A Remark on the Heat Equation with a Point Perturbation, the Feynman-Kac Formula with Local Time and Derivative Pricing

Sergio Albeverio; Silvestro Fassari; Fabio Rinaldi

doi:10.1016/S0034-4877(15)30006-9

A Remark on the Heat Equation with a Point Perturbation, the Feynman-Kac Formula with Local Time and Derivative Pricing

Sergio Albeverio, Silvestro Fassari, Fabio Rinaldi

King Fahd University of Petroleum & Minerals

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

1 Scopus citations

Abstract

We discuss the probabilistic representation of the solutions of the heat equation perturbed by a repulsive point interaction in terms of a perturbation of Brownian motion, via a Feynman-Kac formula involving a local time functional. An application to option pricing is given, interpolating between the extreme cases of classical Black-Scholes options and knockouts having the barrier situated exactly at the exercise price.

Original language	English
Pages (from-to)	257-265
Number of pages	9
Journal	Reports on Mathematical Physics
Volume	75
Issue number	2
DOIs	https://doi.org/10.1016/S0034-4877(15)30006-9
State	Published - 1 Apr 2015

Bibliographical note

Publisher Copyright:
© 2015 Polish Scientific Publishers.

Keywords

Black-Scholes equation
Brownian motion
Feynman-Kac formula
Heat equation
Heat kernel
Local time
Option pricing
Point interactions

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1016/S0034-4877(15)30006-9

Cite this

@article{41c93c21f26d438385b0a3bb903f9347,

title = "A Remark on the Heat Equation with a Point Perturbation, the Feynman-Kac Formula with Local Time and Derivative Pricing",

abstract = "We discuss the probabilistic representation of the solutions of the heat equation perturbed by a repulsive point interaction in terms of a perturbation of Brownian motion, via a Feynman-Kac formula involving a local time functional. An application to option pricing is given, interpolating between the extreme cases of classical Black-Scholes options and knockouts having the barrier situated exactly at the exercise price.",

keywords = "Black-Scholes equation, Brownian motion, Feynman-Kac formula, Heat equation, Heat kernel, Local time, Option pricing, Point interactions",

author = "Sergio Albeverio and Silvestro Fassari and Fabio Rinaldi",

note = "Publisher Copyright: {\textcopyright} 2015 Polish Scientific Publishers.",

year = "2015",

month = apr,

day = "1",

doi = "10.1016/S0034-4877(15)30006-9",

language = "English",

volume = "75",

pages = "257--265",

journal = "Reports on Mathematical Physics",

issn = "0034-4877",

publisher = "Elsevier Ltd.",

number = "2",

}

TY - JOUR

T1 - A Remark on the Heat Equation with a Point Perturbation, the Feynman-Kac Formula with Local Time and Derivative Pricing

AU - Albeverio, Sergio

AU - Fassari, Silvestro

AU - Rinaldi, Fabio

PY - 2015/4/1

Y1 - 2015/4/1

N2 - We discuss the probabilistic representation of the solutions of the heat equation perturbed by a repulsive point interaction in terms of a perturbation of Brownian motion, via a Feynman-Kac formula involving a local time functional. An application to option pricing is given, interpolating between the extreme cases of classical Black-Scholes options and knockouts having the barrier situated exactly at the exercise price.

AB - We discuss the probabilistic representation of the solutions of the heat equation perturbed by a repulsive point interaction in terms of a perturbation of Brownian motion, via a Feynman-Kac formula involving a local time functional. An application to option pricing is given, interpolating between the extreme cases of classical Black-Scholes options and knockouts having the barrier situated exactly at the exercise price.

KW - Black-Scholes equation

KW - Brownian motion

KW - Feynman-Kac formula

KW - Heat equation

KW - Heat kernel

KW - Local time

KW - Option pricing

KW - Point interactions

UR - https://www.scopus.com/pages/publications/84928948732

U2 - 10.1016/S0034-4877(15)30006-9

DO - 10.1016/S0034-4877(15)30006-9

M3 - Article

AN - SCOPUS:84928948732

SN - 0034-4877

VL - 75

SP - 257

EP - 265

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

IS - 2

ER -

A Remark on the Heat Equation with a Point Perturbation, the Feynman-Kac Formula with Local Time and Derivative Pricing

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this