Learning Path-Dependent Option PDEs Through Finite-Difference Pricing

Summary

The document discusses how to deepen study of path-dependent options in a partial differential equation framework. It recommends using Wilmott’s quantitative finance text as an accessible foundation, while adding practical finite-difference methods and implementation exercises.

For finite-difference practice, it points to Hull’s treatment and suggests implementing an American option pricer with explicit and implicit schemes. It also cites Wilmott’s paper on cliquet options, which addresses PDEs, a stochastic volatility model, and code. The practical advice is to work through implementations so the PDE material becomes clearer. The answer is a short set of learning recommendations rather than a derivation or systematic survey, and it does not provide validation results or detailed guidance for every path-dependent product.

Key ideas

• Wilmott’s quantitative finance book is presented as an accessible starting point for path-dependent option PDEs.
• Finite-difference implementation can connect PDE concepts to practical pricing considerations.
• Building explicit and implicit finite-difference pricers for American options is suggested as a learning exercise.
• A paper on cliquet options is offered as a focused example involving PDEs and stochastic volatility.

Tags

# Reference for path dependent options


# Reference for path dependent options












I want to study path dependent options for which I am following the book Paul Wilmott on Quantitative finance.But here I dont find the detailed explanations or derivations for the various PDEs .So is there any other reference which has these in details

## Answer by James Spencer-Lavan (score 4, accepted)

https://quant.stackexchange.com/a/67920

Is not total clear to me what you are looking for - but I would say Wilmott's book is probably the most accessible reference for various forms of path-dependent options in PDE setting, so you're already in the right place IMHO.

However I would add to this two other texts:

- Hull's futures, options and other derivatives. The chapters on FDM are clear and practical on implementation considerations. Implement an American option pricer in FDM (explicit and implicit). You'll learn a lot in "the doing"

- Wilmott himself wrote a paper on cliquet options in PDE, including UVM modeling and code in VBA. This appeared in a Risk paper "Cliquet Options and Volatility Models"

Personally I would go through these exercises, implement them yourself. Wilmott's book will then make a ton of sense thereafter.

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