Related papers: Testing for an Explosive Bubble using High-Frequen…
We propose constructing confidence sets for the emergence, collapse, and recovery dates of a bubble separately by inverting tests for the location of the break date. We examine both likelihood ratio-type tests and the Elliott-Muller-type…
We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series. Our argument is based on the Log-Periodic Power Law Singularity (LPPLS)…
In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by…
Addressing the ongoing examination of high-frequency trading practices in financial markets, we report the results of an extensive empirical study estimating the maximum possible profitability of the most aggressive such practices, and…
In this paper we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the…
We study the nature of fluctuations in variety of price indices involving companies listed on the New York Stock Exchange. The fluctuations at multiple scales are extracted through the use of wavelets belonging to Daubechies basis. The fact…
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…
The stochastic leverage effect, defined as the standardized covariation between the returns and their related volatility, is analyzed in a stochastic volatility model set-up. A novel estimator of the effect is defined using a pre-estimation…
We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that $X$ has…
Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
Volatility-based trading strategies have attracted a lot of attention in financial markets due to their ability to capture opportunities for profit from market dynamics. In this article, we propose a new volatility-based trading strategy…
The Hawkes model is suitable for describing self and mutually exciting random events. In addition, the exponential decay in the Hawkes process allows us to calculate the moment properties in the model. However, due to the complexity of the…
We present a synthesis of all the available empirical evidence in the light of recent theoretical developments for the existence of characteristic log-periodic signatures of growing bubbles in a variety of markets including 8 unrelated…
It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This…
While the use of volatilities is pervasive throughout finance, our ability to determine the instantaneous volatility of stocks is nascent. Here, we present a method for measuring the temporal behavior of stocks, and show that stock prices…
We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and…
Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market…
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic…
As a forward-looking measure of future equity market volatility, the VIX index has gained immense popularity in recent years to become a key measure of risk for market analysts and academics. We consider discrete reported intraday VIX tick…