We analyze the Black‐Scholes model with time‐dependent parameters, and it is governed by a parabolic partial differential equation (PDE). First, we compute the Lie symmetries of the Black‐Scholes model with time‐dependent parameters. It admits 6 plus infinite many Lie symmetries, and thus, it can be reduced to the classical heat equation. We use the invariant criteria for a scalar linear (1+1) parabolic PDE and obtain 2 sets of equivalence transformations. With the aid of these equivalence transformations, the Black‐Scholes model with time‐dependent parameters transforms to the classical heat equation. Moreover, the functional forms of the time‐dependent parameters in the PDE are determined via this method. Then we use the equivalence transformations and known solutions of the heat equation to establish a number of exact solutions for the Black‐Scholes model with time‐dependent parameters.