Work

Modelling the Dependence between a Wiener Process and Its Running Maxima and Running Minima Processes

Year: 2024

Type: article

Abstract: We study a triple of stochastic processes: a Wiener process Wt, t≥0, its running maxima process Mt=sup{Ws:s∈[0,t]}, and its running minima process mt=inf{Ws:s∈[0,t]}. We derive the analytical formula for the corresponding copula and show that it is supported on the hemicube, a convex hexahedron with seven vertices. As an application, we draw out an analytical formula for pricing of a double barrier option.

Source: Mathematics

DOI: 10.3390/math12172707

Authors: Karol Da̧browski, Piotr Jaworski

Institution: University of Warsaw

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $2,955

OpenAlex ID: W4402048754

FWCI:

Cites: 16

Cited by:

Related to: 10