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

Autor:	Vaillant, John-Fritz Thony, Jean
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	stochastic differential equation fractional Black–Scholes jump process maximum likelihood estimation
Zdroj:	Mathematics; Volume 10; Issue 22; Pages: 4190
ISSN:	2227-7390
DOI:	10.3390/math10224190
Popis:	We consider a stochastic differential equation (SDE) governed by a fractional Brownian motion (BtH) and a Poisson process (Nt) associated with a stochastic process (At) such that: dXt=μXtdt+σXtdBtH+AtXt−dNt,X0=x0>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.
Databáze:	OpenAIRE
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