ The most common ones are 1) Stochastic Calculus for Finance II: Continuous-Time Models by Steven Shreve, and 2) Paul Wilmott introduces quantitative finance. So if you could have a look at the sample pages to see where they fail!, and can then recommend more books accordingly! $\endgroup$ – Magic is in the chain May 3 at 21:30
  • $\begingroup$ Thanks for your help! Stochastic Calculus for Finance II seems to include all the topics I am interested in, thanks a lot for this recommendation! Is it necessary to have read the first book "Stochastic Calculus for Finance I: The Binomial Asset Pricing Model" as well, in order to understand the concepts in Stochastic Calculus for Finance II? $\endgroup$ – elemenope May 4 at 14:30
  • $\begingroup$ Thanks! No part I is not necessary, probably best to start directly in continuous time, and then read I for intuition afterward. Normally I is taught before II, but this approach might make it harder as the link between discrete and continuous is not as obvious, so could double the learning time! $\endgroup$ – Magic is in the chain May 4 at 18:33
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First, a word of caution

One of the problem with mathematical finance, as well as the related field of financial economics is that there is more than enough to learn to fill your schedule several times over just with this academic side hustle. So, whether you like it or not, there is an issue of choice which is forced on you: you can't do everything all the way down to their most fundamental expression.

So, what should you do? You should only allow yourself to dig deeper into a subject if you know what you'll do with it. Otherwise, you will be wasting time. It's something I have learned studying in graduate school. We're there because we are curious by nature. If you just start reading about stochastic calculus because it feels "cool," you will stop dead in the middle of your track. The enthusiasm you feel has something to do with exploring the unknown and this will ultimately be the victim of either one or even both of the following two things: (1) other new things might also be interesting and (2) sooner or later, you will hit a wall and you need to persevere to get to the other side.

However, if you have a clear objective in mind, even seemingly boring things can become very engaging. And this tends to survive when you inevitably hit your nose against the wall.

References

I have perused a bit through the famous "Paul Wilmott on Quantitative Finance." I didn't use it personally, but you can find it in PDF format online and, thus far, it seems to be very well written. On the plus side, he gives you related papers at the end of each chapter so if you are interested in a subject, you can read only the relevant chapters and then use his readering list to deepen your knowledge.

Another book I used a bit is "Derivative Analystics with Python" by Yves Hilpsich. It covers a lot of ground and what is really cool about it is that it comes with plenty of examples of python codes, so you can play around with the code yourself to see how these things work. The code really isn't optimal, but it's a nice to see the guts of all that math being written as an algorithm you pass to a computer. Personally, I have always appreciated being able to work through models from start to finish.

On stochastic calculus, it appears that the standard really is Shreeve's second book: "Stochastic Calculus for Finance II: Continuous-Time Models. I didn't read much of it, but it's apparently pretty good. Personally, I didn't have much use for stochastic calculus outside of being able to read some papers in financial economics or finance.

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  • $\begingroup$ Thanks a lot, those points you mentioned sound like good advices. I think I will start with Stochastic Calculus for Finance II, as also "Magic is in the chain" recommended it. But thanks for the other references, "Derivative Analystics with Python" sounds very interesting and useful as well! $\endgroup$ – elemenope May 6 at 10:24
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I am going to deviate from the "Shreve camp" :) If, like me, you like books that are less than 300 pages long, then for an introduction to quantitative finance concepts, I recommend the following two books:

  1. Baxter & Rennie, "Financial Calculus", Cambridge University Press
  2. Bjork, "Arbitrage Theory in Continuous Time", Oxford University Press, First Edition

These are two of the most concise and lucid books I've read on the basics of derivatives pricing and that manage to do it using as few trees as possible. Especially Bjork's book (first edition) is beautifully written, a gem, and unlike Baxter & Rennie also discusses the PDE approach.

Digression:

Note that I specifically wrote "First Edition" for Bjork's book - I actually started with the second edition but ordered the first edition to keep under my pillow because it is just so concise and finely written. Unfortunately, like many other authors, Bjork felt compelled to keep expanding and adding chapters in subsequent editions. I personally feel that that has been detrimental. Hull is another example, he adds about 100 pages with every new edition.

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    $\begingroup$ Agree, for a soft introduction to quant finance, Baxter & Rennie is top-notch. These guys were actually quants at banks so they do a good balance between math and intuition, which is particularly useful if it’s your first take at the subject. Then I would go for Shreve’s $-$ Bjork has an astounding number of typos, at least the editions I’ve read. $\endgroup$ – Daneel Olivaw May 31 at 14:30
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    $\begingroup$ Agreed. There are books you use to learn and there are books you use as a reference. Baxter & Rennie is the former and Shreve is the latter. $\endgroup$ – LazyCat May 31 at 15:46

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