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

ater in economics, this area has attracted physicists and statistical mathematicians and engineers in significant numbers since at least the work of Champernowne. The reason is simple; to a statistical physicist, economics is obviously a multi-body phenomenon. It is messy. There are millions of agents in a t

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

lots of boundary conditions, may be simple enough to be tractable to a traditional statistical mechanical analysis on the lines of Dewar, or indeed Champernowne. Before moving into further discussion I would first like to follow the maths through a little more. I would like to do two things. Firstly I would

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

he details of income and wealth distributions have rarely been studied in mainstream theoretical economics, a notable and important exception being Champernowne. Champernowne was a highly gifted mathematician who was diverted into economics, he was the first person to bring a statistical mechanical approach