Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological, and Engineering Systems
Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological, and Engineering Systems
On weighted possibilistic mean and variance of fuzzy numbers
Fuzzy Sets and Systems - Theme: Basic concepts
A Jump-Diffusion Model for Option Pricing
Management Science
Pricing European options based on the fuzzy pattern of Black-Scholes formula
Computers and Operations Research
Expert Systems with Applications: An International Journal
Option Pricing Under a Double Exponential Jump Diffusion Model
Management Science
Option price sensitivities through fuzzy numbers
Computers & Mathematics with Applications
Fuzzy Logic in Financial Analysis
Fuzzy Logic in Financial Analysis
Option Pricing Under a Mixed-Exponential Jump Diffusion Model
Management Science
Using neural network for forecasting TXO price under different volatility models
Expert Systems with Applications: An International Journal
Long-Term prediction of discharges in manwan reservoir using artificial neural network models
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part III
Pricing double-barrier options under a flexible jump diffusion model
Operations Research Letters
Engineering Applications of Artificial Intelligence
Hi-index | 7.29 |
In this paper we consider the European option valuation problem. We assume that the underlying asset follows a geometric Levy process. The log-price is a sum of a Brownian motion with drift and a linear combination of Poisson processes describing jumps in price. In our approach we use martingale method and theory of fuzzy sets. To obtain the European call and put option pricing formulas we use the mean correcting and the Esscher transformed martingale measures. Application of the first mentioned measure required deep analysis of transformation of characteristics of Levy process. We assume that some model parameters cannot be precisely described and therefore we apply fuzzy numbers. Application of fuzzy arithmetic enables us to consider different sources of uncertainty and introduce experts' opinions or imprecise estimates to the model. In contradistinction to our previous papers, where the European call option price at time zero was analysed, we introduce the valuation expressions of the European call and put options for arbitrary time t. Numerical simulations conducted in the paper are used to analyse and illustrate the theoretical results. This numerical approach is based on L-R numbers and the exact shape of the fuzzy numbers which give us the possibility of comparing behaviour of option prices for various values of the parameters of the underlying asset.