2005/03/12 by Frederik Herzberg, Herzberg, Frederik S.
Economics, Econometrics and Finance · Social Sciences · #65D32 #91B28 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.math/0503235
openalex publication_date 2005/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The subject of this study is an iterative Bermudan option pricing algorithm based on (high-dimensional) cubature. We show that the sequence of Bermudan prices (as functions of the underlying assets' logarithmic start prices) resulting from the iteration is bounded and increases monotonely to the approximate perpetual Bermudan option price; the convergence is linear in the supremum norm with the discount factor being the convergence factor. Furthermore, we prove a characterisation of this approximated perpetual Bermudan price as the smallest fixed point of the iteration procedure.