Related papers: Elements for a Theory of Financial Risks
Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for…
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their…
We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription.…
It is known from previous work of the authors that non-negative arbitrage free price processes in finance can be described in terms of filtered likelihood processes of statistical experiments and vice versa. The present paper summarizes and…
After a brief review of option pricing theory, we introduce various methods proposed for extracting the statistical information implicit in options prices. We discuss the advantages and drawbacks of each method, the interpretation of their…
One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate.…
We present a computational method for measuring financial risk by estimating the Value at Risk and Expected Shortfall from financial series. We have made two assumptions: First, that the predictive distributions of the values of an asset…
Regression plays a key role in many research areas and its variable selection is a classic and major problem. This study emphasizes cost of predictors to be purchased for future use, when we select a subset of them. Its economic aspect is…
The statistical properties of a stochastic process may be described (1)by the expectation values of the observables, (2)by the probability distribution functions or (3)by probability measures on path space. Here an analysis of level (3) is…
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the…
"What are the origins of risks?" and "How material are they?" -- these are the two most fundamental questions of any risk analysis. Quantitative Structuring -- a technology for building financial products -- provides economically meaningful…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…
The option is a financial derivative, which is regularly employed in reducing the risk of its underlying securities. However, investing in option is still risky. Such risk becomes much severer for speculators who utilize option as a means…
We introduce a stochastic price model where, together with a random component, a moving average of logarithmic prices contributes to the price formation. Our model is tested against financial datasets, showing an extremely good agreement…
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the…
In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. This tutorial aims to introduce a number of different stochastic processes that can help in grasping the essential…