Book•
Option pricing: Mathematical models and computation
01 May 1994-
About: The article was published on 1994-05-01 and is currently open access. It has received 854 citations till now. The article focuses on the topics: Finite difference methods for option pricing & Monte Carlo methods for option pricing.
Citations
More filters
TL;DR: The main goal of this article is to quantify this dependence on preferences in the specific example of a European call option by using the utility function approach of Hodges and Neuberger together with an asymptotic analysis of partial differential equations.
Abstract: In a market with transaction costs, generally, there is no nontrivial portfolio that dominates a contingent claim. Therefore, in such a market, preferences have to be introduced in order to evaluate the prices of options. The main goal of this article is to quantify this dependence on preferences in the specific example of a European call option. This is achieved by using the utility function approach of Hodges and Neuberger together with an asymptotic analysis of partial differential equations. We are led to a nonlinear Black-Scholes equation with an adjusted volatility which is a function of the second derivative of the price itself. In this model, our attitude towards risk is summarized in one free parameter a which appears in the nonlinear Black-Scholes equation : we provide an upper bound for the probability of missing the hedge in terms of a and the magnitude of the proportional transaction cost which shows the connections between this parameter a and the risk.
379 citations
TL;DR: In this article, the authors analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning, and exhibit their dynamical behaviors for chosen different parameters.
250 citations
TL;DR: The partial differential equations approach for valuing European-style options is considered and pointwise bounds for the error caused by various boundary conditions imposed on the artificial boundary are derived.
Abstract: In this paper we consider the partial differential equations approach for valuing European-style options. In order to solve the equations numerically by finite difference or finite element methods it is necessary to introduce an artificial boundary in order to make the computational domain bounded. We derive pointwise bounds for the error caused by various boundary conditions imposed on the artificial boundary. The error estimates can be used to determine a priori a suitable location for the artificial boundary in terms of a given error tolerance.
225 citations
TL;DR: Tarzia et al. as discussed by the authors presented a bibliografía on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems, which contains 5869 titles referring to 588 scientific journals, 122 books, 88 symposia, 30 collections, 59 thesis and 247 technical reports.
Abstract: We present a bibliography on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems. It contains 5869 titles referring to 588 scientific Journals, 122 books, 88 symposia (having at least 3 contributions on the subject), 30 collections, 59 thesis and 247 technical reports. It tries to give a comprehensive account of the western existing mathematicalphysical-engineering literature on this research field. RESUMEN Se presenta una bibliografía sobre problemas de frontera móvil y libre para la ecuación del calor-difusión, en particular sobre el problema de Stefan y problemas relacionados. Contiene 5869 títulos distribuidos en 588 revistas científicas, 122 libros, 88 simposios (teniendo al menos 3 contribuciones en el tema), 30 colecciones, 59 tesis y 247 informes técnicos o prepublicaciones. Se da un informe amplio de la bibliografía matemática, física y de las ingenierías existente en occidente sobre este tema de investigación. Primary Mathematics Subject Classification Number (*): 35R35, 80A22 Secondary Mathematics Subject Classification Number (*): 35B40, 35C05, 35C15, 35Kxx, 35R30, 46N20, 49J20, 65Mxx, 65Nxx, 76R50, 76S05, 76T05, 93C20. (*) Following the 1991 Mathematics Subject Classification compiled by Mathematical Reviews and Zentralblatt fur Mathematik. Primary key words: Enthalpy formulation or method, Filtration, Free boundary problems, Freezing, Melting, Moving boundary problems, Mushy region, Phase-change problem, Solidification, Stefan problem. Secondary key words: Continuous mechanics, Diffusion process, Functional analysis, Heat conduction, Mathematical methods, Numerical methods, Partial differential equations, Variational inequalities, Weak solutions. Palabras claves primarias: Método o formulación en entalpía, Filtración, Problemas de frontera libre, Congelación, Derretimiento, Problemas de frontera móvil, Región pastosa, Problema de cambio de fase, Solidificación, Problema de Stefan. Palabras claves secundarias: Mecánica del continuo, Procesos difusivos, Análisis funcional, Conducción del calor, Métodos matemáticos, Métodos numéricos, Ecuaciones diferenciales a derivadas parciales, Inecuaciones variacionales, Soluciones débiles. El manuscrito fue recibido y aceptado en octubre de 1999. D.A. Tarzia, A bibliography on FBP. The Stefan problem, MAT Serie A, # 2 (2000). 3
224 citations
TL;DR: In this article, the theory of real options is used to model the optimal tree harvesting decision and the value of the option to harvest is estimated using a dynamic programming approach and a general numerical solution technique suitable for any type of stochastic process for prices.
214 citations