Epstein Secrets

andom walk process has been removed from it's many body background, and individual prices are treated as moving randomly isolated by themselves. But Black-Scholes is simply the diffusion equation, and things don't diffuse with random jumps in a vacuum. The random movements of dust particles undergoing Brownia

that this chaotic motion is noticeable in objects as large as planets. This is not simply the chaos of quantum effects or the stochasticity found in Black-Scholes. This is 'deterministic chaos' or usually 'chaos theory'. The chaos is present even in problems that can be described in exact mathematics and are

this is a chaotic model, not a stochastic one. There is no stochasticity in this model. All fluctuations in the model are created endogenously from the Lotka-Volterra like differential equations in the model. Figure 4.3.4 shows the detail of couple of cycles. Figure 4.3.4 here These are real live Minskian / Aus

The research on liquidity suggests two implications for finance that are both quite profound, the first area relates to the pricing models based on Black-Scholes, the second to the pricing of shares under the CAPM. Almost all modern option pricing theory is based on the Black-Scholes model, or other closely-

sible), then it may be that measurement of liquidity might be able to give good timely measures for current volatility that can be used directly in Black-Scholes models; rather than the current practice of imputing from historical volatility. A second significant area of interest for the application of liqui

al and ecological scientists have the right mathematical tools for creating a radical and effective new economics, both specifically in the form of the Lotka-Volterra and maximum entropy production models, and more generally in their understanding of complex inter-related evolving systems. Ultimately this maths f

ists working in finance have not only accepted this, but they have built more and more baroque models on these flimsy foundations. The trouble with Black-Scholes is that it works very well, except when it doesn't. This basic flaw has been pointed out from Mandlebrot onwards, to date with no notice taken. Thi

rom top to bottom. But this still results in a distribution with a large bias giving most of the wealth to a minority of individuals. Going back to the Lotka-Volterra and GLV models discussed in section 1.2, it is better to abandon the predator-prey model of foxes killing rabbits, and instead think in terms of a '