Practical Policy Iteration: Generic Methods for Obtaining Rapid and Tight Bounds for Bermudan Exotic Derivatives Using Monte Carlo Simulation

Monte Carlo Bounds for Game Options Including Convertible Bonds

“…This should allow better fits to the continuation value in the different regions relative to using one global regression, and therefore lead to improved exercise strategies. This extends the double regression enhancement introduced by Beveridge and Joshi (2009), and we will refer to it as the multiple regression enhancement. In addition, it should not be very expensive computationally because the leastsquares regressions are usually very quick to perform; again, see Beveridge and Joshi (2009).…”

The least squares method for option pricing revisited

“…Using (1,2,3), and under the technical assumption that P(e m t (X)α m t = Z t ) = 0, the reasoning from [7] can be easily modified to work within our more general setup. In general, this additional technical requirement can be fulfilled by using approximation of the contract functions f t by functions with probabilistically "negligible" fibers and by introduction of small amount of random noise perturbing the probability distribution of X t .…”

“…denote the (k m × k m )-Gram matrix associated with the columns of the matrix    e m t (X (1) ) . .…”

“…the proper variance reduction technique is a crucial step for any market implementation), without adding much to the conclusions drawn in this paper. We refer to [7,1], and references therein, for detailed analysis about convergence speed in univariate Markovian case. For transparency, we use only the standard models for parameter estimation and Monte Carlo simulation.…”

“…prices of various derivatives, based on the same underlying instruments) as well as various modifications of the standard Monte Carlo algorithm (for more advanced models cf. [1] or [10] and references therein).…”