Not-so-complex logarithms in the Heston model

摘要: In Heston’s stochastic volatility framework [ Hes93], semi-analytical formulae for plain vanilla option prices can be derived. Unfortunately, these require the evaluation of logarithms with complex arguments during involved inverse Fourier integration step. This gives rise to an inherent numerical instability as a consequence which most implementations are not robust moderate long dated maturities or strong mean reversion. this article, we propose new approach solve problem enables use analytics practically all levels parameters and even many decades.