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Material on this website referred to in Malcolm Kemp’s book on Extreme Events

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See pages linked to Extreme Events for further information on this book.

 

Section

Section Title

Description

Hyperlink?

2.3.2 [foot]

Risk measures

Coherent risk measures

yes

2.4.1 [foot]

Monte Carlo simulations

Ability to reproduce results of some such exercises analytically, i.e. without resorting to Monte Carlo simulation techniques

no

2.4.2

Statistics

Formulae for skew (skewness) and kurtosis where different weights are given to different observations

yes

2.4.3

Fat tails

Derivation of Cornish-Fisher asymptotic expansion

yes

2.4.5 [foot]

Curve fitting

Techniques for fitting polynomials through data series

yes

2.4.6

Statistical tests for non-Normality

skew, kurtosis and Jarque-Bera tests when n is not large (using Monte Carlo simulations)

no

2.4.6

Statistics

Statistical tests for Normality

yes

2.5.2

Statistics

Characteristic functions for a range of distributional forms

yes

2.6 [foot]

Diversification

(excess) kurtosis of a binomial distribution

yes

2.7.2

Probability distributions

How mixtures of normal distributions can lead to fat-tails

yes

2.8

Stable distributions

Detailed analysis of stable distribution and tools for manipulating stable distributions

no

2.8.2

Stable distributions

Special cases where Stable distribution has analytical form

yes

2.8.4

Stable distributions

Further discussion of QQ-plots for Stable distributions

no

2.9.2

Extreme Value Distributions

Features of Extreme Value Distributions

yes

2.10

Parsimony

Some dangers of over-fitting

yes

2.13.3

Statistics

Giving greater weight to observations that correspond to longer 'proper' time periods

yes

3.3.2

Fat tails (in multiple return series simultaneously)

Box counting algorithms

no

3.8.2 [foot]

Curve fitting

Arranging for curve fits to exhibit 'adequate' smoothness

no

3.8.5

Relative entropy

The concept of entropy in statistics

no

3.8.5

Non-linear cluster analysis

Defining 'similarity' by reference merely to the copula

no

4.3.3 [foot]

Principal components analysis

Weighted covariance matrices

yes

4.7.2

Explaining market dynamics

How traditional time series analysis typically uses regression techniques

yes

4.8.2

Distributional mixtures

The EM algorithm

yes

4.10

Minimisation/maximisation

Run time constraints with large numbers of instruments

no

4.10.2 [foot]

Numerical techniques

Using golden section search techniques to find local extrema

no

5.4.6

Dual benchmarks

Position when we have two different covariance matrices

no

5.9.2

Backtesting risk-reward trade-offs

Arithmetic, geometric and logarithmic relative returns

yes

6.3.3

Probability distributions

The exponential family of distributions

no

6.11.6

Monte Carlo simulations

Simulations when the copula is 'fat-tailed'

no

7.4.8

Portfolio construction

Applying statistical tests to optimal portfolios

no

7.6

Portfolio construction

Optimal strategies in the presence of transaction costs on multiple assets

no

7.9.2

Portfolio construction

Adjusting for time-varying volatility using weighted covariance matrices

yes

7.11.2

Portfolio construction

Numerical integration

no

7.11.5

Portfolio construction

Need for risk measures used with non-Normal distributions to be coherent and sub-additive

no

8.3.2 [foot]

Value-at-risk

What VaR level corresponds to the worst outcome in n events?

yes

 

 


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