Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading
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Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading. / Zhang, Yumo.
I: Journal of Industrial and Management Optimization, Bind 19, Nr. 6, 2023, s. 4022-4063.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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