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Event Type
Research Presentation
Academic Department
Mathematics and Statistics
Location
Dana Science Building, 2nd floor
Start Date
14-4-2023 1:30 PM
End Date
14-4-2023 3:00 PM
Description
Under the direction of Dr. Emelie Curl
The Black-Scholes and Binomial option pricing models are two of the most well-known and widely used methods for valuing options in the financial world. There has been previous work to compare these notable valuation methods all of which highlight that one model is not more accurate and even more so that the valuations which these methods produce converge. We aim to confirm these facts for specific and potentially highly profitable contracts. Amazon is one of the world’s most valuable and semi-ubiquitous brands. The right to buy and sell stock in Amazon are therefore desirable options. This project focuses on those options and uses the relationship between the Binomial and Black-Scholes Option Pricing models as a conduit to predict these prized derivatives. In this research project, we will apply the Black-Scholes and Binomial option pricing patterns within the Python programming language to price the Amazon European Call/Put options using data provided by Yahoo Finance. We will verify that the generated option prices of both models satisfy the Put-Call Parity Equation, confirm that no arbitrage opportunities exist, and option premiums calculated by the Binomial model approach those of the Black-Scholes model. We further explore the relationship between the two models by comparing their respective option premiums as well as discussing the advantages and disadvantages of either model. Finally, we conclude that because both models in this research project use the same simple formula to calculate the stock’s volatility, a future research project would be to further increase both models’ accuracy by changing how we model volatility and therefore improve the precision of this prominent financial theory.
Implementation of Binomial and Black-Scholes Option Pricing Models in Python to Predict Amazon European Option Premiums
Dana Science Building, 2nd floor
Under the direction of Dr. Emelie Curl
The Black-Scholes and Binomial option pricing models are two of the most well-known and widely used methods for valuing options in the financial world. There has been previous work to compare these notable valuation methods all of which highlight that one model is not more accurate and even more so that the valuations which these methods produce converge. We aim to confirm these facts for specific and potentially highly profitable contracts. Amazon is one of the world’s most valuable and semi-ubiquitous brands. The right to buy and sell stock in Amazon are therefore desirable options. This project focuses on those options and uses the relationship between the Binomial and Black-Scholes Option Pricing models as a conduit to predict these prized derivatives. In this research project, we will apply the Black-Scholes and Binomial option pricing patterns within the Python programming language to price the Amazon European Call/Put options using data provided by Yahoo Finance. We will verify that the generated option prices of both models satisfy the Put-Call Parity Equation, confirm that no arbitrage opportunities exist, and option premiums calculated by the Binomial model approach those of the Black-Scholes model. We further explore the relationship between the two models by comparing their respective option premiums as well as discussing the advantages and disadvantages of either model. Finally, we conclude that because both models in this research project use the same simple formula to calculate the stock’s volatility, a future research project would be to further increase both models’ accuracy by changing how we model volatility and therefore improve the precision of this prominent financial theory.