A stochastic algorithm for the valuation of financial derivatives using the hyperbolic distributional variates

摘要

It is a well-known fact that the difference between the continuous compounding rate of returns of financial derivatives X_t and it geometric rate of returns Y_t is negligible if X_t is typically of O(〖10〗^(-2)). The aim of this paper is to find the value of this difference when X_t is not negligible. We first establish that X_t and hence Y_t are distributed according to the Generalized hyperbolic distribution (GHd) to accommodate linear transformation property. We then apply a stochastic algorithm to trace the non-zero value of X_t and hence the value of Y_t and their difference. An illustrative example is given in concrete setting.