# Valuation of Bermudan option as maximum of relevant European options

Assume I need to price a Bermudan option which can be exercised at following dates: $t_1$, $t_2$, ..., $t_n$. I think that the price of such an option will be maximum of the prices of European options with maturities $t_1$, $t_2$, ..., $t_n$. Am I right or wrong?

You are wrong. Using the maximum of the prices of the European options is equivalent to choosing (and making that choice final) on $t=0$ the date $t_i$ on which you will exercise. As such a choice would be sub-optimal, you would be giving up value. Therefore the Bermuda option is worth more than the maximum of the prices of the European options.
• This can be made a little more precise. For example, let $\mathscr{T}$ be the set of stopping times with values in $\{t_1, \ldots, t_n\}$. Then, the Bermudan option value is given by \begin{align*} \sup_{\tau \in \mathscr{T}}E\big(Discount(\tau)\,Option(\tau)\big) \ge \max_{1\le i \le n} E\big(Discount(t_i)\,Option(t_i)\big), \end{align*} as $t_i$, for $i=1, \ldots, n$, are particular stopping times. – Gordon Dec 20 '17 at 17:54