Econometrics of Commodity and Asset Pricing


Objectif

The main objective of this course is to propose discrete time methods for pricing commodities and financial assets. These methods are based on four pillars:

i)  Financial pillar – the absence of arbitrage opportunity (AAO) principle.

ii) Mathematical pillar – the (multi-horizon) Laplace transform.

iii) Probabilistic pillar – the class of discrete-time affine processes.

iv) Statistical pillar – the non-linear state-space models. 

The methods are first applied to commodity markets in order to price forward and futures contracts, taking into account the convenience yields. A modeling of spot and forward electricity prices is developed, as well as a simultaneous modeling of several commodity markets. Then the pricing methods are applied to various financial domains : sovereign and corporate bonds with possible switching regimes and/or zero lower bound spells, interest rate derivatives , default and illiquidity risks , quadratic and Wishart interest rate models , credit event pricing , option pricing including conditional heteroskedasticity  or  stochastic volatilities and/or switching regimes , simultaneous modeling of  exchange rates , interest rates , stock index and international derivatives. The statistical problems of inference, filtering, smoothing and prediction are treated. All the methods are illustrated by applications based on real or simulated data.

Plan

Chapter I – DISCRETE TIME AFFINE PROCESSES

o   Information in the Economy: the factors.

o   Dynamic Models.

o   Some properties of the Laplace transform.

o   Affine (or Car) Processes.

o   Extended affine processes.

o   Truncated Laplace transforms of affine processes.

 

Chapter II – PRICING AND RISK NEUTRAL DYNAMICS

o   Stochastic Discount Factor: equilibrium approach.

o   Stochastic Discount Factor: absence of arbitrage opportunity approach.

o   Exponential-Affine SDF.

o   The Risk Neutral Dynamics.

o   Typology of Econometric Asset Pricing Models.

                                                                              

Chapter III – FORWARDS, FUTURES, DIVIDENDS, COMMODITY PRICING AND CONVENIENCE YIELDS

o   Forward contracts, forward prices.

o   Futures contracts, futures prices.

o   Convenience yields.

o   Pricing with affine models.

o   A Gaussian VAR model.

o   Applications.

 

 

Chapter IV – MODELING OF SPOT AND FORWARD ELECTRICITY PRICES

o   Specific features of electricity markets

(Spikes, Seasonality, Non-Storability, Continuous Delivery).

o   Modelling approach.

o   Pricing.

o   Application.

 

Chapter V – SIMULTANEOUS MODELING OF SEVERAL COMMODITY MARKETS

o   A general affine framework.

o   A Gaussian VAR model.

o   A regime switching Gaussian VAR Model.

 

Chapter VI – GAUSSIAN AFFINE TERM STRUCTURE MODELS

o   Introduction.

o   Affine Term Structure Models (ATSMs).

o   Univariate Gaussian ATSMs.

o   Bivariate Gaussian ATSMs.

o   Multivariate Gaussian ATSMs.

o   Back modelling of Gaussian ATSMs.

o   Empirical analysis of Gaussian ATSMs.

o   An alternative estimation procedure.

 

Chapter VII – SWITCHING REGIMES GAUSSIAN AFFINE TERM STRUCTURE MODELS

o   Switching Regimes Car processes.

o   Univariate Switching Regimes Gaussian ATSMs.

o   Multivariate Switching Regimes Gaussian ATSMs.

o   Empirical analysis.

 

Chapter VIII – NON-NEGATIVE AFFINE TERM STRUCTURE MODELS

o   Autoregressive Gamma ATSMs.

o   Switching Regimes Autoregressive Gamma ATSMs.

o   Wishart and Quadratic TSMs.

o   Non-negative ATSMs.

 

Chapter IX – ESTIMATION OF AFFINE ASSET-PRICING MODELS

o   State-Space models.

o   Kalman-filter-based approaches.

o   Inversion technique.

o   Dealing with unobserved regimes.

o   The persistence problem.

 

Chapter X – PRICING CREDIT AND LIQUIDITY RISKS

o   Notations.

o   Pricing under standard assumptions.

o   Pricing illiquid bonds.

o   Relaxing the classical assumptions.

o   General affine credit-risk framework.

o   CDS pricing in the general framework.

o   Top-Down approach.

 

Chapter XI – ECONOMETRICS OF OPTION PRICING

o   Security Market Models.

o   Truncated Laplace Transforms (TLT) and Transform Analysis.

o   Direct Modelling of Conditionally Normal Processes.

o   Back Modelling of Conditionally Normal Processes.

o   Direct Modelling of Mixed-Normal Processes.

o   Direct Modelling of Conditionally Spline Dynamics.

o   Back Modeling of Regime Switching Dynamics.

o   Back Modeling of Stochastic Volatility Dynamics.

o   Back Modeling of Regime Switching GARCH Dynamics.

o   Back Modeling of Regime Switching IG GARCH Dynamics.

o   A Component Volatility GARCH Model.

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