Choosing Numerical PDE References for Financial Engineering

Summary

The document asks for a rigorous, practical reference on numerical partial differential equation methods used in finance, comparable in scope to a foundational Monte Carlo text. Topics sought include convergence and stability analysis, alternating direction implicit methods, and upwinding schemes. The author is especially interested in applying these methods to local stochastic volatility models and pricing barrier, one-touch, double-no-touch, American, and forward-starting options.

The sole recommendation in the response is Daniel Duffy’s book on finite difference methods in financial engineering, which the respondent says was useful. The post does not compare the book’s coverage with the requested topics, provide details about its mathematical treatment or code, or recommend online courses. It therefore points readers toward a resource but does not establish whether that resource covers every desired model and exotic product.

Key ideas

• Numerical PDE methods in finance can be studied through finite difference methods.
• A useful reference should explain convergence and stability as well as practical schemes such as ADI and upwinding.
• The author seeks methods applicable to local stochastic volatility models and exotic options.
• The response recommends Daniel Duffy’s finite difference text but gives no detailed assessment of its coverage.

Tags

# Canonical text on numerical PDEs in finance


# Canonical text on numerical PDEs in finance












I am looking for a text similar to Glasserman's Monte Carlo Methods in Financial Engineering, but with a focus on numerical methods for PDEs. Glasserman's book seems to cover a lot for what is required from a financial engineer in terms of Monte Carlo methods, in other words, the foundations, the topics that are absolutely necessary to be known. One can then always explore in more detail some of the topics by reading papers on more recent methods.

It would be interesting to have a numerical PDE text that discusses things rigorously, for example proving orders of convergence, stability etc., while covering things such as ADI and upwinding scheme.

I would be especially interested in schemes for more complex modes, such as LSVs. Also useful would be a treatment of barrier options, one touch, double-no-touch, Americans, forward starting and possibly some other exotics. Finally, it would be nice to have some code to try out (any language).

Perhaps there is not a single text covering all of the above. Maybe there are good courses available online on this topic?

Any suggestion would be greatly appreciated.

## Answer by river_rat (score 3)

https://quant.stackexchange.com/a/54638

I got a lot of mileage out of Daniel Duffy's Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach.

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