Black-Scholes Equation with Distributed Order in Time
In this work we consider a Black-Scholes model which consists of a generalization of a fractional Black-Scholes equation model proposed previously. A numerical scheme is presented to solve such type of models and some numerical results are presented for European double-knock out barrier options. In this way, we are able to conclude that this generalized model is able to describe other scenarios than the ones described with the classical (integer-order) and the fractional Black-Scholes models.
The authors acknowledge the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through projects UID/Multi/04621/2013 and UID/MAT/00297/2013 (Centro de Matemática e Aplicações), respectively.
- 2.Diethelm, K.: The analysis of fractional differential equations. In: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Springer, Berlin (2004)Google Scholar