A Note on Pricing Barrier Options Under a Stochastic Volatility Model: An Asymptotic Expansion with Static Hedging

2009 ◽  
Author(s):  
Kenichiro Shiraya ◽  
Akihiko Takahashi ◽  
Masashi Toda
Keyword(s):  
Asymptotic Expansion ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Barrier Options ◽  
Static Hedging ◽  
Volatility Model

scholarly journals An asymptotic expansion formula for up-and-out barrier option price under stochastic volatility model

JSIAM Letters ◽  
2013 ◽  
Vol 5 (0) ◽  
pp. 17-20 ◽  
Author(s):  
Takashi Kato ◽  
Akihiko Takahashi ◽  
Toshihiro Yamada
Keyword(s):  
Asymptotic Expansion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Barrier Option ◽  
Expansion Formula ◽  
Volatility Model

A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion

2019 ◽  
Vol 25 (3) ◽  
pp. 239-252
Author(s):  
Yusuke Okano ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Asymptotic Expansion ◽  
Stochastic Volatility ◽  
Diffusion Processes ◽  
Stochastic Volatility Model ◽  
Weak Approximation ◽  
Numerical Examples ◽  
Control Variate ◽  
Volatility Model ◽  
Multidimensional Diffusion

Abstract The paper shows a new weak approximation method for stochastic differential equations as a generalization and an extension of Heath–Platen’s scheme for multidimensional diffusion processes. We reformulate the Heath–Platen estimator from the viewpoint of asymptotic expansion. The proposed scheme is implemented by a Monte Carlo method and its variance is much reduced by the asymptotic expansion which works as a kind of control variate. Numerical examples for the local stochastic volatility model are shown to confirm the efficiency of the method.

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