Related papers: On the probability flow in the Stock market I: The…
The market weight of a stock is its capitalization (cap) divided by the total market cap. Rank these weights from top to bottom. The capital distribution curve is a plot of weights versus ranks. For the US stock market, it is linear on a…
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for…
We use Wasserstein metrics adapted to study the action of the flow of the BBM equation on probability measures. We prove the continuity of this flow and the stability of invariant measures for finite times.
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback.…
We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully…
We propose a novel Black-Scholes model under which the stock price processes are modeled by stochastic differential equations driven by sub-diffusions. The new framework can capture the less financial activity phenomenon during the bear…
We give three derivations of Polya's approximation for the expected range of a simple random walk in one dimension. This result allows for an estimation of the volatility of a financial instrument from the difference between the high and…
The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete…
Fluid flows are typically studied by solving the Navier--Stokes equation. One of the fundamental assumptions of this equation is Stokes' hypothesis. This hypothesis assumes bulk viscosity, to be identically zero. The Stokes' hypothesis is a…
Based on empirical financial time-series, we show that the "silence-breaking" probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going…
In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume that an…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time,…
We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
The dynamics of a stock market with heterogeneous agents is discussed in the framework of a recently proposed spin model for the emergence of bubbles and crashes. We relate the log returns of stock prices to magnetization in the model and…