Raul Tempone, Georgios E. Zouraris, Thomas Björk, Anders Szepessy
We present two Monte Carlo Euler methods for a weak approximation problem of the HJM term structure model, which is based on Ito stochastic differential equations in infinite dimensional spaces, and prove error estimates useful for the approximation of contingent claims' prices.
These error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling.
Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is mild compared to the work to approximate contingent claims' prices with the Monte Carlo Euler method.
Numerical examples with known exact solution are included in order to show the behavior of the error estimates.