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) a financial pillar : the absence of arbitrage opportunity, ii) a mathematical pillar : the Laplace transform, iii) a probabilistic pillar : the affine processes , iv) a 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 modelling  of spot and forward electricity prices is developed, as well as a simultaneous  modelling 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

AFFINE  (or CAR) PROCESSES
            Information in the Economy : the Factors
            Building Dynamic Models
            Properties of the Laplace Transform
            Affine or Car Processes
PRICING AND RISK NEUTRAL DYNAMICS
            Stochastic Discount Factor : Equilibrium Approach
            Stochastic Discount Factor : Absence of Arbitrage Opportunity Approach
            Exponential Affine SDF
            The Risk Neutral Dynamics
            Typology of Econometric Asset Pricing Models     
FORWARDS,FUTURES ,DIVIDENDS ,COMMODITIES,CONVENIENCE YIELDS
            Pricing forward and futures contracts
            Convenience yields
            Seasonality 
MODELING SPOT AND FORWARD ELECTRICITY PRICES
            Characteristics of Electricity Markets (Splikes, Seasonality, Non Storability Continuous  Delivery)
            Direct Modeling of Spot and Forward Prices
            Application to Spot and Forward Prices in the French Electricity Market
SIMULTANEOUS MODELING OF SEVERAL COMMODITY MARKETS
            Backward Modeling
            Internal Consistency Constraints
            Switching Regime VAR Models in the Historical and Risk Neutral Worlds
REGIME SWITCHING INTEREST RATE MODELS
            A toolbox for Regime Switching and Bond Pricing
            Regime Switching and Default Free Bond Pricing : Application to ECB Policy Rate
            Regime Switching and Defaultable Bond Pricing : Application to Sovereign Yields in the  Euro Zone
            Extensions : Sector Contagion, Credit Ratings
ZERO LOWER BOUND  INTEREST RATE MODELS
            ARG-Zero Processes
            Moments, Stationarity , Lift-off,
            Asymptotic Behavior
            VARG Processes
            Moments, VAR representations, Lift off
            Pricing
            Application to Japanese Interest Rates
CREDIT RISK MODELS
            The Setup
            Term Structure of Corporate Rates
            Term Structure of “First to Default “ Rates
            Credit VaR
            Application to simulated data
            Extensions
QUADRATIC MODELS
            Quadratic Models and the Quadratic Kalman Filter
            Credit Risk and Illiquidity Risk
            Application to Interbank Rate, the Euribor-OIS spreads
CREDIT EVENT PRICING
            Default event surprise
            Default Intensity, Pre-Intensity,
            Exogeneity, Contagion
            Pricing Individual and Joint Defaults
            Applications to the Credit Spread Puzzle and to Recursive Contagion
OPTION PRICING
            Security Market Models
            Truncated Laplace Transforms
            Back Modeling of Switching Regimes
            Back Modeling of Stochastic Volatility Models
            Back Modeling of Switching GARCH Models
            Direct and backward Modeling of Conditionally Gaussian Dynamics
            Extensions:Spline ans Conditionally Mixed Normal Models
            Application to ARCH models
INTERNATIONAL MODELING
            Wishart Processes
            Joint Modeling of Several Term Structures, Exchange Rates and Market Indices
            Pricing Futures, Forwards, Swaps and Options Based on Several Markets
            Application to simulated data

Appendix 1: QUANTITATIVE LATENT VARIABLE MODELS
            Definitions,Kalman Filtering,Kalman Smoothing,Estimations and Tests,First order Extended  Kalman Filter (EKF1),Second order Extended Kalman Filter (EKF2),Unscented Filtering (UKF)
Quadratic Kalman filter (QKF)
Appendix 2: QUALITATIVE LATENT VARIABLE MODELS
            Markov Chain,Definition, Examples,Filtering, Smoothing, Likelihood,Kitagawa-Hamilton Algorithm,EM Algorithm,Stochastic Volatility Models,Prediction,Coding the State Variable, Parameterization of the transition matrix

Références

 Gouriéroux C. et Monfort A. (2006) : « Affine Models for Credit Risk Analysis », Journal of Financial Econometrics, 4, 494-530.
 Monfort A. et Pegoraro F. (2007)  : « Switching VARMA Term Structure Models », Journal of Financial Econometrics, 5, 103-151.
 Bertholon H., Monfort A; et Pegoraro F. (2008) : « Econometric Asset Pricing Modelling », Journal of Financial Econometrics, 4, 407-458.
 Gouriéroux C. et Monfort A. (2010) : « International Money and Stock Market Contingent Claims », Journal of International Money and Finance, 29, 1727-1751.
 Monfort A. et Renne J.P. (2010) : Default, liquidity and crises : an econometric framework, Document de travail CREST 2010-46.
 Jardet C., Monfort A. et Pegoraro F. (2011) : « No-arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth (2011), Document de travail CREST 2011-03.