Variance Risk Premium and VIX Pricing: A Simple GARCH Approach

28 Pages Posted: 3 Oct 2012 Last revised: 12 Apr 2015

See all articles by Qiang Liu

Qiang Liu

Southwestern University of Finance and Economics - Institute of Chinese Financial Studies

Gaoxiu Qiao

Southwest Jiaotong University

Shuxin Guo

Southwest Jiaotong University - School of Economics & Management

Date Written: January 10, 2015

Abstract

This paper assesses variance risk premium and forecasts out-of-sample VIX under GARCH(1,1), GJR, and Heston-Nandi models. With the date-t GARCH parameters estimated in a moving window fashion from 3,500 daily returns of the S&P 500 index, a hypothetical date-t VIX turns out to be below the market VIX by 10.1~29.6% on average between January 1996 and January 2012. The out-of-sample underestimation could be interpreted as variance risk premium. Furthermore, parameters in conjectured formulas can be calibrated by the market VIX of Date t−1; these risk-neutral parameters forecast the date-t VIX accurately with errors of not more than 0.2% on average.

Keywords: Variance Risk Premium; Out-of-sample One-day VIX Pricing; GARCH(1,1); GJR GARCH; Heston-Nandi GARCH

JEL Classification: G13, G12

Suggested Citation

Liu, Qiang and Qiao, Gaoxiu and Guo, Shuxin, Variance Risk Premium and VIX Pricing: A Simple GARCH Approach (January 10, 2015). Available at SSRN: https://ssrn.com/abstract=2155993 or http://dx.doi.org/10.2139/ssrn.2155993

Qiang Liu (Contact Author)

Southwestern University of Finance and Economics - Institute of Chinese Financial Studies ( email )

423 Gezhi Building
555 Liutai Boulevard, Wenjiang
Chengdu, Sichuan 611130
China

HOME PAGE: http://129.news.swufe.edu.cn/4282.html

Gaoxiu Qiao

Southwest Jiaotong University ( email )

No. 111, Sec. North 1, Er-Huan Rd.
Chengdu, Sichuan 610031
China

Shuxin Guo

Southwest Jiaotong University - School of Economics & Management ( email )

No. 111, Sec. North 1, Er-Huan Rd.
Chengdu
Chengdu, Sichuan 610031
China

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