Optimal Stopping in Levy Models, for Non-Monotone Discontinuous Payoffs

We give short proofs of general theorems about optimal entry and exit problems in Levy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, and an entry problem with an embedded option to exit

On pricing of interest rate derivatives

At present, there is an explosion of practical interest in the pricing of interest rate (IR) derivatives. Textbook pricing methods do not take into account the leptokurticity of the underlying IR process. In this paper, such a leptokurtic behaviour is illustrated using LIBOR data, and a possible martingale pricing scheme is discussed.Comment: 9 pages, 13 figure

Electric Conductivity and Gas-Sensing Properties of Nickel Ferrite Thin Films Formed by Ion-Beam Sputtering Deposition

Ferrites with composition of NiMnxFe1-xO4, (with x = 0 ÷ 1.0) have been synthesized by self-propagating high-temperature synthesis (SHS). The particle size of the synthesized ferrite powder was about 10 nm. Additional heat treatment at 1270 K during 50 min allowed us to obtained product with the single phase composition NiFe2O4.  We found out that the increasing of the manganese content (x) increased the lattice constant of the ferrites from 0.833896 nm (x = 0) up to 0.836369 nm (x = 1). The synthesized powder contains two types of ferrite particles that are varied in size and shape. The magnetic properties significantly depend on the microstructure and chemical composition of synthesized ferrites. It has been found that the coercive force Hc increased from 1.75 (x = 0.2) to 2.85 (x = 1). By using of IBSD technology thin film of NiFe2O4 was sputtered on the Si (100) substrate. All sputtered films were X-ray transparent. The structure of ferrite films consisted of agglomerate less than 35 nm. The thickness of the sputtered film was about 600 nm. Additional heat treatment at 770 K during 90 min resulted to homogeneity of the film microstructure. The temperature range 400-750 K corresponds to working temperature range of gas-sensing devices. The ferrite compounds were studied by TOF-SIMS (Time-of-Flight Secondary-Ion-Mass-Spectrometry) for all depth of film. The resistivity R of synthesized film was 39 kΩ. Measurement of gas-sensing sensitivity RCH4/Rair for gas (2%v. CH4) – air mixture showed increase of R up to 12% at the present of methane at 403 K. For further research we plan to replace iron to manganese ions in chemical compounds of ferrite

A finite difference method for pricing European and American options under a geometric Lévy process

In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process

Models for Heavy-tailed Asset Returns

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples