Simple Heuristic Approach To Introduction Of The Black-Scholes Model

A heuristic approach to explaining of the Black-Scholes option pricing model in undergraduate classes is described. The approach draws upon the method of protocol analysis to encourage students to `think aloud' so that their mental models can be surfaced. It also relies upon extensive visualizations to communicate relationships that are otherwise inaccessible at the average student's level of mathematical sophistication. This paper presents visual illustration of the changes in the probability measures with concrete examples breaking the option premium into four different components. The relationship between changes in variables and those components are graphically and algebraically illustrated

Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

The multifractal model of asset returns captures the volatility persistence of many financial time series. Its multifractal spectrum computed from wavelet modulus maxima lines provides the spectrum of irregularities in the distribution of market returns over time and thereby of the kind of uncertainty or randomness in a particular market. Changes in this multifractal spectrum display distinctive patterns around substantial market crashes or drawdowns. In other words, the kinds of singularities and the kinds of irregularity change in a distinct fashion in the periods immediately preceding and following major market drawdowns. This paper focuses on these identifiable multifractal spectral patterns surrounding the stock market crash of 1987. Although we are not able to find a uniquely identifiable irregularity pattern within the same market preceding different crashes at different times, we do find the same uniquely identifiable pattern in various stock markets experiencing the same crash at the same time. Moreover, our results suggest that all such crashes are preceded by a gradual increase in the weighted average of the values of the Lipschitz regularity exponents, under low dispersion of the multifractal spectrum. At a crash, this weighted average irregularity value drops to a much lower value, while the dispersion of the spectrum of Lipschitz exponents jumps up to a much higher level after the crash. Our most striking result, therefore, is that the multifractal spectra of stock market returns are not stationary. Also, while the stock market returns show a global Hurst exponent of slight persistence 0.5Financial Markets, Persistence, Multi-Fractal Spectral Analysis, Wavelets

Blockchain angels or demons of a free international order

"Decentralization and Democratization" is the main promise behind the distributed ledger technology that attracted enthusiasts looking for ways to prop our ailing global socio-economic system. Not surprisingly its best known application "Bitcoin" comes as the "panacea" against the worst offender in the neoliberal order, the Financial Industry. Trends, fads and myths about blockchain technology fuel the imagination allowing for proliferation of hypes and disappointment. This paper offers a discussion of possible blockchain applications for polycentric governance of socio-economic systems in light of building sustainability and resilience. On the opposite side I will analyze the possibility for misuse (e.g. the Internet of Things) of the technology to build ever stronger centralized control system lacking adaptive capacity and leading to total collapse