In [3] it was shown that by writing the solution of the Black-Scholes partial differential equation on a small set of basis functions the computing time can be dramatically reduced. In this study we explore the generalization of the technique to basket options.

Vanilla planifolia is the most widely cultivated species for obtaining natural vanilla. In Mexico, vanilla production has decreased due to negative effects of climate change. We evaluate current, potential, and future cultivation areas in Mexico using bioclimatic models with distinct change scenarios (intermediate emissions, temperature rise 1.1 2.6 °C, high emissions from 4.8 2050 2070), order...

We examine how to approximate a Lévy process by a hyperexponential jump-diffusion (HEJD) process, composed of Brownian motion and of an arbitrary number of sums of compound Poisson processes with double exponentially distributed jumps. This approximation will facilitate the pricing of exotic options since HEJD processes have a degree of tractability that other Lévy processes do not have. The id...

Fungal pathogens pose a major problem in causing reduction in yield of vanilla crop to considerable level. Fusarium oxysporum, was isolated from naturally infected vanilla plants and an attempt was made to minimize the damage caused by the pathogen using biocontrol agents Trichoderma harzianum, and Pseudomonas fluorescens isolated from soil. The combined inoculation of Trichoderma harzianum wit...

We study pricing under the local volatility. Our research is mainly intended for pedagogical purposes. In the first part of our work we study the local volatility modeling. We derive the local volatility formula in terms of the European call prices and in terms of the market implied volatilities. We propose and calibrate to the DAX option data a functional form for the implied volatility which ...