Black-Scholes model under subordination

Details Black-Scholes model under subordination Black-Scholes model under subordination

2011-11-14

arxiv.org/abs/1111.3263v1

Physica A 318, 469(2003)

Economy

Quantitative Finance

Pricing of Securities

8 pages

Scientific paper

10.1016/S0378-4371(02)01372-9

In this paper we consider a new mathematical extension of the Black-Scholes model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the directing process is inverse to the totally skewed, strictly \alpha-stable process. The subordinated process represents the Brownian motion indexed by an independent, continuous and increasing process. This allows us to introduce the long-term memory effects in the classical Black-Scholes model.

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