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

Abstract

<p style='text-indent:20px;'>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 efficient frontiers.</p>