Novel ANN method for solving ordinary and fractional Black-Scholes equation
This work addresses a domain-specific problem in computational finance by providing a potentially faster and more accurate solution method for pricing options, though it appears incremental as it builds on existing ANN and optimization techniques.
The authors tackled solving the Black-Scholes partial differential equation (both ordinary and fractional orders) by introducing a 2-layered Artificial Neural Network (ANN) method, achieving reported improvements in accuracy, speed, and convergence for various model types.
The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed to change the model into a sequence of Ordinary Differential Equations (ODE). Then each of these ODEs is solved with the aid of an ANN. Adam optimization is employed as the learning paradigm since it can add the foreknowledge of slowing down the process of optimization when getting close to the actual optimum solution. The model also takes advantage of fine tuning for speeding up the process and domain mapping to confront infinite domain issue. Finally, the accuracy, speed, and convergence of the method for solving several types of Black-Scholes model are reported.