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TRUE UPPER BOUNDS FOR BERMUDAN PRODUCTS VIA NON‐NESTED MONTE CARLO
Author(s) -
Belomestny Denis,
Bender Christian,
Schoenmakers John
Publication year - 2009
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2008.00357.x
Subject(s) - martingale (probability theory) , estimator , monte carlo method , mathematics , control variates , upper and lower bounds , mathematical optimization , hybrid monte carlo , mathematical analysis , markov chain monte carlo , statistics
We present a generic non‐nested Monte Carlo procedure for computing true upper bounds for Bermudan products, given an approximation of the Snell envelope. The pleonastic “true” stresses that, by construction, the estimator is biased above the Snell envelope. The key idea is a regression estimator for the Doob martingale part of the approximative Snell envelope, which preserves the martingale property. The so constructed martingale can be employed for computing tight dual upper bounds without nested simulation. In general, this martingale can also be used as a control variate for simulation of conditional expectations. In this context, we develop a variance reduced version of the nested primal‐dual estimator. Numerical experiments indicate the efficiency of the proposed algorithms.