Small-Time Asymptotics for an Uncorrelated Local-Stochastic Volatility Model

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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Small-time asymptotics for fast mean-reverting stochastic volatility models

The Annals of Applied Probability ◽

10.1214/11-aap801 ◽

2012 ◽

Vol 22 (4) ◽

pp. 1541-1575 ◽

Cited By ~ 17

Author(s):

Jin Feng ◽

Jean-Pierre Fouque ◽

Rohini Kumar

Keyword(s):

Stochastic Volatility ◽

Small Time ◽

Stochastic Volatility Models ◽

Time Asymptotics ◽

Volatility Models ◽

Small Time Asymptotics

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

SIAM Journal on Financial Mathematics ◽

10.1137/140971397 ◽

2017 ◽

Vol 8 (1) ◽

pp. 82-113 ◽

Cited By ~ 4

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

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SMALL-TIME ASYMPTOTICS IN GEOMETRIC ASIAN OPTIONS FOR A STOCHASTIC VOLATILITY JUMP-DIFFUSION MODEL

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024919500055 ◽

2019 ◽

Vol 22 (02) ◽

pp. 1950005

Author(s):

HOSSEIN JAFARI ◽

GHAZALEH RAHIMI

Keyword(s):

Stochastic Volatility ◽

Lévy Process ◽

Implied Volatility ◽

Option Price ◽

Small Time ◽

Stochastic Volatility Model ◽

Levy Process ◽

Asian Option ◽

Volatility Model ◽

Jump Diffusion Model

The aim of this paper is to study the small time to maturity of the behavior of the geometric Asian option price and implied volatility under a general stochastic volatility model with Lévy process. The volatility process does not need to be a diffusion or a Markov process, but the future average volatility in the model is a nonadapted process. An anticipating Itô formula for Lévy process and the decomposition of the price (Hull–White formula) are obtained using the Malliavin calculus techniques. The decomposition formula is applied to find the small-time limit of the geometric Asian option price and the implied volatility for the model in at-the-money and out-of-the-money cases.

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