The application of Hamilton's principle in the financial market - Zhou, Yan (2015)
The financial market or an economy can be regarded as a system which is similar to the system of a physical entity which has relative definite governing rules. For example, the gravitational field which is governed by the Newton’s laws of motion. Hence, this project aims at finding such laws in a financial market and an economy by considering them an analogy to a physical system. What bridges the world of finance and economy and the world of physics is the study carried out by the econophysicists and the Hamilton’s principle from classical mechanics. The outline of this report is as such that the first part goes to the operation of the financial market by going through the concepts of stock, stock option, stock volatility, forward contract, modern portfolio theory, the Greek letters and hedging etc. The second part of this report is on the detailed study of the Black-Scholes model which is the cornerstone of the modern financial world. The derivation of the model is presented. The model is built on top of the previous works on the Brownian motion and Ito’s calculus. A closer examination of the derivation of the Black-Scholes partial differential equation has shown that there is a mathematical error in the model. The elegance of the Black-Scholes model is that it eliminates the variable which marks uncertainty. However, the mathematically right equation is derived but no longer eliminates the uncertainty variable. Therefore we are caught in a situation to either find an improvement of the model or establish new models. The possible way of improving the model is presented but the more exciting work is to find a new model or to identify the governing rules of the real market. Hence the third part of the report gives a summary of the recent establishment in the field of econophysics in terms of the kinetics of the market, the conservation law of the market and the entropy of the market etc. The fourth part presents the Hamilton’s principle as well as the proposal of this project.