Is Volatility Priced

Yueh-Neng Lin

and

Ken Hung

The asymmetric nature of the volatility response to return shocks could simply reflect the existence of time-varying risk premiums. This study proposes a stochastic volatility process allowing for time-varying correlation with underlying returns, in which the market price of volatility risk is naturally taken into account. Historical S&P 500 returns over the period January 1969óDecember 2004 are investigated under Kalman filtration. We successfully identify and isolate the volatility risk premium in the pricing process, and thereafter demonstrate the relative contributions of price premiums and volatility premiums to underlying returns. The market price of volatility risk is found to be positive and increases with investment horizons. The existence of volatility risk premium may help solve the pricing puzzle in CAPM that empirically underprices low-beta assets but overprices high-beta assets, which reasons the importance
of this study.

Key Words: Volatility risk premium; Stochastic volatility; Kalman filter; Quasi-maximum likelihood.
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