Conditional sampling for barrier option pricing under the LT method

We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance reduction is achieved. We extend the method to allow pricing knock-in barrier options and introduce a root-finding method to obtain a further variance reduction. The effectiveness of the new method is supported by numerical results

ANIMAL BIODIVERSITY CONSERVATION, A KEY OF SUSTAINABLE AGRICULTURE. CASE STUDY: THE ROMANIAN PINZGAU BREED IN TRANSILVANIA REGION

Abstract Pinzgau breed or Pinzgauer is called after its region of origin . These things are the main reasons why race should be kept in a form of active conservation. Moreover, in order to preserve the tradition and traditional products in Romania, is required to maintain this breed and even the formation of its national park

A connection between magma chamber processes and eruptive styles revealed at Nisyros-Yali volcano (Greece)

Arc volcanoes generally emit water-rich, high-viscosity silicic magmas, which are prone to erupt explosively. However, effusive behavior is a common occurrence despite the high-H2O, high viscosity conditions. The contrasting shift from effusive to explosive behavior (and vice-versa) at any individual volcano raises the question on what controls eruptive style. Permeability development in conduits allows magma to outgas and is clearly a key factor. However, an important question is whether magma reservoir processes can also have an influence on eruptive styles. The answer could have direct impact on predicting eruptive behavior. Hence, we explore this potential connection by analyzing nine alternating effusive and explosive silicic deposits that were emplaced during distinct eruptions at the active Nisyros-Yali volcanic center. The lavas and pyroclastic deposits are compositionally similar. This indicates a negligible influence of the bulk rock composition on different eruptive styles. The crystal contents vary between units, without any clear correlation with eruptive style (from nearly aphyric to ~45 vol% crystals). Mineral textures and chemistry do show variations between effusive and explosive eruptions, with a larger proportion of resorbed plagioclase and, in most cases, more evolved amphiboles present in the lava flows. Mineral thermo-barometry and hygrometry show that the storage zones of magmas generating effusive eruptions evolved towards colder and more water-rich conditions (710–790 °C; 5.6–6.5 wt% H2O) than their explosive counterparts (815–850 °C; 4.2–4.6 wt% H2O). At storage pressures of 1.5–2 kbar, relevant for Nisyros-Yali, the volatile saturation level is reached at >5 wt% H2O. Therefore, it is likely that the magmas reached water-saturation before generating effusive eruptions, and were undersaturated before explosive events. We hypothesize that the presence of exsolved volatiles in the subvolcanic reservoir can enhance the outgassing potential of the magma during conduit ascent. Hence, the rhyolitic effusive-explosive transitions can be influenced by the pre-eruptive exsolved versus dissolved state of the volatiles in the magma chamber. This can lead to the less explosive eruptions for the most water-rich reservoir conditions

Positive finite difference schemes for a partial integro-differential option pricing model

[EN] This paper provides a numerical analysis for European options under partial integro-differential Bates model. An explicit finite difference scheme has been used for the differential part, while the integral part has been approximated using the four-points open type formula. The stability and consistency have been studied. Moreover, conditions guaranteing positivity of the solutions are provided. Illustrative numerical examples are included.This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economia y Competitividad Spanish grant MTM2013-41765-P.Fakharany, M.; Company Rossi, R.; Jódar Sánchez, LA. (2014). Positive finite difference schemes for a partial integro-differential option pricing model. Applied Mathematics and Computation. 249:320-332. https://doi.org/10.1016/j.amc.2014.10.064S32033224

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

A robust spectral method for solving Heston’s model

In this paper, we consider the Heston’s volatility model (Heston in Rev. Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the spectral collocation method and the Laplace transforms method. To approximate the two dimensional PDE, we construct a grid which is the tensor product of the two grids, each of which is based on the Chebyshev points in the two spacial directions. The resulting semi-discrete problem is then solved by applying the Laplace transform method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA J. Appl. Math. 23(1): 97–120, 1979)