Fast Greeks by simulation: The block adjoint method with memory reduction

Abstract

The pathwise method is one of the approaches to calculate the option price sensitivities by Monte Carlo simulation. Under the general diffusion process, we usually use the Euler scheme to simulate the path of the underlying asset, which requires small time spaces to assure the convergence. The adjoint method can be used to accelerate the calculation of the Greeks in such case. However, it needs to store the intermediate information along the path. In this paper, we propose to use the block simulation to further accelerate the calculation. Block simulation can be seen as an extension of the common Monte Carlo simulation. It is simple to implement, without any extra work and loss in accuracy. It also has the flexibility on the block division, fitting to the computation environment. Moreover, we use the extended forward-path method along with the real time calculation strategy to do the memory reduction so that it can be combined with the adjoint method better. The numerical tests show our method can accelerate the adjoint method by several times. Our method is relatively even more efficient in the high-dimensional case.