It is a well observed fact that markets follow both positive and/or negative trends, crashes and bubble effects. In general a strong positive trend is followed by a crash--a famous example of these effects was seen in the recent crash on the NASDAQ (April 2000) and prior to the crash in the Hong Kong market, which was associated with the Asian crisis in the early 1994. In this paper we use real market data coupled into a minority game with different payoff functions
to study the dynamics and the location of financial bubbles.
It is well established that volatility has a memory of the past, moreover it is found that volatility correlations are long ranged. As a consequence the volatility cannot be characterized by a single correlation time. Recent empirical work suggests that the volatility correlation functions of various assets actually decay as a power law. In this paper we show that it is possible to derive the path integral for a non-Gaussian option pricing model that can capture fat-tails. We aim to find the most probable path that contributes to the action functional, that describes the dynamics of the entire system, by finding local minima. We obtain a second order differential equation for the functional return. This paper reviews our current progress and the remaining open questions.
Proc. SPIE. 5471, Noise in Complex Systems and Stochastic Dynamics II
KEYWORDS: Probability theory, Stochastic processes, Data modeling, Differential equations, Motion models, Partial differential equations, Signal processing, Statistical analysis, Monte Carlo methods, Numerical analysis
In this short note we propose an approach for calculating option prices in financial markets in the framework of path integrals. We review various techniques from engineering and physics applied
to the theory of financial risks. We explore how the path integral methods may be used to study financial markets quantitatively and we also suggest a method in calculating transition probabilities for option pricing using real data in that framework.
We review various techniques from engineering and physics applied to the theory of financial risks. We also explore at an introductory level how the quantum aspects of physics may be used to study the dynamics of financial markets. In particular we explore how the path integral methods may be used to study financial markets quantitatively.