The SEV-SV Model—Applications in Portfolio Optimization

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.

Robust Portfolio Choice under the Modified Constant Elasticity of Variance

“…In the model setup, it is important to acknowledge that this ambiguity stems from an investor's inability to capture the expected returns precisely in the probability laws governing the stock price process. This assumption aligns with the perspectives presented in seminar studies, such as the work by Merton [15], and more recently shown in Tables 1 and 2 in reference [8] on the large standard errors in estimating the parameter λ.…”

“…where r is a constant risk-free interest rate. As explained in the references [5,6,8], the M-CEV allows for a non-zero probability of the underlying touching zero (default) if β > 1, which makes it realistic for pricing and portfolio problems. We refer to model (3) as the reference model.…”

“…This model, explored for pricing purposes in the reference [5], has been adapted to expected utility optimization in the recent work of Muravei in [6]. Additionally, refer to the references [7,8] for portfolio optimization results on two other types of CEV models: CEV and LVO-CEV.…”

“…To address this issue, the value function incorporates a penalty term designed to discourage significant deviations from the reference model. This penalty term, which appears as the last expectation term in the problem (8), is computed based on relative entropy. The perturbations e S t in the penalty term were scaled by Ψ(τ, X τ ).…”