The wave function more generally spoken the state vector of the quantum system is an element of a linear vector space. In quantum mechanics physically measurable quantities such as energy, position and so on are represented by Hermitian operators that map the linear vector space on itself. The Hamilton operator evolves the system in time. Whereas the Hamilton operator in quantum mechanics is hermitian (Schrödinger equation) in finance it is in general not. Let us take a look at the Black Scholes equation (used for example for option pricing with constant volatility)
Changing of the variable
leads us to a "Black-Scholes-Schrödinger" equation
with the Black Scholes Hamiltonian given by
Seen as a quantum mechanical system, the Black-Scholes equation has one degree of freedom (x). Next week we will compare properties of the Schrödinger equation with properties of our Black-Scholes Schrödinger equation.