Epstein Secrets

city. However, while a few contractors (including GM Hughes, Grumman, and McDonnell Douglas) have div

figures 1.1.1-3 above. This data suggests that a Maxwell-Boltzmann distribution also provides a very good

rprising, as it is known that the log- normal and the Maxwell-Boltzmann have exponential tails, and so are not

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

e should fit together in this way, and in fact it wasn't until many years later that the equation was independently explained at an atomic level by Maxwell and Boltzmann. Thirdly, the equations do not refer to underlying microscopic mechanisms or variables. In equation (4.7a) there are no references to

l regularity and predictability in the aggregate. The Maxwell-Boltzmann-Gibbs methods of statistical mechanics

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

ssipative structure approach, presumably there is a negentropy flow associated with 'maintaining' the dissipative structure in its low entropy form; Maxwell's demon is continually at work narrowing the spread of the distribution. However if this negentropy flow is smaller than the entropy flow through t

distribution [Levy & Solomon 1996]. In contrast the Maxwell-Boltzmann distribution of a normal thermodynamic

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