Valuation by simulation of contingent claims with multiple early exercise opportunities

This paper introduces the application of Monte Carlo simulation technology to the valuation of securities that contain many ( buying or selling) rights, but for which a limited number can be exercised per period, and penalties if a minimum quantity is not exercised before maturity. These securities combine the characteristics of American options, with the additional constraint that only a few rights can be exercised per period and therefore their price depends also on the number of living rights (i.e., American-Asian-style payoffs), and forward securities. These securities give flexibility-of-delivery options and are common in energy markets (e. g., take-or-pay or swing options) and as real options ( e. g., the development of a mine). First, we derive a series of properties for the price and the optimal exercise frontier of these securities. Second, we price them by simulation, extending the Ibanez and Zapatero (2004) method to this problem.