scholarly journals Pricing Parisian Option under a Stochastic Volatility Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Min-Ku Lee ◽  
Kyu-Hwan Jang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Barrier Options ◽  
Barrier Option ◽  
Partial Differential ◽  
Model Based ◽  
Volatility Model ◽  
Black Scholes

We study the pricing of a Parisian option under a stochastic volatility model. Based on the manipulation problem that barrier options might create near barriers, the Parisian option has been designed as an extended barrier option. A stochastic volatility correction to the Black-Scholes price of the Parisian option is obtained in a partial differential equation form and the solution is characterized numerically.

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.

scholarly journals A Comparative Analysis of the Black-Scholes- Merton Model and the Heston Stochastic Volatility Model

2019 ◽  
Vol 39 ◽  
pp. 127-140
Author(s):  
Tahmid Tamrin Suki ◽  
ABM Shahadat Hossain
Keyword(s):  
Comparative Analysis ◽  
Stochastic Volatility ◽  
Stock Prices ◽  
Computer Algebra System ◽  
Stochastic Volatility Model ◽  
Affecting Factors ◽  
Pricing Models ◽  
Merton Model ◽  
Volatility Model ◽  
Black Scholes

This paper compares the performance of two different option pricing models, namely, the Black-Scholes-Merton (B-S-M) model and the Heston Stochastic Volatility (H-S-V) model. It is known that the most popular B-S-M Model makes the assumption that volatility of an asset is constant while the H-S-V model considers it to be random. We examine the behavior of both B-S-M and H-S-V formulae with the change of different affecting factors by graphical representations and hence assimilate them. We also compare the behavior of some of the Greeks computed by both of these models with changing stock prices and hence constitute 3D plots of these Greeks. All the numerical computations and graphical illustrations are generated by a powerful Computer Algebra System (CAS), MATLAB. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 127-140

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