Related papers: Price, Volatility and the Second-Order Economic Th…
We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow…
Managing a portfolio to a risk model can tilt the portfolio toward weaknesses of the model. As a result, the optimized portfolio acquires downside exposure to uncertainty in the model itself, what we call "second order risk." We propose a…
We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically…
In this paper, we propose a price staleness factor model that accounts for pervasive market friction across assets and incorporates relevant covariates. Using large-panel high-frequency data, we derive the maximum likelihood estimators of…
A new multiagent model of the stock market is formulated that contains four states in which the agents may be located. Next, the model is reformulated in the language of the functional integral containing fluctuations of prices and…
This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the…
We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price…
Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and…
Risk management in financial derivative markets requires inevitably the calculation of the different price sensitivities. The literature contains an abundant amount of research works that have studied the computation of these important…
During a speculative episode the price of an item jumps from an initial level p_1 to a peak level p_2 before more or less returning to level p_1. The ratio p_2/p_1 is referred to as the amplitude A of the peak. This paper shows that for a…
We build on theoretical results from the mechanism design literature to analyze empirical models of second-degree price discrimination (2PD). We show that for a random-coefficients discrete choice ("BLP") model to be suitable for studying…
We will compare three types of prices, namely, rational (hedging) prices, geometric (growth rate) prices, and martingale (measure) prices. We will show that rational prices in the complete market theory are sometimes contrary to common…
This paper proposes an alternative to the classical price-adjustment mechanism (called "t\^{a}tonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic…
We confirm and substantially extend the recent empirical result of Andersen et al. \cite{Andersen2015}, where it is shown that the amount of risk $W$ exchanged in the E-mini S\&P futures market (i.e. price times volume times volatility)…
The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change…
We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are…
Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…
Realization of uncertainty of prices is captured by volatility, that is the tendency of prices to vary along a period of time. This is generally measured as standard deviation of daily returns. In this paper we propose and investigate the…
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…