Comparison Of Volatility Models of The S&P 500 Index

Open Access
Author:
Nguyen, Lam Hoang
Area of Honors:
Finance
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • James Alan Miles, Thesis Supervisor
  • James Alan Miles, Honors Advisor
  • Jingzhi Huang, Faculty Reader
Keywords:
  • volatility
  • ARCH
  • GARCH
  • ARIMA
  • Unit Root test
  • Data-snooping
  • S&P 500 Index.
Abstract:
An accurate forecast of financial volatility is very crucial in many applications such as portfolio management when we need to figure out the Efficient Frontier, or risk management when we need to compute the Value-At-Risk, or hedging when we need to calculate the Hedge Ratio for the portfolio, etc. This thesis compares the forecasting power of different ARCH-type models during the recent financial crisis. Those models include ARCH, GARCH, EGARCH, TARCH, GJR-GARCH, SA-ARCH, P-ARCH, NA-ARCH, NA-ARCHK, APARCH, and NPARCH. Using six different loss functions and the Reality Check of White for data snooping, this study found that the results largely depend on the loss functions that are chosen. EGARCH models generally have the best performances during the financial crisis. After the test for data-snooping, we found that ARCH (1) is outperformed by other models for three out of six loss functions but perform just as well for the other three. The exact reverse applies to the GARCH (1, 1).