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Is there an "analytical" method to price American options (approximated as daily Bermudans) in the Black-Scholes model using backward induction?

$$V_T(S) = \max(K-S, 0)$$ $$V_{T-\Delta t}(S) = \max(K-S, \operatorname{BS}(S, K, \Delta t, \sigma,r, q))$$

Then you could find the exercise boundary point (probably numerically) and knowing that, analyically integrate the piecewise function back another step to time $T-2\Delta t$...

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    $\begingroup$ Perhaps Lord et al.'s (2008) CONV method or Fang and Oosterlee's (2009) COS method? Both methods rely on backward induction and apply to a wide class of models. You can then use Richardson extrapolation to get American option prices from the prices of Bermudan options. $\endgroup$
    – Kevin
    Commented Sep 27, 2021 at 13:54

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