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Standard Deviation01:10

Standard Deviation

27.9K
The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
27.9K
Mean Absolute Deviation01:13

Mean Absolute Deviation

3.4K
The mean absolute deviation is also a measure of the variability of data in a sample. It is the absolute value of the average difference between the data values and the mean.
Let us consider a dataset containing the number of unsold cupcakes in five shops: 10, 15, 8, 7, and 10. Initially, calculate the sample mean. Then calculate the deviation, or the difference, between each data value and the mean. Next, the absolute values of these deviations are added and divided by the sample size to...
3.4K
Variation: Normal Distribution, Range, and Standard Deviation02:32

Variation: Normal Distribution, Range, and Standard Deviation

28.5K
In the field of psychology, there are several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative data, such as ethnicity, can be tabulated into a frequency count to provide information about the proportion, as well as the variety of groups in a sample or population. On the other hand, researchers can perform a wider set of calculations on quantitative data. The mean, mode, and median, for instance, are central tendency measures to identify a...
28.5K
Standard Deviation of Calculated Results01:14

Standard Deviation of Calculated Results

8.7K
Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal distribution. This distribution is bell-shaped curved, with the most frequently observed value (mean or central value) in the middle. The farther away from the central value, the greater the deviation from the central value, and the lower the frequency.
A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...
8.7K
Calculating Standard Deviation01:08

Calculating Standard Deviation

13.2K
The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. Further, the standard deviation is always a positive value or zero.
The standard deviation value is small when all the data is concentrated close to the mean. Here the data exhibits low variation. The standard deviation value is larger when the data values are more spread out from the mean. Here, the data displays high...
13.2K
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

9.7K
To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
9.7K

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Operation of Laboratory Photobioreactors with Online Growth Measurements and Customizable Light Regimes
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Option pricing in the moderate deviations regime.

Peter Friz1, Stefan Gerhold2, Arpad Pinter2

  • 1TU and WIAS Berlin Germany.

Mathematical Finance
|July 19, 2018
PubMed
Summary
This summary is machine-generated.

This study provides new estimates for call option prices near expiration in diffusion models. The findings offer accurate calculations for moderately out-of-the-money options, improving financial modeling.

Keywords:
asymptoticsimplied volatilitymoderate deviationsoption pricing

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Area of Science:

  • Quantitative Finance
  • Mathematical Finance
  • Financial Derivatives

Background:

  • Call option pricing is crucial in financial markets, especially near expiration.
  • Existing models often focus on at-the-money or deep out-of-the-money options.
  • A need exists for accurate pricing in the moderately out-of-the-money regime.

Purpose of the Study:

  • To develop and analyze asymptotic estimates for call option prices close to expiry.
  • To bridge the gap between at-the-money and out-of-the-money pricing regimes.
  • To provide accurate approximations for implied volatilities in diffusion models.

Main Methods:

  • Utilizing small-time moderate deviation theory for asymptotic analysis.
  • Deriving first and higher-order expansions for option prices and implied volatilities.
  • Applying methods to generic local and stochastic volatility models.

Main Results:

  • Obtained novel asymptotic expansions for call option prices and implied volatilities.
  • Demonstrated that these expansions involve simple expressions of model parameters.
  • Showcased the applicability to a wide range of volatility models.

Conclusions:

  • The derived estimates accurately price moderately out-of-the-money call options near expiry.
  • The methodology is general and applicable to complex financial models like the Heston model.
  • Numerical results confirm the high accuracy of the proposed asymptotic expansions.