Econometrics of Commodity and Asset Pricing
Teacher
ECTS:
3
Course Hours:
18
Tutorials Hours:
0
Language:
English
Examination Modality:
mém.
Objective
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.
Planning
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.
References
Adrian, T., Crump R. K., Moench E. : “Pricing the Term Structure with Linear Regressions”, Journal of Financial Economics, 2013, 110, 1, 110-138.
Ahn, D., Dittmar, R., and Gallant, R. : "Quadratic Term Structure Models : Theory and Evidence", Review of Financial Studies, 2002, 15, 243-288.
Ang A., Boivin J., Dong, S., Loo-Kung R. : "Monetary Policy Shifts and the Term Structure”, The Review of Economic Studies, 2011, 78, 2, 429-457.
Ang A., Piazzezi M., Wei M. : "What Does the Yield Curve Tell us About GDP Growth”, Journal of Econometrics, 2006, 131, 359-403.
Ang A., Piazzezi M. : “A No-arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables", Journal of Monetary Economics, 2003, 50, 745-787.
Babaoglu, K., Christoffersen, P., Heston, S., Jacobs, K. : “Option Valuation with Volatility Components, Fat Tails, and Non-Monotonic Pricing Kernels", Review of Asset Pricing Studies, 2018, 8, 183-231.
Bauer, M., Rudebusch, G., Wu, C. : “Correcting Estimation Bias in Dynamic Term Structure Models", Journal of Business and Economic Statistics, 2012, 30, 454-467.
Bertholon, H., Monfort, A., and Pegoraro, F. : "Pricing and Inference with Mixtures of Conditionally Normal Processes", 2006, CREST-DP, 2006-28.
Bertholon, H., Monfort, A., and Pegoraro, F. : "Econometric Asset Pricing Modelling", Journal of Financial Econometrics, 2008, 4, 407-458.
Christoffersen, P., Elkamhi, R., Feunou, B., Jacobs, K. : “Option Valuation with Conditional Heteroskedasticity and Nonnormality", The Review of Financial Studies, 2010, 23, 2140-2183.
Christoffersen, P., Heston, S., Jacobs, K. : “Option Valuation with Conditional Skewness", Journal of Econometrics, 2006, 131, 253-284.
Christoffersen, P., Jacobs, K., Ornthanalai, C., Wang, Y. : “Option valuation with long-run and short-run volatility components", Journal of Financial Economics, 2008, 90, 272-297.
Dai Q., Singleton K., Yang W. : “Regime Shifts in Dynamic Term Structure Models of U.S. Treasury bond yields”, The Review of Financial Studies, 2007, 20, 5, 1669-1706.
Dai Q., Le A., Singleton K. : “Discrete-Time AffineQ Term Structure Models with Generalized Market Prices of Risk ”, The Review of Financial Studies, 2010, 23, 5, 2184-2227.
Darolles, S., Gourieroux, C., and Jasiak J. : "Structural Laplace Transform and Compound Autoregressive Models", Journal of Time Series Analysis, 2006, 24(4), 477-503.
Duan, J.-C. : "The GARCH Option Pricing Model", 1995, Mathematical Finance, 5, 13-32.
Duan, J.-C., Popova, I., and Ritchken, P. : "Option Pricing under Regime Switching", Quantitative Finance, 2002, 2, 116-132.
Dubecq, S., Monfort, A., Renne, J.-P. and Roussellet G. : "Credit and Liquidity in Interbank Rates : A Quadratic Approach", Journal of Banking and Finance, 2016, 68, 29-46.
Duffie, D., Pan, J., and Singleton, K. J. : "Transform Analysis and Asset Pricing for Affine Jump Diffusions", Econometrica, 2000, 68, 1343-1376.
Duffie, D., and Singleton, K. J. : "Modeling the Term Structures of Defaultable bonds", Review of Financial Studies, 1999, 12 (4), 687-720.
Garcia, R., Luger, R., and Renault, E. : "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables", Journal of Econometrics, 2003, 116, 49-83.
Giacoletti M., Laursen K. T., Singleton K. : “Learning From Disagreement in the U.S. Treasury Bond Market”, The Journal of Finance, 2021, 76, 1, 395-441.
Gourieroux, C., and Jasiak, J. : "Autoregressive Gamma Processes", Journal of Forecasting, 2006, 25 (2), 129-152.
Gourieroux, C., Jasiak, J., and Sufana, R. : "A Dynamic Model for Multivariate Stochastic Volatility : The Wishart Autoregressive Process", The Journal of Econometrics, 2009, 150 (2), 167-181.
Gourieroux, C., and Monfort, A. : "Indirect Inference", Journal of Applied Econometrics, 1993, 8, 85-118.
Gourieroux, C., and Monfort, A. : "Simulation Based Econometric Methods", 1996, Oxford University Press.
Gourieroux C., Monfort A. : "Pricing with Splines", Annals of Economics and Statistics, 2006, 82, 3-33.
Gourieroux, C., and Monfort, A. : "Econometric Specifications of Stochastic Discount Factor Models", Journal of Econometrics, 136, 509-530.
Gourieroux C., Monfort A, Polimenis V. : “Affine Model for Credit Risk Analysis”, Journal of Financial Econometrics, 2006,4,3,494-530.
Gourieroux C., Monfort A., Renne J.-P. : “Pricing Default Events : Surprise, Exogeneity and Contagion”, Journal of Econometrics, 2014, 182, 2, 397-411.
Gourieroux C., Monfort A., Sufana R. : “International Money and Stock Market Contingent Claims”, Journal of International Money and Finance, 2010, 29, 1727-1751.
Gourieroux C., Sufana R. : “Discrete time Wishart Term Structure Models”, Journal of Economic Dynamics and Control, 2011, 06, 815-824.
Hamilton, J. D., Wu C. : “Identification and Estimation of Gaussian Affine Term Structure Models”, Journal of Econometrics, 2012, 168, 2, 315-331.
Hamilton, J. D., Wu C. : “Testable Implications of Affine Term Structure Models”, Journal of Econometrics, 2014, 178, 231-242.
Han, H., Khrapov, S., Renault, E. : “The leverage effect puzzle revisited : Identification in discrete time”, The Journal of Econometrics, 2020, 217, 230-258.
Heston, S., Nandi S. : “A Closed-Form GARCH Option Valuation Model”, The Review of Financial Studies, 2000, 13, 585-626.
Jardet C., Monfort A., Pegoraro F. : “No-Arbitrage Near Cointegrated VAR(p) Term Structure Model, Term Premia and GDP Growth”, Journal of Banking and Finance, 2013,37,389-402.
Joslin S., Le A., Singleton K. : “Why Gaussian Macro-Finance Term Structure Models Are (Nearly) Unconstrained Factor-VARs”, The Journal of Financial Economics, 2013, 109, 3, 604-622.
Joslin S., Le A., Singleton K. : “Gaussian Macro-Finance Term Structure Models with Lags”, The Journal of Financial Econometrics, 2013, 11, 4, 581-609.
Joslin S., Le A. : “Interest Rate Volatility and No Arbitrage Term Structure Models”, Management Science, 2020, forthcoming.
Joslin S., Priebsch M., Singleton K. : “Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks”, The Journal of Finance, 2014, 69, 3, 1197-1233.
Kim D. H., Orphanides A. : “Term Structure estimation with survey data on interest rate forecasts”, Journal of Financial and Quantitative Analysis, 2012, 47, 241-272.
Leippold, M., and Wu, L. : "Asset Pricing Under the Quadratic Class", Journal of Financial and Quantitative Analysis, 2002, 37(2), 271-295.
Lucia, J., and E. Schwartz, E. : "Electricity Prices and Power Derivatives : Evidence from the Nordic Power Exchange", Review of Derivatives Research, 2002, 5, 5-50.
Moench, E. : “Forecasting the Yield Curve in a Data-Rich Environment: A No-Arbitrage Factor-Augmented VAR Approach”, Journal of Econometrics, 2008, 146, 1, 26-43.
Monfort A., Féron O. : “Joint Econometric Modeling of Spot Electricity Prices, Forwards and Options”, Review of Derivative Research, 2012,15,217-256.
Monfort, A., and Pegoraro, F. : "Multi-Lag Term Structure Models with Stochastic Risk Premia", 2006, CREST DP 2006-29.
Monfort, A., and Pegoraro, F. : "Switching VARMA Term Structure Models", Journal of Financial Econometrics, 2007, 5(1), 105-153.
Monfort A., Pegoraro F. : “Asset Pricing with Second-Order Esscher Transforms“, Journal of Banking and Finance, 2012,1678-1687.
Monfort A., Renne J.-P. : Default, Liquidity and Crises : An Econometric Framework”, Journal of Financial Econometrics, 2013,11,2,221-262.
Monfort A., Renne J.-P. : “Decomposing the Euro area Spreads : Credit and Liquidity Risks”, Review of Finance, 2014, 18, 6, 2103-2151.
Monfort, A., Renne, J.P. and Roussellet, G. : "Quadratic Kalman Filter", Journal of Econometrics, 2015, 187, 1, 43-56.
Monfort A., Renne J.P., Roussellet G., Pegoraro F. : “Staying at Zero with Affine Processes: An Application to Term Structure Modelling”, Journal of Econometrics, 2017, 201, 2, 348-366.
Renne, J.P. : "A Model for the Euro-Area Yield Curve with Discrete Policy Rates", Banque de France, 2012, Working Paper n°395.
Schwarz, E. S. : “The Stochastic Behavior of Commodity Prices : Implications for Valuation and Hedging”, 1997, The Journal of Finance, L11, 3, 923-973.