Coupled Price–Volume Equity Models with Auto-Induced Regime Switching
Manuel L. Esquível (),
Nadezhda P. Krasii,
Pedro P. Mota and
Victoria V. Shamraeva
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Manuel L. Esquível: Department of Mathematics, FCT NOVA, and Nova Math, New University of Lisbon, Quinta da Torre, 2829-516 Monte de Caparica, Portugal
Nadezhda P. Krasii: Department of Mathematics, FCT NOVA, and Nova Math, New University of Lisbon, Quinta da Torre, 2829-516 Monte de Caparica, Portugal
Pedro P. Mota: Department of Mathematics, FCT NOVA, and Nova Math, New University of Lisbon, Quinta da Torre, 2829-516 Monte de Caparica, Portugal
Victoria V. Shamraeva: Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, Leningradsky Prospekt, 49, Moscow 125993, Russia
Risks, 2023, vol. 11, issue 11, 1-20
Abstract:
In this work, we present a rigorous development of a model for the Price–Volume relationship of transactions introduced in 2009. For this development, we rely on the precise formulation of diffusion auto-induced regime-switching models presented in our previous work of 2020. The auto-induced regime-switching models referred to may be based on a finite set of stochastic differential equations (SDE)—all defined on the same bounded time interval—and a sequence of interlacing stopping times defined by the hitting threshold times of the trajectories of the solutions of the SDE. The coupling between price and volume—which we take as a proxy of liquidity—is assumed to be the following: the regime switching in the price variable occurs at the stopping times for which there is a change of region—in the product state space of price and liquidity—for the liquidity variable (and vice versa). The regimes may be defined parametrically—that is, the SDE coefficients keep the same functional form but with varying parameters—or the functional form of the SDE coefficients may change with each regime. By using the same noise source for both the price and the liquidity regime-switching models—volume (liquidity), which, in general, is not a tradable asset—we ensure that despite incorporating information on liquidity, the price part of the coupled model can be assumed to be arbitrage free and complete, allowing the pricing and hedging of derivatives in a simple way.
Keywords: regime switching diffusions; auto-induced regime switching diffusions; price; volume of transactions; liquidity (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:11:y:2023:i:11:p:203-:d:1282722
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