  Fast pricing of American-style options has been a difficult problem since it
was first introduced to financial markets in 1970s, especially when the
underlying stocks' prices follow some jump-diffusion processes. In this paper,
we propose a new algorithm to generate tight upper bounds on the Bermudan
option price without nested simulation, under the jump-diffusion setting. By
exploiting the martingale representation theorem for jump processes on the dual
martingale, we are able to explore the unique structure of the optimal dual
martingale and construct an approximation that preserves the martingale
property. The resulting upper bound estimator avoids the nested Monte Carlo
simulation suffered by the original primal-dual algorithm, therefore
significantly improves the computational efficiency. Theoretical analysis is
provided to guarantee the quality of the martingale approximation. Numerical
experiments are conducted to verify the efficiency of our proposed algorithm.
