This paper compares stochastic models for simulating leveraged Exchange-Traded Funds (LETFs) price paths, focusing on their applications in risk management and option pricing. Using TQQQ (a 3x leveraged ETF tracking NASDAQ-100) as our case study, we evaluate Geometric Brownian Motion (GBM), Generalized Autoregressive Conditional Heteroskedasticity (GARCH), Heston stochastic volatility, Stochastic Volatility with Jumps (SVJD), and propose a novel Multi-Scale Volatility with Jumps (MSVJ) model that captures both fast and slow volatility components. Furthermore, we develop a comprehensive evaluation framework that examines both price and volatility characteristics of the simulated paths against the actual TQQQ data. Our analysis spans different market conditions, including the COVID-19 crash and the 2022 market drawdown. While our proposed MSVJ model excels in capturing volatility dynamics and price range estimation, we find that each model exhibits unique strengths in different aspects of LETFs’ behavior. The choice of most appropriate model depends on specific considerations for different applications, such as risk assessment, options pricing, or portfolio management.
Kartikay Goyle (Tue,) studied this question.