We propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases. We consider the independent and identically distributed (i.i.d.) bootstrap and the wild bootstrap (WB), and prove their first-order asymptotic validity under general assumptions on the log-price process that allow for drift and leverage effects. We derive Edgeworth expansions in a simpler model that rules out these effects. The i.i.d. bootstrap provides a second-order asymptotic refinement when volatility is constant, but not otherwise. The WB yields a second-order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the WB data appropriately. None of these methods provides third-order asymptotic refinements. Both methods improve upon the first-order asymptotic theory in finite samples.

[We propose an asset pricing model with generalized disappointment aversion preferences and long-run volatility risk. With Markov switching fundamentals, we derive closed-form solutions for all returns moments and predictability regressions. The model produces first and second moments of price-dividend ratios and asset returns as well as return predictability patterns in line with the data. Compared to Bansal and Yaron (2004), we generate (i) more predictability of excess returns by price-dividend ratios; (ii) less predictability of consumption growth rates by price-dividend ratios. Our results do not depend on a value of the elasticity of intertemporal substitution greater than one.]

We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit recent nonparametric asymptotic distributional results, are both easy-to-implement and highly accurate in empirically realistic situations. We also illustrate that properly accounting for the measurement errors in the volatility forecast evaluations reported in the existing literature can result in markedly higher estimates for the true degree of return volatility predictability.

We propose an asset pricing model where preferences display generalized disappointment aversion These preferences, which are embedded in the Epstein and Zin (1989) recursive utility framework, overweight disappointing results as compared to expected utility, and display relatively larger risk aversion for small gambles. With a Markov switching model for the endowment process, we derive closed-form solutions for all returns moments and predictability regressions. The model produces first and second moments of price-dividend ratios and asset returns and return predictability patterns in line with the data. Compared to Differently from the Bansal and Yaron model, our results do not depend on a value of the elasticity of intertemporal substitution greater than one.

Many studies have documented that daily realized volatility estimates based on intraday returns provide volatility forecasts that are superior to forecasts constructed from daily returns only. We investigate whether these forecasting improvements translate into economic value added. To do so, we develop a new class of affine discrete-time option valuation models that use daily returns as well as realized volatility. We derive convenient closed-form option valuation formulas, and we assess the option valuation properties using Standard & Poor’s (S&P) 500 return and option data. We find that realized volatility reduces the pricing errors of the benchmark model significantly across moneyness, maturity, and volatility levels.