Regulating Stochastic Clocks to Model Return Skewness and Tails

Summary

This paper proposes regulated stochastic clocks for continuous-time financial models that represent trading activity and help capture asymmetric and heavy-tailed returns. The method modifies clocks formed from Lévy subordinators, or more general processes with nonnegative independent increments, using kernels motivated by repeated averaging. A regulation parameter controls the degree of adjustment without reducing the number of trades or changing trading intensity.

The authors analyze Laplace transforms, characteristic triplets, and cumulants, with potential uses in estimation, option calibration, and simulation. They develop a moment-based estimation procedure with profile likelihood for selected jump-diffusion and tempered stable models, then study daily S&P 500 and Bitcoin returns. The empirical analysis is presented as evidence for desirable effects, but the excerpt does not specify the results or their magnitude. The approach is also tied to the selected clock families and model assumptions.

Key ideas

• Regulated stochastic clocks aim to capture asymmetry and tail risk in returns.
• Kernel choices regulate nonnegative independent-increment processes without changing trading intensity or trade count.
• A hyperparameter controls regulation and can produce a wide range of skewness and excess kurtosis.
• The framework includes theoretical characterization, estimation, option calibration, and simulation applications.
• The empirical study uses daily S&P 500 and Bitcoin returns.

Tags

# Regulating stochastic clocks


# Regulating stochastic clocks









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 developed 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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