IJPAM: Volume 35, No. 2 (2007)

APPROXIMATE BERMUDAN OPTION PRICING BASED
ON THE RÉDUITE OR CUBATURE: SOUNDNESS
AND CHARACTERISATION OF PERPETUAL
PRICES AS FIXED POINTS

Frederik Herzberg
Department of Probability
Institute for Applied Mathematics
University of Bonn
Wegelerstraße 6, Bonn, D-53115, GERMANY
e-mail: herzberg@wiener.iam.uni-bonn.de


Abstract.In this paper, it is shown that Bermudan option pricing based on either the réduite (in a one-dimensional setting: piecewise harmonic interpolation) or cubature - is sensible from an economic vantage point: Any sequence of thus-computed prices for Bermudan options with increasing sets of exercise times is increasing. Furthermore, under certain regularity assumptions on the payoff function and provided the exercise times are equidistant of exercise mesh size $h$, it has a supremum which coincides with the least fixed point of the approximate pricing algorithm - this algorithm being perceived as a map that assigns to any real-valued function $f$ (on the basket of underlyings) the approximate value of the European option of maturity $h$ and payoff function $f$.

Received: December 19, 2006

AMS Subject Classification: 91B24, 91B28, 60J45

Key Words and Phrases: Bermudan option, cubature

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 2