Event Type
Research Presentation
Academic Department
Mathematics and Statistics
Location
Dana Science Building, 2nd floor
Start Date
25-4-2025 1:00 PM
End Date
25-4-2025 2:30 PM
Description
Under the direction of Dr. Giancarlo Schrementi
In 1973, Fischer Black and Myron Scholes introduced the Black-Scholes model as an objective quantitative method to price options that do not pay dividends. Over the years, this model has been modified to cover more complex derivatives and stocks, providing a foundational framework for traders and investors to understand option pricing in a systematic way. The formula is based on key assumptions that the volatility of the underlying asset remains unchanged through time and that the market returns should follow a constant log-normal distribution. However, these ideal assumptions do not always hold in practice, and one famous adaptation of the Black-Scholes formula is the Merton Jump Diffusion model, which extends theoriginal framework by incorporating sudden jumps in the underlying asset price. Previous works comparing these two models have shown that although the Merton Jump Diffusion model is generally considered a better version of Black-Scholes, it does come with disadvantages. When varying the strike price and considering different types of moneyness, Merton Jump Diffusion produces less accurate results unless hyperparameters such as jump intensity and magnitude are set at low values. The goal of this research is to confirm these facts using European call-and-put options from leading companies: Coca-Cola and BioNTech. Since both companies are in different fields with contrasting stock behaviors and characteristics, this difference allows us to evaluate Merton Jump Diffusion and Black-Scholes performance under different types of moneyness and strike price. Specifically, we will use Python to compare the accuracy of Black-Scholes and Merton Jump Diffusion models in valuing Coca-Cola and BioNTech call options under real-time conditions. We further vary the strike price to consider how the moneyness can impact the degree of mispricing. Finally, we discuss potential limitations of each model and conclude that since this project merely focuses on pricing simple call-and-put options, further research is needed to validate whether similar patterns are applied to other types of derivative.
When do jumps matter? A comparison of Black-Scholes and Merton Jump Diffusion models in pricing European Options
Dana Science Building, 2nd floor
Under the direction of Dr. Giancarlo Schrementi
In 1973, Fischer Black and Myron Scholes introduced the Black-Scholes model as an objective quantitative method to price options that do not pay dividends. Over the years, this model has been modified to cover more complex derivatives and stocks, providing a foundational framework for traders and investors to understand option pricing in a systematic way. The formula is based on key assumptions that the volatility of the underlying asset remains unchanged through time and that the market returns should follow a constant log-normal distribution. However, these ideal assumptions do not always hold in practice, and one famous adaptation of the Black-Scholes formula is the Merton Jump Diffusion model, which extends theoriginal framework by incorporating sudden jumps in the underlying asset price. Previous works comparing these two models have shown that although the Merton Jump Diffusion model is generally considered a better version of Black-Scholes, it does come with disadvantages. When varying the strike price and considering different types of moneyness, Merton Jump Diffusion produces less accurate results unless hyperparameters such as jump intensity and magnitude are set at low values. The goal of this research is to confirm these facts using European call-and-put options from leading companies: Coca-Cola and BioNTech. Since both companies are in different fields with contrasting stock behaviors and characteristics, this difference allows us to evaluate Merton Jump Diffusion and Black-Scholes performance under different types of moneyness and strike price. Specifically, we will use Python to compare the accuracy of Black-Scholes and Merton Jump Diffusion models in valuing Coca-Cola and BioNTech call options under real-time conditions. We further vary the strike price to consider how the moneyness can impact the degree of mispricing. Finally, we discuss potential limitations of each model and conclude that since this project merely focuses on pricing simple call-and-put options, further research is needed to validate whether similar patterns are applied to other types of derivative.