Expectation of local times and the Dupire formula

K. Hamza; F. C. Klebaner

doi:10.1016/j.spa.2019.07.013

Expectation of local times and the Dupire formula

K. Hamza, F. C. Klebaner

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

In this paper, we give a sufficient condition under which the local martingale that appears in Itô’s formula is a true martingale. As a consequence, we obtain a rigorous proof of the Dupire formula on local volatility.

Original language	English
Pages (from-to)	782-787
Number of pages	6
Journal	Stochastic Processes and their Applications
Volume	150
DOIs	https://doi.org/10.1016/j.spa.2019.07.013
Publication status	Published - Aug 2022

Keywords

Dupire formula
Itô–Tanaka formula
Martingales
Volatility

Access to Document

10.1016/j.spa.2019.07.013

Cite this

@article{77df841b66504f9aadd74197441c3280,

title = "Expectation of local times and the Dupire formula",

abstract = "In this paper, we give a sufficient condition under which the local martingale that appears in It{\^o}{\textquoteright}s formula is a true martingale. As a consequence, we obtain a rigorous proof of the Dupire formula on local volatility.",

keywords = "Dupire formula, It{\^o}–Tanaka formula, Martingales, Volatility",

author = "K. Hamza and Klebaner, {F. C.}",

year = "2022",

month = aug,

doi = "10.1016/j.spa.2019.07.013",

language = "English",

volume = "150",

pages = "782--787",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

}

TY - JOUR

T1 - Expectation of local times and the Dupire formula

AU - Hamza, K.

AU - Klebaner, F. C.

PY - 2022/8

Y1 - 2022/8

N2 - In this paper, we give a sufficient condition under which the local martingale that appears in Itô’s formula is a true martingale. As a consequence, we obtain a rigorous proof of the Dupire formula on local volatility.

AB - In this paper, we give a sufficient condition under which the local martingale that appears in Itô’s formula is a true martingale. As a consequence, we obtain a rigorous proof of the Dupire formula on local volatility.

KW - Dupire formula

KW - Itô–Tanaka formula

KW - Martingales

KW - Volatility

UR - http://www.scopus.com/inward/record.url?scp=85071500798&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2019.07.013

DO - 10.1016/j.spa.2019.07.013

M3 - Article

AN - SCOPUS:85071500798

SN - 0304-4149

VL - 150

SP - 782

EP - 787

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

Expectation of local times and the Dupire formula

Abstract

Keywords

Access to Document

Other files and links

Cite this