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Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...
Binomial Probability Distribution01:15

Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...
Density00:56

Density

Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
Poisson Probability Distribution01:09

Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...

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Related Experiment Video

Updated: Jul 7, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Risk-neutral density extraction from option prices: improved pricing with mixture density networks.

C Schittenkopf1, G Dorffner

  • 1Austrian Research Institute for Artificial Intelligence, 1010 Vienna, Austria.

IEEE Transactions on Neural Networks
|February 6, 2008
PubMed
Summary

This study introduces a new method for extracting risk-neutral densities from option prices, improving derivative pricing accuracy. The flexible approach captures market dynamics, outperforming existing models and aiding risk management.

Related Experiment Videos

Last Updated: Jul 7, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Area of Science:

  • Quantitative Finance
  • Financial Econometrics
  • Computational Finance

Background:

  • Accurate pricing and hedging of financial derivatives are crucial in finance.
  • Existing models like Black-Scholes and GARCH have limitations in capturing stylized facts.

Purpose of the Study:

  • To develop a novel semi-nonparametric approach for risk-neutral density (RND) extraction.
  • To enhance the flexibility and accuracy of option pricing models.
  • To provide better tools for risk management.

Main Methods:

  • Utilizing an extension of mixture density networks for RND estimation.
  • Modeling RND shape non-linearly as a function of the time horizon.
  • Applying the method to a large dataset of FTSE 100 options data.

Main Results:

  • The proposed method successfully captures stylized facts like negative skewness and excess kurtosis.
  • Demonstrated significantly superior out-of-sample pricing accuracy compared to Black-Scholes and GARCH models.
  • Extracted RNDs offer valuable insights for Value-at-Risk (VaR) estimations.

Conclusions:

  • The new semi-nonparametric approach offers a more flexible and accurate method for RND extraction.
  • This model provides a significant improvement over traditional option pricing models.
  • The findings have practical implications for risk management and derivative pricing.