Black–Scholes model under subordination

A.A. Stanislavsky

Physica A: Statistical Mechanics and its Applications, 2003, vol. 318, issue 3, 469-474

Abstract: In this paper, we consider a new mathematical extension of the Black–Scholes (BS) 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 α-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 BS model.

Keywords: Continuous-time random walk; Brownian motion; Lévy process; Subordination; Fractional calculus; Econophysics (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:318:y:2003:i:3:p:469-474

DOI: 10.1016/S0378-4371(02)01372-9

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