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My aim is to be able to read and understand almost all of the book by Brigo and Mercurio including HJM, LMM and the Local Vol models. So that I am able to implement these models on my own. My question is what background do I need to be able to do this?

I have read Rannie and Baxter as an introduction to Stochastic Calculus and am now reading the book by Shreve. Do I need to read anything else after Shreve as a preparation or will it be sufficient? I am happy to read and put in the hours, as long it helps me understand and master Brigo and Mercurio and then more advanced books on this topic as well.

Your guidance is much appreciated.

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    $\begingroup$ Concerning modeling and implementation i really like Glasserman 2004 but again you'll need a strong background in stochastic calculus (SDEs) etc $\endgroup$
    – adelm
    Commented Jan 28, 2014 at 18:36
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    $\begingroup$ Why have two people voted to close this question? Any explanation would be helpful, because I could really use some recommendations and I dont think this question has been asked before. $\endgroup$
    – InnocentR
    Commented Jan 29, 2014 at 10:59
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    $\begingroup$ The reason why such questions could be closed is because it is not useful to a broad audience. Your question is probably useful if you want to read this very book. Even then it is debatable. The standard textbooks on stochastic calculus are usually known. $\endgroup$
    – Richi Wa
    Commented Jan 29, 2014 at 14:55
  • $\begingroup$ Hi! Your original display name appeared to be a bit offensive so I have just edited it. You can change it yourself by clicking on the edit tab on your profile page. $\endgroup$
    – olaker
    Commented Jun 6, 2014 at 9:45

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You can start to understand Brigo and Mercurio from the standard Shreve material but it does not look at things from the perspective of semimartingales which will possibly be confusing at some point. You're probably going to want to understand $d[X,Y]_t$ quadratic variation notion vs just the whole "$(dW(t))^2 = dt$" concept from the Shreve book that I'm assuming OP is referring to. Shreve wrote another excellent book Karatzsas and Shreve, Brownian Motion and Stochastic Calculus with the follow up Methods of Mathematical Finance both of which I can absolutely recommend as being challenging but amazing to learn from, something like "blue rudin" at times.

There is another book which I have never read personally but have heard great things about regarding stochastic calculus with respect to semimartingales Diffusions, Markov Processes, and Martingales: Volume 1, Foundations and Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus

The books mentioned above would certainly make Brigo and Mercurio easier to understand but there is no reason that they can't be used for reference, once you're through Shreve I and II.

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