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Article

The SEV-SV Model—Applications in Portfolio Optimization

by
Marcos Escobar-Anel
*,† and
Weili Fan
†
Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Risks 2023, 11(2), 30; https://doi.org/10.3390/risks11020030
Submission received: 9 December 2022 / Revised: 11 January 2023 / Accepted: 20 January 2023 / Published: 28 January 2023
(This article belongs to the Special Issue Stochastic Modelling in Financial Mathematics, 2nd Edition)
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Abstract

This paper introduces and studies a new family of diffusion models for stock prices with applications in portfolio optimization. The diffusion model combines (stochastic) elasticity of volatility (EV) and stochastic volatility (SV) to create the SEV-SV model. In particular, we focus on the SEV component, which is driven by an Ornstein–Uhlenbeck process via two separate functional choices, while the SV component features the state-of-the-art 4/2 model. We study an investment problem within expected utility theory (EUT) for incomplete markets, producing closed-form representations for the optimal strategy, value function, and optimal wealth process for two different cases of prices of risk on the stock. We find that when EV reverts to a GBM model, the volatility and speed of reversion of the EV have a strong impact on optimal allocations, and more aggressive (bull markets) or cautious (bear markets) strategies are hence recommended. For a model when EV reverts away from GBM, only the mean reverting level of the EV plays a role. Moreover, the presence of SV leads mainly to more conservative investment decisions for short horizons. Overall, the SEV plays a more significant role than SV in the optimal allocation.
Keywords: CEV model; expected utility theory; stochastic volatility; stochastic elasticity of volatility CEV model; expected utility theory; stochastic volatility; stochastic elasticity of volatility

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MDPI and ACS Style

Escobar-Anel, M.; Fan, W. The SEV-SV Model—Applications in Portfolio Optimization. Risks 2023, 11, 30. https://doi.org/10.3390/risks11020030

AMA Style

Escobar-Anel M, Fan W. The SEV-SV Model—Applications in Portfolio Optimization. Risks. 2023; 11(2):30. https://doi.org/10.3390/risks11020030

Chicago/Turabian Style

Escobar-Anel, Marcos, and Weili Fan. 2023. "The SEV-SV Model—Applications in Portfolio Optimization" Risks 11, no. 2: 30. https://doi.org/10.3390/risks11020030

APA Style

Escobar-Anel, M., & Fan, W. (2023). The SEV-SV Model—Applications in Portfolio Optimization. Risks, 11(2), 30. https://doi.org/10.3390/risks11020030

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