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.

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
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