Using a Multiple Linear Regression Model to Calculate Stock Market Volatility

Timothy A. Smith; with Alex Caligiuri; J Rhet Montana

doi:https://doi.org/10.14445/22315373/IJMTT-V57P531

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 4 | Year 2018 | Article Id. IJMTT-V57P531 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P531

Using a Multiple Linear Regression Model to Calculate Stock Market Volatility

Timothy A. Smith, with Alex Caligiuri, J Rhet Montana

Citation :

Timothy A. Smith, with Alex Caligiuri, J Rhet Montana, "Using a Multiple Linear Regression Model to Calculate Stock Market Volatility," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 4, pp. 220-224, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P531

Abstract

In mathematical finance, regression models can be used to determine the value of an asset based on its underlying traits and/or returns relative to the overall market performance. In prior work [6-7] a regression model was created to predict the value of the S&P 500 based on macroeconomic indicators. In the current study the model is updated with the addition of recent data, and then applied to define a new measure to model market volatility. The results are compared to the S&P 500’s implied volatility in a simulation utilizing the BlackSholes model attempting to predict the value of the S&P 500 one year in the future. While no definition could be expected to perfectly predict the market volatility, the new definitions of volatility did outperform the currently utilized implied volatility.

Keywords

Partial differential equations, regression analysis, stochastic, financial mathematics. AMS classification: 35K10.

References

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[3] Moyaert, T. & Petitjean, M . “The performance of popular stochastic volatility option pricing models during the subprime crisis.” Applied Financial Economics. 21(14), 2011.
[4] Summa, John; Option Volatiliy: Historical Volatility, Investopedia (2007)
[5] Park, Sam. “Reducing the Noise in Forecasting the SP 500,” Wentworth, 2005.
[6] Smith, T. et al, “A Regression Model to Predict Stock Market Mega Moverments and/or Volatility using both Macroeconomic indicatiors & Fed Bank Variables.” International Journal of Mathematics Trends and Technology, 2017.
[7] Smith, T. at al, “An Economic Regression Model to Predict Market Movements.” International Journal of Mathematics Trends and Technology, 2014
[8] Smith, T. et al, “A regression model to investiage the performance of the Black-Sholes using macroeconomic predictors.” International Journal of Mathematics Trends and Technology, 2013.