scholarly journals Option Pricing Using Stochastic Volatility Model under Fourier Transform of Nonlinear Differential Equation

Fractals ◽  
2021 ◽  
Author(s):  
Zhichao Liu ◽  
Yuncheng Wang ◽  
Ya Cheng ◽  
Tareq Saeed ◽  
Yong Ye
Keyword(s):  
Differential Equation ◽  
Fourier Transform ◽  
Option Pricing ◽  
Stochastic Volatility ◽  
Nonlinear Differential Equation ◽  
Stochastic Volatility Model ◽  
Volatility Model

scholarly journals Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Alexandre F. Roch
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Option Pricing ◽  
Stochastic Volatility ◽  
Viscosity Solution ◽  
Lipschitz Condition ◽  
Payoff Function ◽  
Stochastic Volatility Model ◽  
American Option Pricing ◽  
Volatility Model

We study the valuation of American-type derivatives in the stochastic volatility model of Barndorff-Nielsen and Shephard (2001). We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condition.

Option pricing under the fractional stochastic volatility model

2021 ◽  
Vol 63 ◽  
pp. 123-142
Author(s):  
Yuecai Han ◽  
Zheng Li ◽  
Chunyang Liu
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

GENERALIZED BN–S STOCHASTIC VOLATILITY MODEL FOR OPTION PRICING

2016 ◽  
Vol 19 (02) ◽  
pp. 1650014 ◽  
Author(s):  
INDRANIL SENGUPTA
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Gaussian Distribution ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Inverse Gaussian ◽  
Martingale Measures ◽  
Structure Preserving ◽  
Volatility Model ◽  
Equivalent Martingale

In this paper, a class of generalized Barndorff-Nielsen and Shephard (BN–S) models is investigated from the viewpoint of derivative asset analysis. Incompleteness of this type of markets is studied in terms of equivalent martingale measures (EMM). Variance process is studied in details for the case of Inverse-Gaussian distribution. Various structure preserving subclasses of EMMs are derived. The model is then effectively used for pricing European style options and fitting implied volatility smiles.

scholarly journals A Stochastic Volatility Model With Realized Measures for Option Pricing

2019 ◽  
Vol 38 (4) ◽  
pp. 856-871 ◽  
Author(s):  
Giacomo Bormetti ◽  
Roberto Casarin ◽  
Fulvio Corsi ◽  
Giulia Livieri
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model

scholarly journals Malliavin differentiability of the Heston volatility and applications to option pricing

2008 ◽  
Vol 40 (01) ◽  
pp. 144-162 ◽  
Author(s):  
Elisa Alòs ◽  
Christian-Oliver Ewald
Keyword(s):  
Option Pricing ◽  
Explicit Expression ◽  
Stochastic Volatility ◽  
Malliavin Calculus ◽  
Numerical Results ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Malliavin Derivative ◽  
Volatility Model

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore, we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of Alòs (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.

OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

2021 ◽  
pp. 1-20
Author(s):  
Y. HAN ◽  
Z. LI ◽  
C. LIU
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

Abstract We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented.

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