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Choosing Resources for Practical Computational Finance and Numerical Methods

Article Quant Q&A · Author: Deli
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Summary

The document seeks practical study materials for someone already familiar with continuous-time finance theory. It lists computational finance topics of interest, including Monte Carlo option pricing and variance reduction, simulation of diffusion or Lévy processes, American options, numerical transforms, model calibration, and partial differential equation methods. The desired approach emphasizes programming numerical methods, with R preferred.

The answer recommends a computational finance book that follows the course curriculum but uses C++, and separately points to a substantial interest-rate modeling reference that covers models and numerical algorithms without hands-on programming. These suggestions distinguish implementation-focused study from theory and algorithm reference material. The text does not compare the books in detail, assess R resources, or provide evidence about their suitability beyond the stated coverage and language, so readers seeking R examples may need supplementary materials.

Key ideas

  • The requested learning path connects continuous-time finance theory to numerical implementation.
  • Monte Carlo pricing, variance reduction, simulation, calibration, transforms, and PDE methods are among the listed topics.
  • One recommendation is programming-oriented but uses C++ rather than the preferred R.
  • A second reference covers interest-rate models and numerical algorithms but omits practical programming.

Tags

OptionsDerivatives pricingMachine learningStatistics
Full text
# What's a good book to learn computational finance topics?


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












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 by Antoine Savine (score 2)

https://quant.stackexchange.com/a/42949

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.