Related papers: Volatility and Arbitrage
This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage…
We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors…
Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe…
We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family $\mathcal{P}$ of possible physical measures. A robust notion ${\rm NA}_{1}(\mathcal{P})$ of no-arbitrage of the first…
This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of…
Using high frequency data, we have studied empirically the change of volatility, also called volatility derivative, for various time horizons. In particular, the correlation between the volatility derivative and the volatility realized in…
We conclude from an analysis of high resolution NYSE data that the distribution of the traded value $f_i$ (or volume) has a finite variance $\sigma_i$ for the very large majority of stocks $i$, and the distribution itself is non-universal…
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of…
The variance measures the portfolio risks the investors are taking. The investor, who holds his portfolio and doesn't trade his shares, at the current time can use the time series of the market trades that were made during the averaging…
We exploit a continuous time random walk description of stock prices to obtain a fast and accurate evaluation of their volatility from intraday data. We show that financial markets are usefully described as open physical systems. Indeed we…
The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which…
We consider economic obstacles that limit the reliability and accuracy of value-at-risk (VaR). Investors who manage large market transactions should take into account the impact of the randomness of large trade volumes on predictions of…
We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of…
We consider an arbitrage-free, discrete time and frictionless market. We prove that an investor maximising the expected utility of her terminal wealth can always find an optimal investment strategy provided that her dissatisfaction of…
The discrepancy between realized volatility and the market's view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast's ability to predict…
We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market…
We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can…
We present the unified market-based description of returns and variances of the trades with shares of a particular security, of the trades with shares of all securities in the market, and of the trades with the market portfolio. We consider…
Working on different aspects of algorithmic trading we empirically discovered a new market invariant. It links together the volatility of the instrument with its traded volume, the average spread and the volume in the order book. The…
We reanalyze high resolution data from the New York Stock Exchange and find a monotonic (but not power law) variation of the mean value per trade, the mean number of trades per minute and the mean trading activity with company…