GARCH模型下的封闭式投资组合优化

IF 3.7 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Operations Research Perspectives Pub Date : 2022-01-01 DOI:10.1016/j.orp.2021.100216
Marcos Escobar-Anel , Maximilian Gollart , Rudi Zagst
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引用次数: 5

摘要

对于方差服从GARCH(1,1)过程的现货资产,给出了近似的封闭式最优投资组合配置公式。在Heston和Nandi (2000) GARCH (HN-GARCH)模型下,我们考虑一个具有恒定相对风险厌恶(CRRA)效用的投资者,他希望最大化终端财富的预期效用。基于Campbell和Viceira(1999)对对数回报的近似,我们得到了最优投资策略、价值函数和最优终端财富的封闭公式。我们发现最优策略与风险资产的发展无关,并且在附加条件下,其解收敛于连续时间Heston随机波动率模型(Kraft, 2005)的解。对于日常交易场景,最优解对参数变化具有较强的鲁棒性,而数值财富等效损失(WEL)分析表明,赫斯顿解的性能较好,默顿解的性能较差。Escobar-Anel et al.(2020)在多元仿射GARCH下将该解扩展到二维。
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Closed-form portfolio optimization under GARCH models

This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a Heston and Nandi (2000) GARCH (HN-GARCH) model. Based on an approximation of the log returns from Campbell and Viceira (1999), we obtain closed formulas for the optimal investment strategy, the value function and the optimal terminal wealth. We find the optimal strategy is independent of the development of the risky asset, and the solution converges to that of a continuous-time Heston stochastic volatility model (Kraft, 2005), albeit under additional conditions. For a daily trading scenario, the optimal solutions are quite robust to variations in the parameters, while the numerical wealth equivalent loss (WEL) analysis shows good performance of the Heston solution, with a quite inferior performance of the Merton solution.The solution is extended to two dimensions under the multivariate affine GARCH in Escobar-Anel et al. (2020).

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来源期刊
Operations Research Perspectives
Operations Research Perspectives Mathematics-Statistics and Probability
CiteScore
6.40
自引率
0.00%
发文量
36
审稿时长
27 days
期刊最新文献
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