Financial Correlations - Modeling, Trading, Risk Management and AI

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Introduction: What are Financial Correlations and why are they Critical in Finance?

• Investments and Correlation – A new Correlation based Portfolio Performance measure
• Trading and Correlation
• Risk Management and Correlation
• The Global Financial Crisis and Correlation
• Regulation and Correlation
• AI and Correlation

Empirical Properties of Correlation: How do Correlations behave in the Real World?

• How do equity correlations behave in a recession, normal economic period, and economic expansion?
• Do equity correlations exhibit Mean Reversion?
  Excel Exercise: Programming a Mean Reversion Test of a Time Series          
• Do equity correlations exhibit Autocorrelation?
   Excel Exercise: Programming Autocorrelation of a Time Series.
• Is Mean Reversion the ‘reverse property’ of Autocorrelation?
• How are equity correlations distributed?

How can we Quantify Financial Correlations?

• An Overview of 15 Models
  The most Critical Models:
• The popular Pearson correlation model – Work of the Devil?
  Excel Exercise: Programming the Pearson multiple Regression Function and 
• Correlation Parameters
• Correlating Brownian motions (Heston 1993) and Extensions
  Excel Exercise: Programming the Heston Correlation Model
• Copulas (Sklar 1959, Vasicek 1987, Li 2000)
  Excel Exercise: Programming the Gaussian Copula Model
• Limitations of Copulas: Should we apply Copulas in Financial modelling?
• Conclusion: Will there be a Black-Scholes-Merton Correlation model, which will dominate Correlation modelling?

Cointegration – A Superior Model to Correlation?

• Basics: Stationary process and Integration to the order d
• Application of Cointegration in Finance: Tracking an Index, Pairs Trading, Cost-effective Hedging
• A practical Approach to Implementing Cointegration
• Granger Causality: True causality or just Granger causality?
• Conclusion: Is Cointegration superior to Pearson correlation?

Should we model Financial Correlations with a Stochastic Process?           

• Recap from Chapter 2: Empirical Properties of Financial Correlations 
• Which ingredients should a Stochastic Process for Financial Correlations have?
  a) Should we include Mean Reversion
  b) Should we bound the Process?
  Excel Exercise: Programming White Noise, the Geometric Brownian Motion with Jumps and the bounded Jacobi process
• The Buraschi et al 2010 model and the Lu and Meissner 2018 model

Correlation Trading

• Empirical Correlation Trading
• Pairs Trading
• Multi-asset Options
• Structured Products
• Correlation Swaps
• Dispersion trading
• Which Trading Strategy is the most promising?

How to quantify Market Correlation Risk and Credit Correlation Risk

• The Correlation Risk Parameters Cora and Gora
• Applying Cora and Gora to Market Risk Modeling, i.e. VaR and ES 
• Applying Cora and Gora to Credit Risk Modeling, i.e. to CDS and CDOs
• The 2007-2009 CDO disaster. Are Cora and Gora of Copulas to blame?     

Correlation and AI

• What fuels AI?
• Will AI funds outperform the market?
• Neural Networks and Correlation
• Ridge and Lasso Regression – Pros and Cons
• Ensemble learning – Consensus Clustering, Bayesian optimal classifier, Boosting