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Abstract:
Options traders use a pricing formula which they adapt by fudging and changing the tails and skewness by varying one parameter, the standard deviation of a Gaussian. Such formula is popularly called "Black-Scholes-Merton" owing to an attributed eponymous discovery (though changing the standard deviation parameter is in contradiction with it). However we have historical evidence that 1) Black, Scholes and Merton did not invent any formula, just found an argument to make a well known (and used) formula compatible with the economics establishment, by removing the "risk" parameter through "dynamic hedging", 2) Option traders use (and evidently have used since 1902) heuristics and tricks more compatible with the previous versions of the formula of Louis Bachelier and Edward O. Thorp (that allow a broad choice of probability distributions) and removed the risk parameter by using put-call parity. 3) Option traders did not use formulas after 1973 but continued their bottom-up heuristics. The Bachelier-Thorp approach is more robust (among other things) to the high impact rare event. The paper draws on historical trading methods and 19th and early 20th century references ignored by the finance literature. It is time to stop calling the formula by the wrong name.

Option pricing, put-call parity, delta hedging, Black-Scholes-Merton, Bachelier, Thorp

Abstract:
Finance professionals, who are regularly exposed to notions of volatility, seem to confuse mean absolute deviation with standard deviation, causing an underestimation of 25% with theoretical Gaussian variables. In some fat tailed markets the underestimation can be up to 90%. The mental substitution of the two measures is consequential for decision making and the perception of market variability.

finance, volatility, risk, intuition, statistics, metrics

Abstract:
While modern financial theory holds that options values are derived by dynamic replication, they can be correctly valued far more simply by long familiar static and actuarial arguments that combine stochastic price evolution with the no-arbitrage relation between cash and forward contracts.

Option Pricing, Replication, Valuation,

Abstract:
Outside the Platonic world of financial models, assuming the underlying distribution is a scalable power law, we are unable to find a consequential difference between finite and infinite variance models - a central distinction emphasized in the econophysics literature and the financial economics tradition. While distributions with power law tail exponents α>2 are held to be amenable to Gaussian tools, owing to their finite variance, we fail to understand the difference in the application with other power laws (1<α<2) held to belong to the Pareto-Lévy-Mandelbrot stable regime. The problem invalidates derivatives theory (dynamic hedging arguments) and portfolio construction based on mean-variance. This paper discusses methods to deal with the implications of the point in a real world setting.

Portfolio theory, power laws, option pricing, fat tails, risk management

Abstract:
The paper presents evidence that econometric techniques based on variance- L2 norm are flawed -and do not replicate. The result is un-computability of role of tail events. The paper proposes a methodology to calibrate decisions to the degree (and computability) of forecast error. It classifies decision payoffs in two types: simple payoffs (true/false or binary) and complex (higher moments); and randomness into type-1 (thin tails) and type-2 (true fat tails) and shows the errors for the estimation of small probability payoffs for type 2 randomness. The Fourth Quadrant is where payoffs are complex with type-2 randomness. We propose solutions to mitigate the effect of the Fourth Quadrant based on the nature of complex systems.

complexity, decision theory, fat tails, risk management

Abstract:
Large institutions are disproportionately more fragile to Black Swans.

This paper establishes the case for a fallacy of economies of scale in large aggregate institutions. The problem of rogue trading is taken as a case example of hidden risks where rogue traders and losses are considered independently and dependently of the institution’s size. Both independent and dependent loss and hidden positions are shown to lead to the paper’s conclusion, that size and economies of scale have commensurate risks that mitigate the advantages of size.

economies of scale, banking crisis, risk management, operational risk

Abstract:
The point of The Black Swan is that both empirical knowledge (i.e. extrapolating statistics) and a priori theories fail in the tails and it is vital to "robustify" against it using the concepts of "the fourth quadrant". The point has been garbled by members of the economics establishment that claim mistakenly "we know that" and "we know about fat tails" or "power laws". This is both wrong and not my point. The paper presents corrections to the misperceptions.

Black Swan, Risk Management, Finance, Markets

Abstract:
This paper examines the risk externalities stemming from the size of institutions. Assuming (conservatively) that a firm risk exposure is limited to its capital while its external (and random) losses are unbounded we establish a condition for a firm to be too big to fail. In particular, expected risk externalities’ losses conditions for positive first and second derivatives with respect to the firm capital are derived. Examples and analytical results are obtained based on firms’ random effects on their external losses (their risk externalities) and policy implications are drawn that assess both the effects of “too big to fail firms” and their regulation.

banking crisis, risk management, too big to fail