A model for stocks dynamics based on a non-Gaussian path integral

  title={A model for stocks dynamics based on a non-Gaussian path integral},
  author={Giovanni Paolinelli and Gianni Arioli},
  journal={Physica A: Statistical Mechanics and its Applications},
  • G. Paolinelli, G. Arioli
  • Published 4 September 2018
  • Mathematics, Economics
  • Physica A: Statistical Mechanics and its Applications
We introduce a model for the dynamics of stock prices based on a non quadratic path integral. The model is a generalization of Ilinski’s path integral model, more precisely we choose a different action, which can be tuned to different time scales. The result is a model with a very small number of parameters that provides very good fits of some stock prices and indices fluctuations. 
Path integral Monte Carlo method for option pricing
The MCMC method is developed by discretizing the path integral on a time lattice and evaluating this discretized form for various scenarios, with particular attention paid to the existence of autocorrelations, their decay with the number of sweeps, and the resulting estimate of the corresponding errors. Expand
Modeling Accelerated Growth of Bacteria Population Through Feynman Diagrams
  • H. Nieto-Chaupis
  • Mathematics
  • 2019 IEEE Fourth Ecuador Technical Chapters Meeting (ETCM)
  • 2019
In Quantum Physics normally the well-known Feynman Diagrams are used to calculate transition probabilities by which we can estimate predictions as to the expected measurement of a certain physicalExpand


A path integral based model for stocks and order dynamics
We introduce a model for the short-term dynamics of financial assets based on an application to finance of quantum gauge theory, developing ideas of Ilinski. We present a numerical algorithm for theExpand
Option pricing for non-Gaussian price fluctuations
From the path integral description of price fluctuations with non-Gaussian distributions we derive a stochastic calculus which replaces Ito's calculus for harmonic fluctuations. We set up a naturalExpand
Option pricing from path integral for non-Gaussian fluctuations. Natural martingale and application to truncated Lèvy distributions
Within a path integral formalism for non-Gaussian price fluctuations, we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options,Expand
Pricing derivatives by path integral and neural networks
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, whileExpand
Replicating financial market dynamics with a simple self-organized critical lattice model
A simple lattice field model intended to describe statistical properties of high frequency financial markets and its signature feature is the emergence of a self-organized critical state implies scale invariance of the model, without tuning parameters. Expand
Path integral approach to Asian options in the Black-Scholes model
We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to aExpand
Stochastic calculus for assets with non-Gaussian price fluctuations
From the path integral formalism for price fluctuations with non-Gaussian distributions we derive the appropriate stochastic calculus replacing Ito's calculus for stochastic fluctuations.
Probability distribution of returns in the Heston model with stochastic volatility
Abstract We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker‐PlanckExpand
Arbitrage-Free Self-Organizing Markets with GARCH Properties: Generating Them in the Lab with a Lattice Model
The studies of a quantum field model defined on a lattice having the dilation group as a local gauge symmetry are extended, adding an updating prescription for the simulation that drives the model market into a self-organized critical state. Expand
Pricing exotic options in a path integral approach
A general formula to price European path-dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms, which exhibits competitive performances when pricing at-the-money and out-of- the-money options. Expand