Joint estimation of volatility risk and tail risk premia with time-varying macro-state-dependent property

We propose a new method to jointly estimate volatility risk and two-tail risk price with state-dependent features. Rather than assuming a constant risk price, as in existing models, this new method estimates an extended pricing kernel with macro-state-dependent risk prices. In contrast to the widely accepted constant risk price assumption, we find that the prices for equity, volatility, positive jump, and negative jump risks are strongly dependent on economic conditions. The empirical evidence shows that this new estimation for the macro-state-dependent property adds new pricing information that existing constant risk-price models do not provide. The estimation of macro-state-dependent property has important economic implications for the underlying dynamics and derivative markets. State-dependent risk prices substantially improve the explanation of the dynamic link between the underlying and option markets, and are important factors in the option market. With the out-of-sample test, the new method provides a stable estimation of the risk price dynamics.