Invariant solutions and linearized invariant submodels of some option pricing equations

Some subalgebras of the Lie algebra obtained earlier in the group classification of the option pricing model, taking into account costs and market influence, are considered. For a five-dimensional Lie algebra, invariant submodels are found in the case of one-dimensional subalgebras and invariant solutions are derived in the case of two-dimensional subalgebras of a general type. For three six-dimensional Lie algebras, one-dimensional and two-dimensional subalgebras are considered and exact solutions for a number of linearized invariant submodels are obtained.