Physics of Finance

We give a brief introduction to the Gauge Theory of Arbitrage [1]. Treating a calculation of net present values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. This allows us to map the theory of capital market onto the theory of quantized gauge field interacted with a money flow field. The gauge transformations of the matter field correspond to a dilatation (redefinition) of security units which effect is eliminated by a proper tune of the connection. The curvature tensor for the connection consists of the excess returns to the risk-free interest rate for the local arbitrage operation. Free quantum gauge theory is equivalent to the assumption about the lognormal walks of assets prices. In general case the consideration maps the capital market onto QED, i.e. quantum system of particles with positive (securities) and negative (”debts”) charges which interact with each other through electromagnetic field (gauge field of the arbitrage). In the case of a local virtual arbitrage opportunity money flows in the region of configuration space (money poor in the profitable security) while ”debts” try to escape from the region. Entering positive charges and leaving negative ones screen up the profitable fluctuation and restore the equilibrium in the region where there is no arbitrage opportunity any more, i.e. speculators washed out the arbitrage opportunity.