A Regression Model to Investigate the Performance of Black-Scholes using Macroeconomic Predictors

Timothy A. Smith; Ersoy Subasi; Aliraza M Rattansi

doi:https://doi.org/10.14445/22315373/IJMTT-V5P527

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 5 | Number 2 | Year 2014 | Article Id. IJMTT-V5P527 | DOI : https://doi.org/10.14445/22315373/IJMTT-V5P527

A Regression Model to Investigate the Performance of Black-Scholes using Macroeconomic Predictors

Timothy A. Smith , Ersoy Subasi , Aliraza M Rattansi

Abstract

As it is well known an option is defined as the right to buy sell a certain asset, thus, one can look at the purchase of an option as a bet on the financial instrument under consideration. Now while the evaluation of options is a completely different mathematical topic than the prediction of future stock prices, there is some relationship between the two. It is worthy to note that henceforth we will only consider options that have a given fixed expiration time T, i.e. we restrict the discussion to the so called European options. Now, for a simple illustration of the relationship between true stock prices and options let us consider the following situation: if at the begging of January the S&P index is valued at $1277 and then at the end of December of the same year the price of the index became $1400 then the fair price of the option to buy this in January would be $123, assuming T=1. This is a fair price because if the holder purchases the option for $122 or less then he or she gains while if the holder purchases the option for $124 or more then the bank wins while $123 is neutral for both parties. As one can see from this simple illustration predicting the fair price of an option is directly related to predicting the value of the stock price in a future time T.

Keywords

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

References

[1] Black, Fisher and Scholes, Myron. “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81 (3), 1973.
[2] Stewart, Ian. “The Mathematical equation that caused the banks to crash,” The Observer 2/12/12, 2012.
[3] Park, Sam. “Reducing the Noise in Forecasting the SP 500,” Wentworth, 2005.

Citation :

Timothy A. Smith , Ersoy Subasi , Aliraza M Rattansi, "A Regression Model to Investigate the Performance of Black-Scholes using Macroeconomic Predictors," International Journal of Mathematics Trends and Technology (IJMTT), vol. 5, no. 2, pp. 108-111, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V5P527