Pricing Asian power options under jump-fraction process

• Autores: Peng, Bin, Peng, Fei
• Formato: artículo
• Fecha de Publicación: 2012
• Institución: Universidad ESAN
• Repositorio: ESAN-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.esan.edu.pe:20.500.12640/1880
• Enlace del recurso: https://revistas.esan.edu.pe/index.php/jefas/article/view/219; https://hdl.handle.net/20.500.12640/1880; https://doi.org/10.1016/S2077-1886(12)70002-1
• Nivel de acceso: acceso abierto
• Materia: Asian power option; Geometric average; Arithmetic average; Jump-fraction process; Control variate; Opciones energéticas de Asia; Media geométrica; Media aritmética; Método de fracciones discontinuas; Variable de control; https://purl.org/pe-repo/ocde/ford#5.02.04

A framework for pricing Asian power options is developed when the underlying asset follows a jump-fraction process. The partial differential equation (PDE) in the fractional environment with jump is constructed for such option using general Itô's lemma and self-financing dynamic strategy. With the boundary condition an analytic formula for the option with geometric average starting at any time before maturity is derived by solving the PDE and the option with arithmetic average is evaluated in Monte Carlo simulation using control variate technique with the help of the above analytic solution. Overwhelming numerical evidence indicates that the technique proposed is computationally efficient and dramatically improves the accuracy of the simulated price. Moreover this study will pave a novel way to copy with the option contracts based on thinly-traded assets like oil or currencies or interest rates.