Pseudo Hermitian formulation of Black-Scholes equation

Abstract

We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly constructed for this class of Hamitonians. It is also shown that the effective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system.

References in corpus (2)

• Quantum Finance
• Hamiltonian and Potentials in Derivative Pricing Models: Exact Results and Lattice Simulations

Cited by in corpus (4)

• A description of pseudo-bosons in terms of nilpotent Lie algebras
• Appearances of pseudo-bosons from Black-Scholes equation
• Susy for non-Hermitian Hamiltonians, with a view to coherent states
• Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing