Exploring Risk Premia, Pricing Kernels, and No-Arbitrage Restrictions in Option Pricing Models

The literature on dynamic option valuation typically does not explicitly specify a pricing kernel. Instead it characterizes the kernel indirectly by specifying prices of risk, or defines it implicitly as the ratio of the risk-neutral and physical probabilities. We propose explicit pricing kernels for stochastic volatility option pricing models that satisfy absence of arbitrage. Different affine price-of-risk specifications correspond to pricing kernels with radically different, and sometimes implausible, economic implications. It can be difficult to statistically distinguish between pricing kernels with widely different economic implications and risk premia. We attribute this to the inherent statistical problem with the estimation of the equity and variance risk premia. This finding extends Merton's (1980) observations on the estimation of the market equity premium to joint estimation of the equity and variance risk premia using the cross-section of options and the underlying returns