Stochastic Society

Abstract

In this chapter we give some examples of applying the stochastic methods to financial markets and economy. The volatile character of prices and economic indicators is a manifestation of significantly stochastic dynamics of the corresponding systems, and the δW term plays the leading role in the Ito equations. First we make a small diversion into the financial markets and the empirical properties of financial instruments’ prices. Then we consider the theory of diversification and beta-coefficients. Stochastic methods appear to be very useful when studying the complex financial instruments. Options are one example of such instrument. We will consider the main properties of the options and derive the Black-Scholes formula in two different ways. After that a simple one-factor model of the yield curve will be considered.