This project entails an in-depth analysis on the current mathematical methods used to calculate volatility in the stock market like the Black-Scholes Stochastic Partial Differential Equation (PDE). Ex..
This project entails an in-depth analysis on the current mathematical methods used to calculate volatility in the stock market like the Black-Scholes Stochastic Partial Differential Equation (PDE). Expanding upon the faculty mentor’s previously published work, a new method for calculating volatility using multiple linear regression on key macroeconomic factors was tested in predicting the price for the Standard and Poor’s 500 Index (S&P 500) for a given month. The results from the new volatility model were then compared with the well-known Chicago Board Options Exchange Volatility Index (VIX) since the VIX’s creation in 1991. While the new models for volatility could not be used to adequately price S&P 500 options for the future, it performed similar to VIX over time, and while the value for VIX was always high, the values for new volatility only spiked significantly when there was a potential crash in the market caused by weak fundamentals, like the dot com crash in 2001. With this information in hand, one could use a disparity between the regression model and the actual S&P 500 value to forecast a future crash caused by poor fundamentals in the market.
