Proxy simulation schemes for generic robust Monte Carlo sensitivities, process-oriented importance sampling and high-accuracy drift approximation

Partial Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks

“…The proxy simulation scheme proposed in [5] corresponds to K 1 = K 0 . Thus, it is a special case of (3), (5) if Π is the identity and if…”

“…We propose an improvement and extension to the proxy simulation scheme method proposed in [5]. Proxy simulation schemes are a method of simplifying the development of prices and sensitivities in Monte Carlo simulations by allowing perturbations of inputted data to be shifted from the evolution to a likelihood ratio weight.…”

“…Again, note that for a full proxy simulation scheme (K 0 ), as originally proposed in [5], the first property may fail.…”

“…Yet it is generic and not restricted to TARNs. The method works seamlessly for low-factor LIBOR market models, a situation where the (full) proxy scheme method proposed in [5] has only a limited scope of application or fails.…”

“…We start in Section 2 with a short review of the full proxy simulation scheme as proposed in [5]. In Section 3 we will define the k-dimensional partial proxy scheme, point out the differences to the full proxy scheme and derive an analytic formula for its Monte-Carlo weight when the scheme is an Euler scheme.…”