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Currently, I am working on a Monte Carlo simulation for a path dependent interest rate product that I want to hedge. In my current simulation I am using a simple discretized Vasicek shortrate process.

However, I want to switch to a (one-factor) Hull-White shortrate model. This in itself is not a big problem since I am somewhat familiar with the Hull-White model though in the end I want to be able to also hedge this product using swaptions.

For the pricing of the swaptions, I want to use the SABR model. However, since I want to project these simulations some $t$ into the future I was thinking I would need a combined Hull-White SABR model. Up to now, I have been unable to find any examples of how these two are used in combination in literature.

Does anybody have experience with these kind of combined simulations? All help would be much appreciated! Thanks in advance!

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    $\begingroup$ No, it is not possible. In fact, the dynamic of the interest rate are well determined in Hull White model (and SABR). And the two models are based on two distinct sets of assumptions. $\endgroup$ Commented Apr 16 at 17:14
  • $\begingroup$ Thank you for your reply, could you please elaborate on why not? I found some literature on a Libor market model SABR combination and since both LMM and HW fall under HJM i thought that it would maybe be possible. $\endgroup$ Commented Apr 17 at 11:06
  • $\begingroup$ LMM does not fall under HJM framework, you could read this $\endgroup$ Commented Apr 17 at 18:42
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    $\begingroup$ Hmm, wouldn't bermudan swaptions priced off a HW generated grid with swaption vols from a SABR vol cube be considered combining the two models? $\endgroup$ Commented Apr 20 at 6:09

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