اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPower, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems
143
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents $alpha$ of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Levy regime $alpha < 2$, the power law decay with large exponent ($alpha > 2$), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement.
قيم البحث
اقرأ أيضاً
We investigate the herd behavior of returns for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution $P(R)$ of returns $R$ satisfies the power-law behavior $P(R) simeq R^{-beta}$ with the exp
onents $ beta=3.11$(the time interval $tau=$ one minute) and 3.36($tau=$ one day). The informational cascade regime appears in the herding parameter $Hge 2.33$ at $tau=$ one minute, while it occurs no herding at $tau=$ one day. Especially, we find that the distribution of normalized returns shows a crossover to a Gaussian distribution at one time step $Delta t=1$ day.
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L{e}vy distribution. For
both (i) and (ii), we find that due to the correlations in the variance, the process ``dynamically generates power-law tails in the distributions, whose exponents can be controlled through the way the correlations in the variance are introduced. For (ii), we find that the process can extend a truncated distribution {it beyond the truncation cutoff}, which leads to a crossover between a L{e}vy stable power law and the present ``dynamically-generated power law. We show that the process can explain the crossover behavior recently observed in the $S&P500$ stock index.
Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed. We develop a new and alternative method to estimate this
noise. To this end, we simulate certain time series and random matrices which can model financial correlations. With our approach, different correlation structures buried under this noise can be detected. Moreover, we introduce a measure for the relation between noise and correlations. Our method is based on a power mapping which efficiently suppresses the noise. Neither further data processing nor additional input is needed.
We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock prices traded
in are consistent approximately with the Zipfs law or a power law. It is also obtained that the probability density of normalized returns for listed stocks almost has the form of the exponential function. Our results are compared with those of other numerical calculations.
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first
-passage time probability and expected occupation time of sets of a Levy bridge process that relies in part on a randomisation of the time parameter. We establish this recursion for general Levy processes and derive its explicit form for mixed-exponential jump-diffusions, a dense subclass (in the sense of weak approximation) of Levy processes, which includes Brownian motion with drift, Kous double-exponential model and hyper-exponential jump-diffusion models. We present a highly accurate numerical realisation and derive error estimates. By way of illustration the method is applied to the valuation of range accruals and barrier options under exponential Levy models and Bates-type stochastic volatility models with exponential jumps. Compared with standard Monte Carlo methods, we find that the method is significantly more efficient.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
