Parameter Estimation for a Fractional Black–Scholes Model with Jumps from Discrete Time Observations

John-Fritz Thony and Jean Vaillant ()
Additional contact information
John-Fritz Thony: Laboratoire de Mathématiques et Informatique et Applications (LAMIA), Université des Antilles, 97157 Pointe-à-Pitre, France
Jean Vaillant: Laboratoire de Mathématiques et Informatique et Applications (LAMIA), Université des Antilles, 97157 Pointe-à-Pitre, France

Mathematics, 2022, vol. 10, issue 22, 1-17

Abstract: We consider a stochastic differential equation (SDE) governed by a fractional Brownian motion ( B t H ) and a Poisson process ( N t ) associated with a stochastic process ( A t ) such that: d X t = μ X t d t + σ X t d B t H + A t X t − d N t , X 0 = x 0 > 0 . The solution of this SDE is analyzed and properties of its trajectories are presented. Estimators of the model parameters are proposed when the observations are carried out in discrete time. Some convergence properties of these estimators are provided according to conditions concerning the value of the Hurst index and the nonequidistance of the observation dates.

Keywords: stochastic differential equation; fractional Black–Scholes; jump process; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/22/4190/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/22/4190/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:22:p:4190-:d:967517

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().