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RFR's will be compounded in-arrears, if I have an option on this rate am I forced to use Monte Carlo or are there techniques in the literature that will price path-dependent trades with a backwards pricing method (PDE/lattice etc)?

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    $\begingroup$ It depends on what payoff you are thinking. For many of them, transition from IBORs to RFRs poses no analytical challenge. What product did you had in mind? $\endgroup$ Nov 4 '20 at 16:56
  • $\begingroup$ Let’s assume I want to price a caplet type cashflow in Hull-White model in a backwards numerical method, this is an example that doesn’t carry over from IBOR to RFR due to asianisation of the payoff. $\endgroup$ Nov 4 '20 at 20:50
  • $\begingroup$ Just to clarify I’m not after closed form solutions. $\endgroup$ Nov 5 '20 at 7:35
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Yes you can price Asian-style options in PDEs, by introducing an extra state variable which is the accumulated Asian variable (in your case the RFR rate). It is well covered in literature, a quick Google search on "pricing Asian options in PDE" should bring plenty of results. For example this, equation (3) shows the PDE to solve. Notwithstanding your comment, for caplets on RFR rates in the Hull-White model there are closed-form solutions.

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    $\begingroup$ Welcome to Quantitative Finance Stack Exchange Mr. Piterbarg. $\endgroup$ Nov 6 '20 at 12:47
  • $\begingroup$ What Daneel Olivaw said. $\endgroup$ Nov 6 '20 at 13:14
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    $\begingroup$ Pleasure to be here! $\endgroup$
    – piterbarg
    Nov 6 '20 at 13:34
  • $\begingroup$ Thank you and welcome. Since posting the question I happened to find the same answer in your book :) $\endgroup$ Nov 6 '20 at 15:25
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    $\begingroup$ :-) I did not want to say "read my book" in the answer! $\endgroup$
    – piterbarg
    Nov 6 '20 at 15:28

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