Improving Analytic Approximation of Log-Normal Interest Rate Model with Neural Network

Interest rates have long been at the foundation of financial modelling, and as a result the dynamics of interest rates has received substantial scrutiny. As part of this log-normal models were developed to increase the plausibility of rate dynamics in stochastic context. In particular, within Black-Karasinski model the equation governing process has only one difference relative to the normal models like Hull-White, but this change makes the model intractable. With increased interest of tackling the problem, come new perspectives as to how to increase the accuracy of these approaches. The class path integral estimation which is one of the more recent attempts at approximation to analytic pricing of financial instruments with this model produces an approach which is open to enhancements with Neural Network. The research demonstrates that the method is able to achieve superior outcomes for multiple calibrations across extended projection horizons.