Garch Option Pricing and Volatility Scaling for Leveraged Exchange-Traded Funds

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Abstract

The main purpose of this project is to develop a new pricing method for options on Leveraged Exchange-Traded Funds. It compares the traditional Heston-Nandi GARCH ( Heston and Nandi, 2000) with the new Beta-Leveraged method. The traditional HN-GARCH model is calibrated using log-returns on the LETF, and the Beta-Leveraged model is calibrated using log-returns on the ETF. The parameters are estimated using the maximum likelihood estimator. The data set that we use are DDM ( X2 Leverage on DIA ETF) and DOG ( -X1 Leverage on DIA ETF). For DDM, the new model performs better than the traditional HN-GARCH method. For DOG, the two models are performing closely to each other, which is reasonable because the absolute scaling factor is 1.

Researchers:

Research Group (2016 Fall):

Amit Kumar Singh, Master in Financial Engineering, Graduated in May 2017
Mehrab Kooner, Master in Financial Engineering, Graduated in May 2017

Advisor:
Dr. Zhenyu Cui

Research Topics:

Heston-Nandi GARCH model, Beta-Leveraged Model, option pricing, volatility smile, LETF, ETF

Main Results:

For DDM, the option prices predicted by our model are within the bid and ask spread of the market option quotes. Where as, the traditional HN-GARCH model overprices the option. Also, the HN-GARCH model generates relatively flat volatility smiles, but our model generates smiles that follows closely to the shape of the underlying ETFs option volatility smile.

For DOG, the two models are producing similar option prices. This is because that the absolute scaling factor is 1.

Conclusions

This project evaluates the performance of Heston and Nandi's closed-form Garch model versus our Beta-Leveraged HN-GARCH model to evaluate which model prices options and scaled volatility discrepancies better between ETFs and LETFs. We find that our model outperforms or tie the traditional HN-GARCH for pricing options in all benchmarks. Also, our Beta-Leveraged model was able to generate a volatility smile that mi micks the shape of the volatility smile of the underlying ETF. Furthermore, we believe that our model could be used on other models that contain a daily return innovation process.