Portfolio of Volatility Smiles versus Volatility Surface: Implications for pricing and hedging options

2021 ◽  
Author(s):  
Sol Kim
Keyword(s):  
Volatility Surface

scholarly journals An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 994
Author(s):  
Elisa Alòs ◽  
Jorge A. León
Keyword(s):  
Malliavin Calculus ◽  
Numerical Experiments ◽  
Implied Volatility ◽  
Natural Approach ◽  
Volatility Models ◽  
Implied Volatility Surface ◽  
Short Memory ◽  
White Type ◽  
Volatility Surface ◽  
Theoretical Results

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

Candidate point selection using a self-attention mechanism for generating a smooth volatility surface under the SABR model

2021 ◽  
Vol 173 ◽  
pp. 114640
Author(s):  
Hyeonuk Kim ◽  
Kyunghyun Park ◽  
Junkee Jeon ◽  
Changhoon Song ◽  
Jungwoo Bae ◽  
...  
Keyword(s):  
Attention Mechanism ◽  
Point Selection ◽  
Sabr Model ◽  
Volatility Surface ◽  
Candidate Point

Arbitrage in the Perfect Volatility Surface

Wilmott ◽  
2018 ◽  
Vol 2018 (97) ◽  
pp. 16-17
Author(s):  
Uwe Wystup
Keyword(s):  
Volatility Surface

scholarly journals Control-Theoretic Framework for a Quasi-Newton Local Volatility Surface Inversion

2009 ◽  
Author(s):  
Gabriel Turinici ◽  
George Maroulis ◽  
Theodore E. Simos
Keyword(s):  
Local Volatility ◽  
Surface Inversion ◽  
Volatility Surface ◽  
Local Volatility Surface ◽  
Quasi Newton

Dynamics of the Volatility Surface

2015 ◽  
pp. 101-106
Keyword(s):  
Volatility Surface
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