Analysis of an uncertain volatility model

Journal of Applied Mathematics and Decision Sciences ◽

10.1155/jamds/2006/15609 ◽

2006 ◽

Vol 2006 ◽

pp. 1-17 ◽

Cited By ~ 5

Author(s):

Marco Di Francesco ◽

Paolo Foschi ◽

Andrea Pascucci

Keyword(s):

Parabolic Pdes ◽

Kolmogorov Type ◽

Volatility Model ◽

Uncertain Volatility ◽

Degenerate Parabolic

We examine, from both analytical and numerical viewpoints, the uncertain volatility model by Hobson-Rogers in the framework of degenerate parabolic PDEs of Kolmogorov type.

Download Full-text

Principle of localization of solutions of the Cauchy problem for one class of degenerate parabolic equations of Kolmogorov type

Ukrainian Mathematical Journal ◽

10.1007/s11253-011-0462-7 ◽

2011 ◽

Vol 62 (11) ◽

pp. 1707-1728

Author(s):

V. A. Litovchenko ◽

O. V. Strybko

Keyword(s):

Cauchy Problem ◽

Parabolic Equations ◽

Degenerate Parabolic Equations ◽

Kolmogorov Type ◽

The Cauchy Problem ◽

Degenerate Parabolic

Download Full-text

Double barrier American put option pricing under uncertain volatility model

International Journal of Financial Engineering ◽

10.1142/s2424786321500389 ◽

2021 ◽

pp. 2150038

Author(s):

El Kharrazi Zaineb ◽

Saoud Sahar ◽

Mahani Zouhir

Keyword(s):

Single Point ◽

Option Prices ◽

Double Barrier ◽

Early Exercise ◽

Put Option ◽

Volatility Model ◽

Uncertain Volatility ◽

Exercise Boundary ◽

Early Exercise Boundary ◽

American Style

This paper aims to study the asymptotic behavior of double barrier American-style put option prices under an uncertain volatility model, which degenerates to a single point. We give an approximation of the double barrier American-style option prices with a small volatility interval, expressed by the Black–Scholes–Barenblatt equation. Then, we propose a novel representation for the early exercise boundary of American-style double barrier options in terms of the optimal stopping boundary of a single barrier contract.

Download Full-text

Fundamental solutions of the Cauchy problem for some degenerate parabolic equations of the Kolmogorov type

Ukrainian Mathematical Journal ◽

10.1007/s11253-012-0606-4 ◽

2012 ◽

Vol 63 (11) ◽

pp. 1670-1705

Author(s):

S. D. Ivasyshen ◽

V. V. Layuk

Keyword(s):

Cauchy Problem ◽

Parabolic Equations ◽

Fundamental Solutions ◽

Degenerate Parabolic Equations ◽

Kolmogorov Type ◽

The Cauchy Problem ◽

Degenerate Parabolic

Download Full-text

The fundamental solution of Cauchy problem for a single equation of the diffusion equation with inertia

Carpathian Mathematical Publications ◽

10.15330/cmp.6.2.320-328 ◽

2014 ◽

Vol 6 (2) ◽

pp. 320-328

Author(s):

H.P. Malytska ◽

I.V. Burtnyak

Keyword(s):

Cauchy Problem ◽

Fundamental Solution ◽

Diffusion Equation ◽

Finite Number ◽

Explicit Form ◽

Single Equation ◽

Kolmogorov Type ◽

Spatial Variables ◽

Degenerate Parabolic

The paper found the explicit form of the fundamental solution of Cauchy problem for the equation of Kolmogorov type that has a finite number groups of spatial variables which are degenerate parabolic.

Download Full-text