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One knows that the price of a bermudan claim exercisable at times $T_1, T_2,\ldots, T_N$ is $$V_0 = \sup_{\tau\in\Gamma} \mathbf{E} \left[ e^{\int_0^{\tau} r_s ds} \varphi_{\tau}\left( x_{\tau} \right) \right]$$ where

  • $x$ is the $d$-dimensional underlying
  • $\varphi_t(x_t)$ is the payoff value if exercised at $t$
  • $\Gamma$ is the set of all stopping times with values in $\{T_1, T_2,\ldots, T_N\}$, also called exercise strategies, $\Gamma$ being also called the exercise boundary.

In both methods that I know of (Andersen and Longstaff & Schwartz), an exercise boundary is computed and then the computed exercise boundary is used for forward pricing using classical Monte-Carlo, as once the bounday is known, it can be used to price the option like a trigger option.

Both methods are regressions somehow. Are there other regression methods than these two ?

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There is a method called stochastic mesh that has been proposed in the literature but it is not much used in practice

https://www0.gsb.columbia.edu/faculty/pglasserman/Other/bgh.pdf

There are numerical methods to make it faster (fast gauss transform for instance), but in the end not a lot of advantage compared to using good old LS in my experience.

Cheers

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