By Maria Elvira Mancino, Maria Cristina Recchioni, Simona Sanfelici

This quantity is a straight forward presentation of the most theoretical houses of the Fourier-Malliavin volatility estimation, permitting the readers to adventure the opportunity of the method and its program in a variety of monetary settings. Readers are given examples and tools to enforce this system in numerous monetary settings and functions of real-life information. a close bibliographic reference is incorporated to allow an in-depth learn.

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Extra resources for Fourier-Malliavin Volatility Estimation: Theory and Practice

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4(b)), this choice makes the estimates of the instantaneous cross volatility of quality comparable with 1,2 (t) in the those of the instantaneous volatilities. The estimated cross volatility Σn,N,M asynchronous case turns out to be a very smooth function. 13). 5 time Fig. 6 Asynchronous data. True (dotted line) and estimated (solid line) cross volatility Σ 1,2 (t) as a function of time obtained by the Fourier estimator (upper panel) and by the Realized Covariance (lower panel). 85 n3/4 , M = 21π 18 n3/4 log n3/4 ).

1. The Fourier spot volatility estimator works also as a pointwise estimator inside the time interval, but it slightly loses its accuracy near the boundaries. 1) satisfies p(0) = p(2π ), the process p is eventually modified into the process p(t) = p(t) − t (p(2π ) − p(0))/(2π ), which has the same volatility as p and p(0) = p(2π ). 2 will show. With the purpose of avoiding this artificial periodization subjacent to Fourier series method, Curato et al. (2016) define an estimator based on the Laplace transform, which has similar features with the Fourier estimator but it is statistically efficient both inside the interval of observations and near the boundary.

Chapter 4 Estimation of Instantaneous Volatility Unlike the integrated volatility, the nonparametric estimation of instantaneous volatility is a relatively recent topic. In the case of deterministic volatility function, Genon-Catalot et al. (1992) proposed a first approach through wavelet series, while Florens-Zmirou (1993), Jacod (2000) developed functional methods, which are local in space, for estimating the volatility as function of the underlying state variable level. Under the stochastic volatility paradigm, Foster and Nelson (1996) first proposed a local estimator of spot volatility from which many refinements have been derived in the subsequent literature.

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