Joint Arbitrage Conditions for Stock Index Options and Volatility Index Options

We analyze the joint cross-section of monthly S&P500 stock index options and monthly CBOE Volatility Index options by constructing and evaluating option combinations that appear undervalued for all permissible values of the latent parameters of the unifying option pricing model and the joint stochastic process. The analysis combines dual risk restrictions with the Heston stochastic volatility model and Distributionally Robust Optimization. Significant pricing errors appear if the Stochastic Discount Factor depends only on market risk. A combination of writing in-the-money stock index calls and buying out-of-the-money volatility index puts appears particularly appealing to pure market risk averters. The evidence against option market efficiency however disappears if volatility risk is also taken into account, consistent with the existence of risk premiums for both types of risk