We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed …

asset underlying an option. Our test examines the prices of at­the­money and out­of­the­money options as the option maturity … options data, we conclude that the sample path behavior of this index contains both a continuous component and a jump …

well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference … options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five …

We consider the hedging of options when the price of the underlying asset is always exposed to the possibility of jumps … and a continuum of shorter-term options written on the same asset. In this portfolio of shorter-term options, the … finite set of shorter-term options and use Monte Carlo simulation to determine the hedging error thereby introduced. We …