What's a good book to learn computational finance topics?

Question

I know continuous finance theory roughly equivalent to what's in Bjork's Arbitrage Theory In Continuous Time (most chapters).

I'd like to supplement that knowledge with a more hands-on practical approach that deals with programming the theory in practice with numerical methods. What's a good book to learn these topics, using R preferably?

I found this university course called Computational Finance (http://kurser.ku.dk/course/nmak16004u) and it has the following listed under "learning outcome":

Rudimentary low-level programming.
Data and computational resources at Copenhagen University and beyond.
Monte Carlo simulation techniques in option pricing: Variance reduction, diffusion (and possibly Levy) process simulation, American options, adjoint techniques.
Numerical transform methods for option pricing.
Numerical optimization and model calibration.
Numerical methods for solving parabolic partial differential equations. 

So, I'm guessing a book that covers those topics would be what I am looking for?

Answer 1

The curriculum for this course (which I teach with David and Rolf) is my Modern Computational Finance book with Wiley: https://medium.com/@antoine_savine/modern-computational-finance-aad-and-parallel-simulations-c8cd42e7ad6e but it is in C++ not in R.

Andersen and Piterbarg's https://www.amazon.com/Interest-Rate-Modeling-Foundations-Vanilla/dp/0984422102 is a quant bible on models and numerical algorithms but its doesn't include any actual programming.

I hope this helps.

Antoine Savine