Implied risk aversion and volatility risk premiums

Abstract

Since investor risk aversion determines the premium required for bearing risk, a comparison thereof provides evidence of the different structure of risk premium across markets. This article estimates and compares the degree of risk aversion of three actively traded options markets: the S&P 500, Nikkei 225 and KOSPI 200 options markets. The estimated risk aversions is found to follow S&P 500, Nikkei 225 and KOSPI 200 options in descending order, implying that S&P 500 investors require more compensation than other investors for bearing the same risk. To prove this empirically, we examine the effect of risk aversion on volatility risk premium, using delta-hedged gains. Since more risk-averse investors are willing to pay higher premiums for bearing volatility risk, greater risk averseness can result in a severe negative volatility risk premium, which is usually understood as hedging demands against the underlying asset's downward movement. Our findings support the argument that S&P 500 investors with higher risk aversion pay more premiums for hedging volatility risk.

Keywords:

• risk aversion
• volatility risk premium
• S&P 500 index options
• Nikkei 225 index options
• KOSPI 200 index options

JEL Classification:

• G13
• G15

Acknowledgement

This research was supported by Hallym University Research Fund, 2011(HRF-201109-039).

Notes

¹ Jackwerth (2004) uses the option prices traded in the S&P 500, DAX, FTSE 100 and Nikkei 225 index options markets to show that the U-shape of implied risk aversion is not only a local aspect but also a worldwide phenomenon. However, that study uses only one cross-sectional dataset observed at a particular date.

² Carr and Wu (2009) define the variance risk premium as realized variance minus risk-neutral variance, while others define it oppositely, i.e. risk-neutral variance minus realized variance. To avoid confusion, in this article, the variance premium indicates the latter case.