Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading. / Zhang, Yumo.

In: Journal of Industrial and Management Optimization, Vol. 19, No. 6, 2023, p. 4022-4063.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Zhang, Y 2023, 'Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading', Journal of Industrial and Management Optimization, vol. 19, no. 6, pp. 4022-4063. https://doi.org/10.3934/jimo.2022121

APA

Zhang, Y. (2023). Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading. Journal of Industrial and Management Optimization, 19(6), 4022-4063. https://doi.org/10.3934/jimo.2022121

Vancouver

Zhang Y. Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading. Journal of Industrial and Management Optimization. 2023;19(6):4022-4063. https://doi.org/10.3934/jimo.2022121

Author

Zhang, Yumo. / Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading. In: Journal of Industrial and Management Optimization. 2023 ; Vol. 19, No. 6. pp. 4022-4063.

Bibtex

@article{a8153471d95149338d9d880554a6eda4,
title = "Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading",
abstract = "This paper investigates the effects of derivative trading on the performance of asset-liability management in the presence of stochastic interest rate and stochastic volatility under the mean-variance criterion. Specifically, the asset-liability manager can invest not only in a money market account, a zero-coupon (rollover) bond, and a stock index but also in stock derivatives. It is assumed that the interest rate follows a Cox-Ingersoll-Ross (CIR) process, and the instantaneous variance of the stock index is governed by the family of 4/2 stochastic volatility models, which embraces the Heston model and 3/2 model, as particular cases. By solving a system of three backward stochastic differential equations, closed-form expressions for the optimal strategies and optimal value functions are derived in two cases: with and without the stock derivatives. Moreover, we consider the special cases without random liabilities. Numerical examples are provided to illustrate theoretical results and explore the effects of derivative trading on eficient frontiers.",
keywords = "4/2 stochastic volatility, Asset-liability management, backward stochastic differential equation, CIR interest rate, derivative trading",
author = "Yumo Zhang",
note = "Publisher Copyright: {\textcopyright} 2023,Journal of Industrial and Management Optimization. All Rights Reserved.",
year = "2023",
doi = "10.3934/jimo.2022121",
language = "English",
volume = "19",
pages = "4022--4063",
journal = "Journal of Industrial and Management Optimization",
issn = "1547-5816",
publisher = "American Institute of Mathematical Sciences (AIMS)",
number = "6",

}

RIS

TY - JOUR

T1 - Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading

AU - Zhang, Yumo

N1 - Publisher Copyright: © 2023,Journal of Industrial and Management Optimization. All Rights Reserved.

PY - 2023

Y1 - 2023

N2 - This paper investigates the effects of derivative trading on the performance of asset-liability management in the presence of stochastic interest rate and stochastic volatility under the mean-variance criterion. Specifically, the asset-liability manager can invest not only in a money market account, a zero-coupon (rollover) bond, and a stock index but also in stock derivatives. It is assumed that the interest rate follows a Cox-Ingersoll-Ross (CIR) process, and the instantaneous variance of the stock index is governed by the family of 4/2 stochastic volatility models, which embraces the Heston model and 3/2 model, as particular cases. By solving a system of three backward stochastic differential equations, closed-form expressions for the optimal strategies and optimal value functions are derived in two cases: with and without the stock derivatives. Moreover, we consider the special cases without random liabilities. Numerical examples are provided to illustrate theoretical results and explore the effects of derivative trading on eficient frontiers.

AB - This paper investigates the effects of derivative trading on the performance of asset-liability management in the presence of stochastic interest rate and stochastic volatility under the mean-variance criterion. Specifically, the asset-liability manager can invest not only in a money market account, a zero-coupon (rollover) bond, and a stock index but also in stock derivatives. It is assumed that the interest rate follows a Cox-Ingersoll-Ross (CIR) process, and the instantaneous variance of the stock index is governed by the family of 4/2 stochastic volatility models, which embraces the Heston model and 3/2 model, as particular cases. By solving a system of three backward stochastic differential equations, closed-form expressions for the optimal strategies and optimal value functions are derived in two cases: with and without the stock derivatives. Moreover, we consider the special cases without random liabilities. Numerical examples are provided to illustrate theoretical results and explore the effects of derivative trading on eficient frontiers.

KW - 4/2 stochastic volatility

KW - Asset-liability management

KW - backward stochastic differential equation

KW - CIR interest rate

KW - derivative trading

UR - http://www.scopus.com/inward/record.url?scp=85152011443&partnerID=8YFLogxK

U2 - 10.3934/jimo.2022121

DO - 10.3934/jimo.2022121

M3 - Journal article

AN - SCOPUS:85152011443

VL - 19

SP - 4022

EP - 4063

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

SN - 1547-5816

IS - 6

ER -

ID: 359602670