We present a new theory of homogeneous volatility (and variance) estimators for arbitrary stochastic processes. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval by the joint distributions of the high-minusopen,...

We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process,...

We present a simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of intertrade...

We construct risk-neutral return probability distributions from S&P 500 options data over the decade 2003 to 2013, separable into pre-crisis, crisis and post-crisis regimes. The pre-crisis period is characterized by increasing realized and, especially, option-implied returns. This translates...

We present a new theory of homogeneous volatility (and variance) estimators for arbitrary stochastic processes. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval by the joint distributions of the high-minusopen,...

Zipf's law states that, for most countries, the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. We show that...

We present a new theory of homogeneous volatility (and variance) estimators for arbitrary stochastic processes. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval by the joint distributions of the high-minusopen,...

We present a theory of homogeneous volatility bridge estimators for log-price stochastic processes. The main tool of our theory is the parsimonious encoding of the information contained in the open, high and low prices of incomplete bridge, corresponding to given log-price stochastic process,...

Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes and effects. This review and essay evaluates some of...

Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes and effects. This review and essay evaluates some of...