Spanning tests for options using principal components methods

This article proposes a new test to evaluate whether options are a redundant asset class. The methodology permits to test between two sets of competing option pricing models: the deterministic volatility models and the stochastic models. In the deterministic volatility framework, options are redundant assets and their payoff can be replicated by dynamic trading in the underlying and the risk-free assets. A stochastic model introduces an additional risk factor and in this setting options are needed in order to complete the market. The procedure relies on principal components methods. The Monte Carlo simulations reported in the article indicate that the new procedure provides simple and useful diagnostics for detection if options are redundant. We apply the method to S&P 500 index and options with different moneyness. The empirical results suggest that options are not redundant.