Sorry for the confusing notations in my paper. Thank you, Alan, for your suggestion. The link for the Broadie and Kaya paper is broke though. Is the following paper what you are referring to?
Broadie, M., and Kaya, O., (2004), Exact Simulation of Option Greeks under Stochastic Volatility and Jump Diffusion Models, in Proceedings of the 2004 Winter Simulation Conference, eds: R.G. Ingalls, M.D. Rossetti, J.S. Smith, and B.A. Peters, The Society for Computer Simulation
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