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I recently stumbled upon a paper titled "Markov Chain Monte Carlo Analysis of Option Pricing Models" thanks to another post on this site (see: link).

I have the ultimate goal of implementing a MCMC algorithm for pricing FX options and in the process of doing so would like to write a brief and "simple" paper/set of notes on how to do so (which also covers the preliminary mathematics). The aforementioned paper has been incredibly insightful yet it doesn't cover much on the implementation side of the matter.

I found that this chapter of a book is perfect for all the preliminary mathematics: MCMC Handbook: Chapter 1

So I have two questions:

  1. Can anyone point me in the direction of relevant literature about MCMC in the context of FX options or something a bit more general regarding MCMC w.r.t. options? And,

  2. If such literature about MCMC for FX options doesn't exist, do you think such a paper would be of any value other than that of a learning exercise for myself?

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  • $\begingroup$ Are FX options really so different from other options (equity, etc.) that they deserve separate treatment of their model estimation with MCMC? I don't know. $\endgroup$ – noob2 Nov 20 '17 at 19:29
  • $\begingroup$ If you hold that position, you'd probably consider the Garman-Kohlhagen model a trivial extension of Black-Scholes, no? My thinking is that if they extended the model for FX options, it would be interesting to use MCMC method(s) on that model instead. Additionally, I've yet to see a paper that goes from explaining Markov Chains/Monte Carlo theory all the way to an implementation of a MCMC algorithm (e.g., Metropolis-Hastings) with detailed analysis of results all in a somewhat "easy" way suitable for practitioners. So maybe it is worthwhile? $\endgroup$ – Vladimir Nabokov Nov 21 '17 at 8:13
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This online course might be helpful for implementation and basic theory (although it does not touch FX options): https://iversity.org/en/courses/monte-carlo-methods-in-finance

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  • $\begingroup$ Thank you. But this also doesn't (to the best of my knowledge after skimming through the course outline) cover any MCMC methods either. $\endgroup$ – Vladimir Nabokov Nov 21 '17 at 10:48

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