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Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads…
This work builds upon the long-standing conjecture that linear diffusion models are inadequate for complex market dynamics. Specifically, it provides experimental validation for the author's prior arguments that realistic market dynamics…
We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
The distribution of the return intervals $\tau$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined…
Fluctuation theorems show how coarse graining transforms microscopic symmetry into observable irreversibility. Here we ask whether an analogous symmetrybased diagnostic can be constructed for financial markets. At the microscopic level,…
The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions…
Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture…
The daily volume of transaction on the New York Stock Exchange and its day-to-day fluctuations are analysed with respect to power-law tails as well long-term trends. We also model the transition to a Gaussian distribution for longer time…
In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval,…
Analogies between the price dynamics in the foreign exchange market and 3-dimensional fully developed turbulence were recently presented in Nature vol. 381, 767-769 (1996). Independently, we have carried out a study comparing the parallel…
Modeling the evolution of a financial index as a stochastic process is a problem awaiting a full, satisfactory solution since it was first formulated by Bachelier in 1900. Here it is shown that the scaling with time of the return…
We perform a detailed comparison between a Markov Switching Jump Diffusion Model and a Markov Switching {\alpha}-Stable Distribution Model with respect to the analysis of non-stationary data. We show that the jump diffusion model is…
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…
According to the classical theory of Brownian motion, the mean squared displacement of diffusing particles evolves linearly with time whereas the distribution of their displacements is Gaussian. However, recent experiments on mesoscopic…
Non-trivial inflaton self-interactions can yield calculable signatures of primordial non-Gaussianity that are measurable in cosmic surveys. Surprisingly, we find that the phase transition to slow-roll eternal inflation is often incalculable…
This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and…