American Options vs. European Options vs. Bermudan Options

The general principle of put-call parity for options is applicable to all options with adjustments for differences in the domestic risk-free rate; (i.e. government bond yield - inflation rate). Nonetheless, the method of execution varies vastly among various domains, such as Bermuda, the United States, and Europe where options must be executed at specific dates prior to expiration, at any time between acquisition/writing and expiry, or on the exact date of expiration respectively. Thus, an alternate options pricing model distinct from Black-Scholes and Put-Call Parity was derived exclusively for the valuation Bermudan  options. This model relies upon a method known as the Monte Carlo simulation which accounts for the randomity of the intervals between preset dates of execution and potential variance in price at these dates of expiration as a probabilistic model.