scholarly journals Small-Time Asymptotics under Local-Stochastic Volatility with a Jump-to-Default: Curvature and the Heat Kernel Expansion

2017 ◽  
Vol 8 (1) ◽  
pp. 82-113 ◽  
Author(s):  
John Armstrong ◽  
Martin Forde ◽  
Matthew Lorig ◽  
Hongzhong Zhang
Keyword(s):  
Heat Kernel ◽  
Stochastic Volatility ◽  
Small Time ◽  
Heat Kernel Expansion ◽  
Time Asymptotics ◽  
Small Time Asymptotics

Small-Time smile for the multifactor volatility heston model

2020 ◽  
Vol 57 (4) ◽  
pp. 1070-1087
Author(s):  
Dohyun Ahn ◽  
Kyoung-Kuk Kim ◽  
Younghoon Kim
Keyword(s):  
Stochastic Volatility ◽  
Small Time ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Mild Conditions ◽  
Time Asymptotics ◽  
Volatility Model ◽  
Small Time Asymptotics

AbstractWe extend the existing small-time asymptotics for implied volatilities under the Heston stochastic volatility model to the multifactor volatility Heston model, which is also known as the Wishart multidimensional stochastic volatility model (WMSV). More explicitly, we show that the approaches taken in Forde and Jacquier (2009) and Forde, Jacqiuer and Lee (2012) are applicable to the WMSV model under mild conditions, and obtain explicit small-time expansions of implied volatilities.

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