Pusan National University researchers develop precise pricing formula for perpetual American strangle options

Options are a financial instrument that give the holder the right to buy and sell an underlying asset, at a predetermined price, on or before a specified date. For example, European-style options allow the buyer to exercise this right at its maturity date, while American style options can be exercised at any time up to and including the expiration date. These are generally traded in public financial markets, such as stock exchanges.

With the increasing complexity of markets, a wide range of products have emerged, including strangle options. A strangle option is an investment strategy that combines call and put options, both with same expiration date but different strike prices. This strategy is typically used by investors who anticipate a large fluctuation in the market in either direction, as it helps minimize potential losses. PASOs take this further by allowing the holder to exercise the options at any time, without an expiration date, providing considerable benefits. Consequently, PASOs have been the focus of considerable research. However, despite such studies, the pricing of PASOs and their early exercise boundaries have not yet been studied using a stochastic volatility (SV) model, which more accurately captures real market behavior compared to the Black-Scholes model.

Addressing this gap, a team of researchers led by Associate Professor Ji-Hun Yoon from Pusan National University, Korea developed a pricing formula for PASOs under an SV model with fast mean reversion. Their findings were made available online on July 27, 2024, and to be published in Volume 227 of Mathematics and Computers in Simulation on January 01, 2025.

“In recent years, financial markets have experienced considerable fluctuations during global financial crisis, such as the US subprime mortgage crisis in 2007 and 2008, the Eurozone crisis in 2010, the COVID-19 pandemic, and the Russia-Ukraine conflict. American strangle options can help investors minimize risk during such crises,” says Dr. Yoon.

In this study, researchers first established a partial differential equation (PDE) for the value of PASOs under an SV model (PASOSV). A PDE is a mathematical equation that helps to model how one variable changes with respect to another, in this case the value of the PASOSV relative to the underlying asset’s price. However, due to the complexity of SV, an exact solution was not possible. Instead, the researchers applied an asymptotic analysis approach, incorporating a special term representing the fast reversion rate of highly volatile markets.

To validate their formula, they used the Monte-Carlo simulation method, which predicts potential future values of assets through thousands of simulated scenarios. They also conducted numerical simulations to analyze how SV impacts the option price and the free boundary values using various parameters. The findings revealed that SV significantly influences option price and exercise boundary values when volatility is low, indicating that while high volatility can give higher returns, low volatility can increase risk from investing in PASOs.

“Our study lays the foundation for development of more resilient products by financial institutions, thereby providing investors with better tools and strategies to manage risk and maximize returns, especially in low volatility environments,” concludes Dr. Yoon.

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Reference                                   

Title of original paper: Pricing for perpetual American strangle options under stochastic volatility with fast mean reversion

Journal: Mathematics and Computers in Simulation

DOI: https://doi.org/10.1016/j.matcom.2024.07.030

About the institute

Pusan National University, located in Busan, South Korea, was founded in 1946 and is now the No. 1 national university of South Korea in research and educational competency. The multi-campus university also has other smaller campuses in Yangsan, Miryang, and Ami. The university prides itself on the principles of truth, freedom, and service, and has approximately 30,000 students, 1200 professors, and 750 faculty members. The university is composed of 14 colleges (schools) and one independent division, with 103 departments in all.

Website: https://www.pusan.ac.kr/eng/Main.do

About the author

Dr. Ji-Hun Yoon is currently an Associate Professor at the Department of Mathematics at Pusan National University. He received his Ph.D. from Yonsei University in 2013 and subsequently served as a postdoctoral fellow at Seoul National University. His research group specializes in developing closed-form solutions for the various financial derivatives and options calibration, using data sourced from the financial markets. In 2015, he assumed the role of Assistant Professor in the Department of Mathematics at Pusan National University. Throughout his career, he has authored numerous research articles published in esteemed journals, showcasing his significant contributions to the field .