Substantial progress has been made in developing more realistic option pricing models. Empirically, however, it is not known whether and by how much each generalization improves option pricing and hedging. We fill this gap by first deriving an option model that allows volatility, interest rates and jumps to be stochastic. Using S&P 500 options, we examine several alternative models from three perspectives: (1) internal consistency of implied parameters/volatility with relevant timeseries data, (2) out-of-sample pricing, and (3) hedging. Overall, incorporating stochastic volatility and jumps is important for pricing and internal consistency. But for hedging, modeling stochastic volatility alone yields the best performance. IN THE LAST TWO DECADES

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Any admissible portfolio performance measure should satisfy four minimal conditions: it assigns zero performance to each reference portfolio and it is linear, continuous, and nontrivial. Such an admissible measure exists if and only if the securities market obeys the law of one price. A positive admissible measure exists if and only if there is no arbitrage. This article characterizes the (infinite) set of admissible performance measures. It is shown that performance evaluation is generally quite arbitrary. A mutual funddata set is also used to demonstrate how the measurement method developed here can be applied.