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In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse the statistical properties of General Electric stock…
In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…
Volatility dynamics of wavelet - filtered stock price time series is studied. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative…
Studying the micro-trading behaviors before stock price jumps is an important problem for financial regulations and investment decisions. In this study, we provide a new framework to study pre-jump trading behaviors based on multivariate…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
The main focus of this work is to understand the dynamics of non regulated markets. The present model can describe the dynamics of any market where the pricing is based on supply and demand. It will be applied here, as an example, for the…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
A deterministic trading strategy can be regarded as a signal processing element that uses external information and past prices as inputs and incorporates them into future prices. This paper uses a market maker based method of price…
The price-bubble and crash process formation is theoretically investigated in a two-asset equilibrium model. Sufficient and necessary conditions are derived for the existence of average equilibrium price dynamics of different agent-based…
In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed…
We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for…
A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…
Grasping the historical volatility of stock market indices and accurately estimating are two of the major focuses of those involved in the financial securities industry and derivative instruments pricing. This paper presents the results of…
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…
We study the relation between the trading behavior of agents and volatility in toy markets of adaptive inductively rational agents. We show that excess volatility, in such simplified markets, arises as a consequence of {\em i)} the neglect…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
In this study, we introduce a physical model inspired by statistical physics for predicting price volatility and expected returns by leveraging Level 3 order book data. By drawing parallels between orders in the limit order book and…
We introduce the price probability measure {\eta}(p;t) that defines the mean price p(1;t), mean square price p(2;t), price volatility {\sigma}p2(t)and all price n-th statistical moments p(n;t) as ratio of sums of n-th degree values C(n;t)…
We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the…
In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation…