Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
(BQ) Part 2 book "Quantitative finance for physicists an introduction" has contents: Nonlinear dynamical systems, scaling in financial time series, option pricing, portfolio management, portfolio management, agent based modeling of financial markets. | Chapter 7 Nonlinear Dynamical Systems 7.1 MOTIVATION It is well known that many nonlinear dynamical systems, including seemingly simple cases, can exhibit chaotic behavior. In short, the presence of chaos implies that very small changes in the initial conditions or parameters of a system can lead to drastic changes in its behavior. In the chaotic regime, the system solutions stay within the phase space region named strange attractor. These solutions never repeat themselves; they are not periodic and they never intersect. Thus, in the chaotic regime, the system becomes unpredictable. The chaos theory is an exciting and complex topic. Many excellent books are devoted to the chaos theory and its applications (see, e.g., references in Section 7.7). Here, I only outline the main concepts that may be relevant to quantitative finance. The first reason to turn to chaotic dynamics is a better understanding of possible causes of price randomness. Obviously, new information coming to the market moves prices. Whether it is a company’s performance report, a financial analyst’s comments, or a macroeconomic event, the company’s stock and option prices may change, thus reflecting the news. Since news usually comes unexpectedly, prices change in unpredictable ways.1 But is new information the only source reason for price randomness? One may doubt this while observing the price fluctuations at times when no relevant news is 69 70 Nonlinear Dynamical Systems released. A tempting proposition is that the price dynamics can be attributed in part to the complexity of financial markets. The possibility that the deterministic processes modulate the price variations has a very important practical implication: even though these processes can have the chaotic regimes, their deterministic nature means that prices may be partly forecastable. Therefore, research of chaos in finance and economics is accompanied with discussion of limited predictability of the processes under investigation
