ABSTRACT
Historically, financial economics has been cast in terms of linearized Newtonian physics, i.e., in the form of simple linear price or volatility diffusion equations. However, many phenomena in financial economics are complex, nonlinear, selforganizing, adaptive, feedback processes. An example is financial turbulence, which we currently conjecture to be a process to minimize friction between cash flows with different degrees of liquidity, with different investment horizons, or with different trading speeds, resulting in different degrees of persistence (Peters, 1994, pp. 39-64). Moreover, if an investment portfolio contains options as well as stocks, not only is the sum of lognormally distributed stock prices not lognormal, but the option price distribution is also complicated and the portfolio’s rates of return form a nonlinear process. Understanding these nonlinear pricing processes is of importance to portfolio management, dynamic asset valuation, derivative pricing, hedging and trading strategies, asset allocation, risk management and the development of market neutral strategies (cf. MacDonald, 2002, pp. 763-770).
