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- Document type:
- Masterarbeit
- Author(s):
- Lausser, Tobias
- Title:
- Closed-form portfolio optimization under generalized GARCH models
- Abstract:
- This thesis introduces a new model designed for asset prices, the generalized Heston Nandi GARCH (GHN-GARCH), and it derives the corresponding approximated closed-form op[1]timal portfolio allocation. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth un[1]der the GHN-GARCH(1,1) model. Based on an approximation of the log-returns from Campbell and Viceira [CV99], a closed-form optimal portfolio allocation under the Hes[1]ton and Nandi GARCH (HN-GARCH) from [EGZ22] and an idea based on a change of control from [CE23], we obtain formulas for the optimal investment strategy, the optimal value function and the optimal terminal wealth for a very general form of the model’s volatility. Due to the flexibility the GHN-GARCH framework provides in the choice of its volatility, we find that these results reveal a large class of discrete-time stochastic volatil[1]ity models solvable in closed form. These models can be divided into endogenous and exogenous cases. One particular example for each of those classes is introduced. These are the 4/2-HN-GARCH(1,1) model, inspired by the continuous-time 4/2 stochastic volatility model of [Gra17], and the Crisis-HN-GARCH(1,1) model, inspired by the continuous-time model of [Gon22] that is driven by the likelihood of an upcoming market turbulence. A robust parameter estimation procedure for the former is developed, and a correspond[1]ing sensitivity analysis in a daily trading scenario reveals that the optimal solution is quite stable towards variations in the parameters. The numerical wealth-equivalent loss analysis shows good performance of the HN-GARCH(1,1) solution and slightly inferior performance of the Merton solution [Mer69] compared to the optimal allocation in a 4/2- HN-GARCH(1,1) market. Moreover, an empirical data analysis on S&P500 price index returns indicates comparable performance to the HN-GARCH(1,1) model.
- Supervisor:
- Prof. Dr. Rudi Zagst
- Advisor:
- Prof. Marcos Escobar-Anel
- Year:
- 2024
- University:
- Technische Universität München
- Commencing Date:
- 01.02.2024
- End of processing:
- 18.03.2024
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