The time value of an option balances the loss from time decay with expected gains from the variations in the underlying security price and volatility. Under the Black-Merton-Scholes option pricing representation, the rate of time decay is measured by the option's theta, and the option's convexity exposures to the underlying security price and volatility are measured by the option's gamma, volga, and vanna. In this paper, we identify a striking stylized evidence on the time decay behavior of options across asset classes. We find that for options on both equity indexes and a long list of currencies, at each calendar date and option expiry, the options time decay variation across strikes can be explained extremely well by the gamma, vanna, and volga exposures of these options. A cross-sectional regression of the options theta on the three exposures across strikes generate R-squared estimates over 95% across maturities, calendar times, and investigated asset classes. The high R-squared estimates suggest that portfolios of options at the same maturity with the same pricing-weighted risk exposures on gamma, vanna, and volga experience virtually the same time decay and hence should expect to make the same magnitude of excess return. We propose to use this relation as a universal relative pricing relation for options across strikes, and show that temporal deviations from this pricing relation constitute fast-reverting profitable trading opportunities
