Related papers: Markovian approximation in foreign exchange market…
Since its introduction, some sixty years ago, the Montroll-Weiss continuous time random walk has found numerous applications due its ease of use and ability to describe both regular and anomalous diffusion. Yet, despite its broad…
We empirically analyze the scaling properties of daily Foreign Exchange rates, Stock Market indices and Bond futures across different financial markets. We study the scaling behaviour of the time series by using a generalized Hurst exponent…
We consider a novel use case for the Double Heston model (Christoffersen et al,, 2009), where the two Heston sub-variances have different spot/volatility correlations but the same volatility of volatility and mean reversion speed. This…
We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
We focus on the influence of external sources of information upon financial markets. In particular, we develop a stochastic agent-based market model characterized by a certain herding behavior as well as allowing traders to be influenced by…
This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval {\Delta} results in…
This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
We study the continuous time random walk theory from financial tick data of the yen-dollar exchange rate transacted at the Japanese financial market. The dynamical behavior of returns and volatilities in this case is particularly treated at…
In this paper we describe three stochastic models based on a semi-Markov chains approach and its generalizations to study the high frequency price dynamics of traded stocks. The three models are: a simple semi-Markov chain model, an indexed…
Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of…
We study the performance of the euro/Swiss franc exchange rate in the extraordinary period from September 6, 2011 and January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Based on the…
This paper expands on stochastic volatility models by proposing a data-driven method to select the macroeconomic events most likely to impact volatility. The paper identifies and quantifies the effects of macroeconomic events across…
A new stochastic theory of a foreign exchange markets dynamics is developed. As a result we have the new probability distribution which well describes statistical and scaling dependencies ''experimentally'' observed in foreign exchange…
We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…
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…
This study presents contemporaneous modeling of asset return and price range within the framework of stochastic volatility with leverage. A new representation of the probability density function for the price range is provided, and its…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this…
We pose the estimation and predictability of stock market performance. Three cases are taken: US, Japan, Germany, the monthly index of the value of realized investment in stocks, prices plus the value of dividend payments (OECD data). Once…