We study the probabilistic and statistical properties of the variation based realized third and fourth moments of financial returns . The realized moments of the return are unbiased and relative efficient estimators for the actual moments of the return distribution under a martingale condition in the return process. For the estimation of a stochastic volatility model , we employ a simple method of estimation and a generalized method of moments estimation based on the realized second and third moments . Conditional thin tale property of the return distribution with given quadratic variation of the return is discussed. We explain the structure of moments variation swaps and analyze the thin tale property of the portfolio return hedged by the third moment variation swap .
We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use a square root stochastic volatility model for the derivations of moment conditions for estimations. Using the S\&P 500 index high frequency data, the realized versions of the moment variations is used for the estimation of a stochastic volatility model . We propose a simple estimation method of a stochastic volatility model using the sample averages of the variations and ARMA estimation. In addition, we compare the results with a generalized method of moments estimation based on the successive relation between realized moments and their lagged values .
R
study the probabilistic and statistical
discuss the probabilistic
D
realized
R
. The realized moments of the return are unbiased and relative efficient estimators for the
as estimators of the
R
distribution under a martingale condition in the return process. For the
distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use a square root stochastic volatility model for the derivations of moment conditions for estimations. Using the S\&P 500 index high frequency data, the realized versions of the moment variations is used for the
R
, we employ a simple method of estimation and
. We propose a simple estimation method of a stochastic volatility model using the sample averages of the variations and ARMA estimation. In addition, we compare the results with
R
realized second and third moments . Conditional thin tale property of the return distribution with given quadratic variation of the return is discussed. We explain the structure of moments variation swaps and analyze the thin tale property of the portfolio return hedged by the third moment variation swap
successive relation between realized moments and their lagged values