Nonparametric jump variation measures from options

Todorov, Viktor

doi:10.1016/j.jeconom.2021.04.005

Cited by 4 publications

(1 citation statement)

References 28 publications

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“…samples. However, in reality, the aggregate number of trades cannot be expected to be unlimitedly small, or close to zero, leading effectively to degeneracy, or trading halts; on the other hand, the long-term trading intensity is generally specified a priori without being optimized and may be estimated in a dynamical fashion using techniques of empirical power variations (see, e.g., [Aït-Sahalia and Jacod, 2009] [3], [Todorov and Tauchen, 2011] [62], [Jing et al, 2012] [34], and [Todorov, 2021] [61]), which of course varies with the frequencies at which data are observed. With restrictions on these two important dimensions, nearly 1 The same processes also play an important role in many nonfinancial fields, especially in reliability engineering to model the degradation phenomena of structural components (see the overview by [Ye and Xie, 2015] [70]).…”

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confidence: 99%

Regulating stochastic clocks

Fei¹,

Xia²

2022

Preprint

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Stochastic clocks represent a class of time change methods for incorporating trading activity into continuous-time financial models, with the ability to deal with typical asymmetrical and tail risks in financial returns. In this paper we propose a significant improvement of stochastic clocks for the same objective but without decreasing the number of trades or changing the trading intensity. Our methodology targets any Lévy subordinator, or more generally any process of nonnegative independent increments, and is based on various choices of regulating kernels motivated from repeated averaging. By way of a hyperparameter linked to the degree of regulation, arbitrarily large skewness and excess kurtosis of returns can be easily achieved. Generic-time Laplace transforms, characterizing triplets, and cumulants of the regulated clocks and subsequent mixed models are analyzed, serving purposes ranging from statistical estimation and option price calibration to simulation techniques. Under specified jump-diffusion processes and tempered stable processes, a robust moment-based estimation procedure with profile likelihood is employed for statistical estimation and a comprehensive empirical study involving S&P500 and Bitcoin daily returns is conducted to demonstrate a series of desirable effects of the proposed methods.

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