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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

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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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