3-D shape approximation using parametric geons
Image and Vision Computing
Application of statistical mechanics methodology to term-structure bond-pricing models
Mathematical and Computer Modelling: An International Journal
Mathematical comparison of combat computer models to exercise data
Mathematical and Computer Modelling: An International Journal
Very fast simulated re-annealing
Mathematical and Computer Modelling: An International Journal
Genetic Algorithms and Very Fast Simulated Reannealing: A comparison
Mathematical and Computer Modelling: An International Journal
Volatility of volatility of financial markets
Mathematical and Computer Modelling: An International Journal
Data mining and knowledge discovery via statistical mechanics in nonlinear stochastic systems
Mathematical and Computer Modelling: An International Journal
A simple options training model
Mathematical and Computer Modelling: An International Journal
Simulated annealing: Practice versus theory
Mathematical and Computer Modelling: An International Journal
Path-integral evolution of chaos embedded in noise: Duffing neocortical analog
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Gaussian mixture modelling to detect random walks in capital markets
Mathematical and Computer Modelling: An International Journal
Hi-index | 0.98 |
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and also consider multifactor models including stochastic volatility. We use a previous development of statistical mechanics of financial markets to model these issues. Daily Eurodollar futures prices and implied volatilities are fit to determine exponents of functional behavior of diffusions using methods of global optimization, Adaptive Simulated Annealing (ASA), to generate tight fits across moving time windows of Eurodollar contracts. These short-time fitted distributions are then developed into long-time distributions using a robust non-Monte Carlo path-integral algorithm, PATHINT, to generate prices and derivatives commonly used by option traders. The results of our study show that there is only a very small change in at-the-money option prices for different probability distributions, both for the one-factor and two-factor models. There still are significant differences in risk parameters, partial derivatives, using more sophisticated models, especially for out-of-the-money options.