Valuation by Simulation of Contingent Claims with Multiple Early Exercise Opportunities

26 Pages Posted: 6 May 2004


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.

Keywords: American options, simulation methods, swing options, take-or-pay options, commodities, energy securities

Suggested Citation

Ibañez, Alfredo, Valuation by Simulation of Contingent Claims with Multiple Early Exercise Opportunities. Mathematical Finance, Vol. 14, No. 2, pp. 223-248, April 2004. Available at SSRN:

Alfredo Ibañez (Contact Author)

Comillas Pontifical University ( email )

Alberto Aguilera 21
Madrid, Madrid 28015

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