A scaled version of the double-mean-reverting model for VIX derivatives

Jeonggyu Huh, Jaegi Jeon, Jeong-Hoon Kim

Research output: Contribution to journalArticle

Abstract

As the Heston model is not consistent with VIX data in real market well enough, alternative stochastic volatility models including the double-mean-reverting model of Gatheral (in: Bachelier Congress, 2008) have been developed to overcome its limitation. The double-mean-reverting model is a three factor model successfully reflecting the empirical dynamics of the variance but there is no closed form solution for VIX derivatives and SPX options and thus calibration using conventional techniques may be slow. In this paper, we propose a fast mean-reverting version of the double-mean-reverting model. We obtain a closed form approximation for VIX derivatives and show how it is effective by comparing it with the Heston model and the double-mean-reverting model.

Original languageEnglish
Pages (from-to)495-515
Number of pages21
JournalMathematics and Financial Economics
Volume12
Issue number4
DOIs
Publication statusPublished - 2018 Sep 1

Fingerprint

Derivative
Heston Model
Model
Stochastic Volatility Model
Factor Models
Closed-form Solution
Closed-form
Calibration
Volatility index
Mean-reverting
Derivatives
Alternatives
Approximation
Heston model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

Cite this

@article{903f3bada78b41e399d6d120d32bd47f,
title = "A scaled version of the double-mean-reverting model for VIX derivatives",
abstract = "As the Heston model is not consistent with VIX data in real market well enough, alternative stochastic volatility models including the double-mean-reverting model of Gatheral (in: Bachelier Congress, 2008) have been developed to overcome its limitation. The double-mean-reverting model is a three factor model successfully reflecting the empirical dynamics of the variance but there is no closed form solution for VIX derivatives and SPX options and thus calibration using conventional techniques may be slow. In this paper, we propose a fast mean-reverting version of the double-mean-reverting model. We obtain a closed form approximation for VIX derivatives and show how it is effective by comparing it with the Heston model and the double-mean-reverting model.",
author = "Jeonggyu Huh and Jaegi Jeon and Jeong-Hoon Kim",
year = "2018",
month = "9",
day = "1",
doi = "10.1007/s11579-018-0213-8",
language = "English",
volume = "12",
pages = "495--515",
journal = "Mathematics and Financial Economics",
issn = "1862-9679",
publisher = "Springer Verlag",
number = "4",

}

A scaled version of the double-mean-reverting model for VIX derivatives. / Huh, Jeonggyu; Jeon, Jaegi; Kim, Jeong-Hoon.

In: Mathematics and Financial Economics, Vol. 12, No. 4, 01.09.2018, p. 495-515.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A scaled version of the double-mean-reverting model for VIX derivatives

AU - Huh, Jeonggyu

AU - Jeon, Jaegi

AU - Kim, Jeong-Hoon

PY - 2018/9/1

Y1 - 2018/9/1

N2 - As the Heston model is not consistent with VIX data in real market well enough, alternative stochastic volatility models including the double-mean-reverting model of Gatheral (in: Bachelier Congress, 2008) have been developed to overcome its limitation. The double-mean-reverting model is a three factor model successfully reflecting the empirical dynamics of the variance but there is no closed form solution for VIX derivatives and SPX options and thus calibration using conventional techniques may be slow. In this paper, we propose a fast mean-reverting version of the double-mean-reverting model. We obtain a closed form approximation for VIX derivatives and show how it is effective by comparing it with the Heston model and the double-mean-reverting model.

AB - As the Heston model is not consistent with VIX data in real market well enough, alternative stochastic volatility models including the double-mean-reverting model of Gatheral (in: Bachelier Congress, 2008) have been developed to overcome its limitation. The double-mean-reverting model is a three factor model successfully reflecting the empirical dynamics of the variance but there is no closed form solution for VIX derivatives and SPX options and thus calibration using conventional techniques may be slow. In this paper, we propose a fast mean-reverting version of the double-mean-reverting model. We obtain a closed form approximation for VIX derivatives and show how it is effective by comparing it with the Heston model and the double-mean-reverting model.

UR - http://www.scopus.com/inward/record.url?scp=85042193383&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042193383&partnerID=8YFLogxK

U2 - 10.1007/s11579-018-0213-8

DO - 10.1007/s11579-018-0213-8

M3 - Article

AN - SCOPUS:85042193383

VL - 12

SP - 495

EP - 515

JO - Mathematics and Financial Economics

JF - Mathematics and Financial Economics

SN - 1862-9679

IS - 4

ER -