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We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the…
This paper examines volatility in REITs using a multivariate GARCH based model. The Multivariate VAR-GARCH technique documents the return and volatility linkages between REIT sub-sectors and also examines the influence of other US equity…
The correlation coefficient between stocks depends on price history and includes information on hierarchical structure in financial markets. It is useful for portfolio selection and estimation of risk. I introduce the Life Time of…
In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling price fluctuations as GARCH(1,1) process. The…
Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility…
We propose a set of dependence measures that are non-linear, local, invariant to a wide range of transformations on the marginals, can show tail and risk asymmetries, are always well-defined, are easy to estimate and can be used on any…
In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable…
HYGARCH model is basically used to model long-range dependence in volatility. We propose Markov switch smooth-transition HYGARCH model, where the volatility in each state is a time-dependent convex combination of GARCH and FIGARCH. This…
We consider the randomness of market trade as the origin of price and return stochasticity. We look at time series of trade values and volumes as random variables during the averaging interval {\Delta} and describe the dependences of…
We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the…
Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…
The influence of the past price behaviour on the realized volatility is investigated in the present article. The results show that trending (drifting) prices lead to increased (decreased) realized volatility. This ``volatility induced by…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…
It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect.…
Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We establish that this so-called gain/loss asymmetry is present also for…
We review the advancement of nonstationary time series analysis from the perspective of Cowles Commission structural equation approach. We argue that despite the rich repertoire nonstationary time series analysis provides to analyze how do…
Science progresses by building upon previous discoveries. It is commonly believed that the impact of scientific papers, as measured by citations, is positively correlated with the impact of past discoveries built upon. However, analyzing…
The lack of predictability of citation-based measures frequently used to gauge impact, from impact factors to short-term citations, raises a fundamental question: Is there long-term predictability in citation patterns? Here, we derive a…
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…
Stress time series from the PLC effect typically exhibit stick-slips of upload and download type. These data contain strong short-term correlations of a nonlinear type. We investigate whether there are also long term correlations, i.e. the…