VIX and term spread drive shifts in conditional pricing kernel
Federal Reserve Board research introduces a semi-nonparametric framework to estimate forward-looking conditional pricing kernels using index options. S&P 500 empirical tests show the VIX and Treasury term spread best capture time-varying state prices and conditional risk premia.
Resolving the tail risk puzzle
Federal Reserve researcher Hyung Joo Kim developed a modified conditional density integration method incorporating 12 state variables across 1996 to 2020 S&P 500 options data.
Statistical tests show that the VIX and the 10-year minus 2-year Treasury term spread provide the most informative conditioning set for identifying state prices.
The model enforces a physical density constraint and Euler equations via two-step GMM with a second-order polynomial.
The resulting conditional equity risk premium averages 0.63 percent monthly, closely tracking the 0.67 percent realized market return, whereas unconditional models overestimate it at 0.76 percent.
The specification also improves out-of-sample option pricing.
Bridging forward and backward densities
Existing pricing kernel literature often pairs forward-looking risk-neutral densities with backward-looking historical returns or rigid parametric GARCH and jump-diffusion models.
This timing mismatch generated the empirical pricing kernel puzzle, where state prices appeared U-shaped rather than downward-sloping.
Kim demonstrates that the conditional kernel remains monotonically decreasing up to an 8 percent monthly return.
During crisis episodes such as 2008 and 2020, left-tail compensation fully accounts for conditional risk premia.
Useful mechanics, persistent tail limits
The paper provides an elegant econometric fix that eliminates timing mismatches in empirical asset pricing.
Yet the second-order polynomial still struggles to price deep out-of-the-money put options during market panics.
Central bank researchers nevertheless gain a superior tool for monitoring real-time market risk appetite.