# Regression techniques for bermudan Monte-Carlo

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 ?