This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black–Scholes model is a simpler case that has a velocity dependent Lagrangian.

We study the range accrual swap in the quantum finance formulation of the Libor Market Model (LMM). It is shown that the formulation can exactly price the path dependent instrument. An approximate price is obtained as an expansion in the volatility of Libor. The Monte Carlo simulation method is...

This paper develops a model to describe the unequal time correlation between rate of returns of different stocks. A non-trivial fourth order derivative Lagrangian is defined to provide an unequal time propagator, which can be fitted to the market data. A calibration algorithm is designed to find...