A Stochastic Volatility Model, Volatility Smile and Forecasting Volatility

2004 ◽  
Author(s):  
Bogdan Negrea
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Smile ◽  
Volatility Model ◽  
Forecasting Volatility

scholarly journals From characteristic functions to implied volatility expansions

2015 ◽  
Vol 47 (03) ◽  
pp. 837-857 ◽  
Author(s):  
Antoine Jacquier ◽  
Matthew Lorig
Keyword(s):  
Characteristic Function ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Volatility Smile ◽  
Model Free ◽  
Implied Volatility Surface ◽  
Volatility Model ◽  
Volatility Surface

For any strictly positive martingaleS= eXfor whichXhas a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log-strike. We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Lévy model, Merton (1976), one infinite activity exponential Lévy model (variance gamma), and one stochastic volatility model, Heston (1993). Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.

scholarly journals From characteristic functions to implied volatility expansions

2015 ◽  
Vol 47 (3) ◽  
pp. 837-857 ◽  
Author(s):  
Antoine Jacquier ◽  
Matthew Lorig
Keyword(s):  
Characteristic Function ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Volatility Smile ◽  
Model Free ◽  
Implied Volatility Surface ◽  
Volatility Model ◽  
Volatility Surface

For any strictly positive martingale S = eX for which X has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log-strike. We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Lévy model, Merton (1976), one infinite activity exponential Lévy model (variance gamma), and one stochastic volatility model, Heston (1993). Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.

FUZZY UNCERTAINTY IN THE HESTON STOCHASTIC VOLATILITY MODEL

2011 ◽  
Vol 16 (02) ◽  
Author(s):  
G. Figà-Talamanca ◽  
M. L. Guerra ◽  
L. Stefanini
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Fuzzy Uncertainty ◽  
Volatility Model

Introducing two mixing fractions to a lognormal local-stochastic volatility model

2020 ◽  
Author(s):  
Bowie Owens ◽  
Zili Zhu ◽  
Geoffrey Lee
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model

A non-Gaussian stochastic volatility model

1998 ◽  
Vol 2 (2) ◽  
pp. 33-47 ◽  
Author(s):  
Yuichi Nagahara ◽  
Genshiro Kitagawa
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Non Gaussian

Macroeconomic Uncertainty and Asset Prices: A Stochastic Volatility Model

2009 ◽  
Author(s):  
Hwagyun Kim ◽  
Hyoung Il Lee ◽  
Joon Y. Park ◽  
Hyosung Yeo
Keyword(s):  
Stochastic Volatility ◽  
Asset Prices ◽  
Stochastic Volatility Model ◽  
Macroeconomic Uncertainty ◽  
Volatility Model

Forecasting Future Volatility from Option Prices under the Stochastic Volatility Model

2009 ◽  
Author(s):  
Suk-Joon Byun ◽  
Sol Kim ◽  
Dongwoo Rhee
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
Volatility Model
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