Minnesota Center for Financial and Actuarial Mathematics
MCFAM Seminar - FM Graduate Student Presentations
These talks were prepared by MCFAM graduate students participating in directed study (FM5993) during the 2023 summer term under John Dodson's guidance.
Presenter: Abdullahi Abdullahi
Title: A study on simulating financial market dynamics using a mean field approximation incorporated three-state opinion dynamics model
Abstract: This research work investigates the application of a three-state opinion dynamics model to simulate financial market dynamics. This model, which captures the wide-ranging decision-making behaviors of market participants, is implemented using Mean Field Approximation (MFA) to ease computational complexities. The validity of this model is scrutinized using empirical data and the model's accuracy in reflecting real-world financial market dynamics is discussed.
Presenter: Linghe Gong
Title: Option smile from an information-based asset pricing model
Abstract: Implied volatility is crucial for understanding market views on future stock price changes and is key for predicting asset prices, especially in option pricing and risk management. Lane Hughston’s information process model explains the relationship between asset prices and the flow of information. This model, however, assumes that all market players have the same expectations and respond similarly to news, which is not always true. A known challenge with implied volatility is its unpredictable nature, often seen in the ”volatility smile” or ”skew” of the volatility surface. Even widely-accepted models like Black-Scholes cannot explain this. Hughston’s model focuses on assets rather than derivatives. To value options, we have introduced a risk premium concept, based on the Constant Relative Risk Aversion (CRRA) utility. This function helps to factor in risk preferences of investors. With this addition, the model can better represent actual market risks and the diverse risk-taking behavior of investors. Our research shows that this improved model can replicate the volatility smile when set with the right parameters. It offers a more accurate depiction of market activities and emphasizes the need to combine human behavior insights with mathematical models for a better grasp of market complexities. This paves the way for better option pricing and risk management methods.
Presenter: Heeth Surana
Title: A HAR-DRD implementation using low-frequency OHLC candlestick data
Abstract: A new approach to the HAR-DRD model is developed using lower frequency daily candle-stick price (Open, High, Low, Close) data. Contrary to using a noisy and expensive measure for daily realized volatility with squared intraday returns sampled at high frequency, we employ an alternative estimator for daily realized volatility that only uses daily candlestick prices. Additionally, daily correlation estimation and forecasting is replaced by weekly correlation forecasts on a daily rolling basis, in favor of producing less noisy and more stable correlation forecasts. The model is calibrated (2002-2017) and tested (2018-2022) in the context of a portfolio of four assets: US 10-Year Treasuries, US S&P 500 Index, WTI Crude Oil, and Gold. Evaluation of out-of-sample forecasting errors show the model is reasonably stable across time. Testing the model in a minimum variance portfolio optimization problem yields favorable portfolio outcomes.