From Constant to Rough: A Survey of Continuous Volatility Modeling-Reference-Cited by-同舟云学术

From Constant to Rough: A Survey of Continuous Volatility Modeling

Published:2023-10-08 Issue:19 Volume:11 Page:4201
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Di Nunno Giulia¹²^ORCID,Kubilius Kęstutis³^ORCID,Mishura Yuliya⁴⁵^ORCID,Yurchenko-Tytarenko Anton¹

Affiliation:

1. Department of Mathematics, University of Oslo, 0851 Oslo, Norway

2. Department of Business and Management Science, NHH Norwegian School of Economics, 5045 Bergen, Norway

3. Faculty of Mathematics and Informatics, Vilnius University, LT-03225 Vilnius, Lithuania

4. Department of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine

5. Division of Mathematics and Physics, Mälardalen University, 722 20 Västerås, Sweden

Abstract

In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: without advocating for either roughness or long memory, we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/19/4201/pdf

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