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 ?


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


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.



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