The Conditionally Exponential Decay (CED) model is used to explain the scaling laws observed in financial data. This approach enables us to identify the distributions of currency exchange rate or economic indices returns (changes) corresponding to the empirical scaling laws. This is illustrated...

We use the Conditionally Exponential Decay (CED) model to explain the scaling behavior in currency exchange (FX) rates. This approach enables us not only to show that FX returns satisfy scaling with an exponent qualitatively different from that of a random walk, but also to identify the...

The purpose of this paper is to show that using the toolkit of interest rate theory, already well known in financial engineering as the HJM model [D. Heath, R. Jarrow, A. Morton, Econometrica 60, 77 (1992)], it is possible to derive explicite option pricing formula and calibrate the theoretical...

In this paper we apply a new approach to build bidding strategies for power suppliers on electricity market and assume that each supplier’s bid is a linear function. Moreover each supplier tends to maximise his profit and minimize his risk, which are dependent on the generation output,...

In this paper we consider a jump-diffusion type approximation of the classical risk process by a gamma Levy process. We derive here the asymptotic behavior (lower and upper bounds) of the finite time ruin probability for any gamma Levy process.

The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property is manifested by the random (infinitely...

In this paper we discuss subdiffusive mechanism for the description of some stock markets. We analyse the fractional Black–Scholes model in which the price of the underlying instrument evolves according to the subdiffusive geometric Brownian motion. We show how to efficiently estimate the...

The main purpose of the paper is to present, how derivatives valuing methodology, known from financial and commodities markets, can be applied to the electricity market. We compare an application of three recent models. We start with the convenience yield approach, then we analyse the...

In this paper we establish a spectral representation of any symmetric stable self-similar process in terms of multiplicative flows and cocycles. Applying the Lamperti transformation we obtain a unique decomposition of a symmetric stable self-similar process into three independent parts: mixed...

In this paper we introduce a generalization of the De Vylder approximation. Our idea is to approximate the ruin probability with the one for a different process with gamma claims, matching first four moments. We compare the two approximations studying mixture of exponentials and lognormal...