> ## Content Index
> Fetch the complete content index at: https://fsc.stevens.edu/llms.txt
> Use this file to discover other available public pages before exploring further.

# Robust Test of Processes Underlying Leveraged Exchange Traded Funds
- URL: https://fsc.stevens.edu/robust-test-of-processes-underlying-leveraged-exchange-traded-funds/
- Published: 2019-10-29T17:47:07.000Z
- Updated: 2026-05-16T22:41:37.000Z
- Author: Zheng Xing
- Tags: FE 800 Projects, 2018 Fall, Exchange Traded Funds (ETF Studies), Research, #Import 2024-05-30 10:26, #Import 2025-11-08 22:14

**Authors:**

- Yishi Xu
- Yufan Qiu

**Supervisor:**

- Dr. Zhenyu Cui

### Abstract

As we all know, leveraged exchange-traded funds (LETFs) are cogent and complicated trading instruments that allow traders to magnify the return on investment. They seek to multiple the daily return of a particular index. In this paper, we develop a simple robust method to study the price processes of at-the-money (ATM) and out-of-the-money (OTM) options as the time approaches to maturities. We show the different asymptotic behaviors for ATM and OTM options by simulating six popular parametric models to examine whether the option price process is purely continuous, purely discontinuous, or a combination of both. We apply the method to ProShares UltraPro QQQ (TQQQ) which is one of the more heavily traded leveraged ETFs in the U.S and find the existence of a jump component in the index.