EXPANDED LIE GROUP TRANSFORMATIONS AND SIMILARITY REDUCTIONS FOR THE CELEBRITY BLACK-SCHOLES EQUATION IN FINANCE

In this study, we consider continuous groups of transformations acting on expanded space of variables, which includes the equation parameters in addition to independent and dependent variables. We have shown that the use of the expanded transformations and similarity reductions enable us to reduce celebrity Black-Scholes equation to formerly unknown reduced (target) ordinary differential equations. Moreover, the obtained reduced ordinary equations are used to find the exact solution of celebrity Black-Scholes equation in finance.