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Sofie Jahnsen

Sofie Jahnsen
Analytical Finance
Handelshøyskolen ved UiA
12. desember 2022

Investor’s risk preferences and implied volatility smiles

From March to November, I had the honor to participate in a research project on implied volatility surfaces led by Professor Valeriy Zakamulin. As a student research assistant, my role was to review the numerical results of this project, which was related to my previous courses on ”Investments”, ”Derivatives” and the operational statistical programming language R.

The implied volatility surface captures cross-sectional information on implied volatilities as a two-dimensional function of option strike price and time to expiration. The well-known Black-Scholes option pricing model predicts that the shape of the implied volatility surface is flat. However, empirical studies have revealed mixed results. This project contributes to the existing literature by evoking the utility indifference argument to explain this phenomena in a completely new way. For instance, the standard utility function used in mainstream finance produces a flat implied volatility surface shape. In stark contrast, behavioral finance-driven utility functions generate implied volatility surface shapes that more closely resemble those observed in real markets. The findings are expected to yield insight of implication for option pricing management and risk management.

During this time, I developed a solid theoretical understanding of various utility functions under normal and non-normal distributions. In practice, I was able to utilize numerical analysis tools in the statistical software R to optimize, compute and finally obtain the implied volatility surface shapes of different models. This project did not merely challenge my current accumulation of knowledge, but also optimized it on a larger scale.

I would like to convey my sincere appreciation to Professor Valeriy Zakamulin for providing me with this great opportunity, and always patiently responding and helping me to solve the problems I encountered. This is a valuable experience I gained during my study at UiA, and I highly recommend others to experience it as well.