HIGHER DERIVATIVE MODELS AND LIBOR MARKET MODEL IN QUANTUM FINANCE

Abstract

This thesis is focused on the Lagrangian with acceleration models for interest rates, equities and foreign exchange rates.

The quantum finance Libor market model is empirically studied.

The equity model was developed to calibrate the unequal time correlation of stock market data. The detailed results of this Gaussian model show that the different stocks can have strong correlation and the empirical unequal time correlator can be described by the model¿s propagator.

The at the money (ATM) option volatility of foreign exchange rate is obtained from solving the classical equation of Lagrangian with acceleration in Euclidean time. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. The volatility formula was calibrated with market data.