Valuation of multidimensional Bermudan options

Multi-dimensional option pricing becomes an important topic in financial markets (Franke et al., 2008). Among which, the American-type derivative (e.g. the Bermudan option) pricing is a challenging problem. Unlike the European options which can only be exercised on the expiration date, the owner of a Bermudan option has the right to exercise early on a contractually specified finite set of dates. The dynamic programming approach is a practical and popular approach used to price the Bermudan option (Shreve, 2004, p. 91). In that approach, the option value on each possible early exercise date is set to be the maximum of the payoff associated with immediate exercise, called the intrinsic value, and the discounted conditional expectation of the future option value, called the continuation value. The major problem of the approach lies in the computation of the continuation value.