The Optimal Method for Pricing Bermudan Options by Simulation

Mathematical Finance, Forthcoming

50 Pages Posted: 18 Nov 2009 Last revised: 22 Apr 2017

See all articles by Alfredo Ibañez

Alfredo Ibañez

Comillas Pontifical University

Carlos Velasco

Universidad Carlos III de Madrid - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: April 16, 2017

Abstract

Least-squares methods enable us to price Bermudan-style options by Monte Carlo simulation. They are based on estimating the option continuation value by least squares. We show that the Bermudan price is maximized when this continuation value is estimated near the exercise boundary, which is equivalent to implicitly estimating the optimal exercise boundary by using the value-matching condition. Localization is the key difference with respect to global regression methods, but is fundamental for optimal exercise decisions, and requires estimation of the continuation value by iterating local least-squares (because we estimate and localize the exercise boundary at the same time). In the numerical example, in agreement with this optimality, the new prices or lower bounds (i) improve upon the prices reported by other methods and (ii) are very close to the associated dual upper bounds. We also study the method's convergence.

Keywords: American and Bermudan options, optimal stopping times, Monte Carlo simulation, least-squares, local polynomial estimates, series estimates

JEL Classification: G11, G12, G13, C14, C15

Suggested Citation

Ibañez, Alfredo and Velasco, Carlos, The Optimal Method for Pricing Bermudan Options by Simulation (April 16, 2017). Mathematical Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1507994 or http://dx.doi.org/10.2139/ssrn.1507994

Alfredo Ibañez

Comillas Pontifical University ( email )

Alberto Aguilera 21
Madrid, Madrid 28015
Spain

Carlos Velasco (Contact Author)

Universidad Carlos III de Madrid - Department of Economics ( email )

Calle Madrid 126
Getafe, 28903
Spain
+34-91 6249646 (Phone)
+34-91 6249875 (Fax)

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