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2020 Projects

Empirical Testing of Option Pricing Models

Rujun (Gillian) Xu ’21; Yinting Zhong ’22
Major: Psychology; Undecided

Rujun (Gillian) Xu ’21; Yinting Zhong ’22

Major: Psychology; Undecided

Minor: Mathematics

Research Collaborator: John Koerner ’20

Faculty Collaborator: Flavia Sancier-Barbosa, Mathematics & Computer Science

This project enacted the Option Pricing model from last summer, which was developed by Flavia Sancier-Barbosa and Makayla McDevitt. The model was developed to predict the future index prices using currently available prices. This current study aimed to assess how well the model could perform in the current 2020 financial crisis, compared with the previous Black-Scholes model that has been developed and used for index prices. This project is completed by Flavia Sancier-Barbosa, John Koerner, Yinting Zhong, and Rujun Xu. We first tested dates before and during the crisis to determine the memory length and simulation so that the model takes enough data into account without losing predictability at the same time. At last, we decided to run daily price data for 97 dates, half before and the other half during the crisis for the following three indexes: the Russell index, the S&P 500 index, and the S&P 100 index.For the Russell index (RUT), when there were noticeable differences between two models, the Black-Scholes model mostly outperformed the Model with memory. Both models tended to better fit the actual data with smaller strike prices than larger strike prices and had better performance with shorter expiration time compared with longer expiration time for most dates. Besides, both models consistently overestimate the data.For the S&P500 index (SPX), Black-Scholes model performs better than Option Pricing model in most of the cases, though both models overestimate the data. One example when BS performs better is when expiration time is larger than 254 days.For the S&P100 index (XEO), both BS model and OP model perform better and more stable for current crisis than before crisis. Using longer memory lengths bring less errors and more accuracy for the models compared with the data. The two models predict well for small expiration dates, but need to work on longer expiration dates like bigger than 100 days.

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