A Bayesian Beta Markov Random Field Calibration of the Term Structure of Implied Risk Neutral Densities

We build on Fackler and King (1990) and propose a general calibration model for implied risk neutral densities. Our model allows for the joint calibration of a set of densities at different maturities and dates. The model is a Bayesian dynamic beta Markov random field which allows for possible time dependence between densities with the same maturity and for dependence across maturities at the same point in time. The assumptions on the prior distribution allow us to compound the needs of model flexibility, parameter parsimony and information pooling across densities.

[1]  Peter F. CHRISTOFFERSENti.  EVALUATING INTERVAL FORECASTS , 2016 .

[2]  [PDF] Asset Pricing Theory (Princeton Series In Finance) , 2016 .

[3]  V. Ivanova,et al.  Interest rate forecasts, state price densities and risk premium from Euribor options , 2014 .

[4]  George Kapetanios,et al.  Generalised Density Forecast Combinations , 2014 .

[5]  G. Durham.  Risk-neutral Modeling with Affine and Nonaffine Models , 2013 .

[6]  V. Ivanova,et al.  Getting real forecasts, state price densities and risk premium from Euribor options , 2013 .

[7]  Jukka Sihvonen,et al.  Forward-Looking Monetary Policy Rules and Option-Implied Interest Rate Expectations , 2012 .

[8]  Vu,et al.  Time-Varying Combinations of Predictive Densities Using Nonlinear Filtering , 2012 .

[9]  Estimating Probability Distributions of Future Asset Prices: Empirical Transformations from Option-Implied Risk-Neutral to Real-World Density Functions , 2012 .

[10]  W. Lai.  Comparison of methods to estimate option implied risk-neutral densities , 2014 .

[11]  Olivier Vergote,et al.  Interest Rate Expectations and Uncertainty During ECB Governing Council Days: Evidence From Intraday Implied Densities of 3-Month EURIBOR , 2011, SSRN Electronic Journal.

[12]  T. Gneiting,et al.  Combining Predictive Distributions , 2011, 1106.1638.

[13]  Radford M. Neal.  Optimal Proposal Distributions and Adaptive MCMC , 2008 .

[14]  Faming Liang,et al.  A double Metropolis–Hastings sampler for spatial models with intractable normalizing constants , 2010 .

[15]  R. Casarin,et al.  Bayesian Model Selection for Beta Autoregressive Processes , 2010, 1008.0121.

[16]  Fabrizio Durante,et al.  Copula Theory and Its Applications , 2010 .

[17]  D. Filipović.  Term-Structure Models: A Graduate Course , 2009 .

[18]  Henryk Gzyl,et al.  Determination of risk pricing measures from market prices of risk , 2008 .

[19]  J. Geweke,et al.  Optimal Prediction Pools , 2008 .

[20]  Enrique ter Horst,et al.  Bayesian dynamic density estimation , 2008 .

[21]  Christian P. Robert,et al.  Bayesian computation for statistical models with intractable normalizing constants , 2008, 0804.3152.

[22]  Gianluca Fusai,et al.  Implementing Models in Quantitative Finance: Methods and Cases , 2008 .

[23]  W. Johnson,et al.  BAYESIAN BETA REGRESSION: APPLICATIONS TO HOUSEHOLD EXPENDITURE DATA AND GENETIC DISTANCE BETWEEN FOOT‐AND‐MOUTH DISEASE VIRUSES , 2007 .

[24]  Fabrice Douglas Rouah,et al.  Option Pricing Models and Volatility Using Excel-VBA , 2007 .

[25]  S. Hall,et al.  Combining density forecasts , 2007 .

[26]  Iain Murray,et al.  MCMC for Doubly-intractable Distributions , 2006, UAI.

[27]  Nizar Bouguila,et al.  Practical Bayesian estimation of a finite beta mixture through gibbs sampling and its applications , 2006, Stat. Comput..

[28]  J. Møller,et al.  An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants , 2006 .

[29]  Walter Schachermayer,et al.  The Mathematics of Arbitrage , 2006 .

[30]  William R. Melick,et al.  Recovering Market Expectations of FOMC Rate Changes With Options on Federal Funds Futures , 2005 .

[31]  Anton H. Westveld,et al.  Calibrated Probabilistic Forecasting Using Ensemble Model Output Statistics and Minimum CRPS Estimation , 2005 .

[32]  R. Schilling.  Financial Modelling with Jump Processes , 2005 .

[33]  S. Ferrari,et al.  Beta Regression for Modelling Rates and Proportions , 2004 .

[34]  Robert L. Kimmel.  Modeling the term structure of interest rates: A new approach , 2004 .

[35]  R. Bliss,et al.  Option-Implied Risk Aversion Estimates , 2004 .

[36]  R. Cont,et al.  Financial Modelling with Jump Processes , 2003 .

[37]  P. Schönbucher.  Credit Derivatives Pricing Models: Models, Pricing and Implementation , 2003 .

[38]  Nikolaos Panigirtzoglou,et al.  A new approach to modeling the dynamics of implied distributions: Theory and evidence from the S&P 500 options , 2004 .

[39]  Yacine Ait-Sahalia,et al.  Nonparametric Option Pricing Under Shape Restrictions , 2002 .

[40]  S. Levendorskii,et al.  Non-Gaussian Merton-Black-Scholes theory , 2002 .

[41]  C. Robert,et al.  A Mixture Approach to Bayesian Goodness of Fit , 2002 .

[42]  Jeremy Berkowitz.  Testing Density Forecasts, With Applications to Risk Management , 2001 .

[43]  John Odentrantz,et al.  Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues , 2000, Technometrics.

[44]  R. Bhar,et al.  Expectations of monetary policy in Australia implied by the probability distribution of interest rate derivatives , 2000 .

[45]  Nikolaos Panigirtzoglou,et al.  Testing the Stability of Implied Probability Density Functions , 2002 .

[46]  Anthony S. Tay,et al.  Multivariate Density Forecast Evaluation and Calibration In Financial Risk Management: High-Frequency Returns on Foreign Exchange , 1999, Review of Economics and Statistics.

[47]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[48]  Anthony S. Tay,et al.  Evaluating Density Forecasts with Applications to Financial Risk Management , 1998 .

[49]  Virginia R. Young,et al.  Risk-adjusted credibility premiums using distorted probabilities , 1998 .

[50]  A. Lo,et al.  Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices , 1998 .

[51]  C. Sims,et al.  Bayesian methods for dynamic multivariate models , 1998 .

[52]  Allan M. Malz.  Estimating the Probability Distribution of the Future Exchange Rate from Option Prices , 1997 .

[53]  Shaun S. Wang,et al.  Axiomatic characterization of insurance prices , 1997 .

[54]  Anthony S. Tay,et al.  Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters , 1997 .

[55]  J. Campa,et al.  Implied Exchange Rate Distributions: Evidence from OTC Option Markets , 1997 .

[56]  Robert S. Goldstein.  The Term Structure of Interest Rates as a Random Field , 1997 .

[57]  J. Campa,et al.  Erm Bandwidths for Emu and after: Evidence from Foreign Exchange Options , 1997 .

[58]  Lars E. O. Svensson,et al.  New Techniques to Extract Market Expectations from Financial Instruments , 1997 .

[59]  R. Engle,et al.  Testing the Volatility Term Structure Using Option Hedging Criteria , 1997 .

[60]  Andrew W. Lo,et al.  Nonparametric estimation of state-price densities implicit in financial asset prices , 1995, Proceedings of 1995 Conference on Computational Intelligence for Financial Engineering (CIFEr).

[61]  Siddhartha Chib,et al.  Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models☆ , 1995 .

[62]  Hans U. Gerber,et al.  Option pricing by Esscher transforms. , 1995 .

[63]  D. P. Kennedy.  THE TERM STRUCTURE OF INTEREST RATES AS A GAUSSIAN RANDOM FIELD , 1994 .

[64]  A. Raftery,et al.  Prediction Rules for Exponential Family State Space Models , 1993 .

[65]  Noel A Cressie,et al.  NEW MODELS FOR MARKOV RANDOM FIELDS , 1992 .

[66]  M. West,et al.  Modelling Probabilistic Agent Opinion , 1992 .

[67]  M. West,et al.  Modelling Agent Forecast Distributions , 1992 .

[68]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[69]  R. King,et al.  Calibration of Option-Based Probability Assessments in Agricultural Commodity Markets , 1990 .

[70]  J. Hull.  Options, Futures, and Other Derivatives , 1989 .

[71]  Kenneth F. Wallis,et al.  TIME SERIES ANALYSIS OF BOUNDED ECONOMIC VARIABLES , 1987 .

[72]  E. McKenzie,et al.  An Autoregressive Process for Beta Random Variables , 1985 .

[73]  Robert B. Litterman.  Forecasting with Bayesian Vector Autoregressions-Five Years of Experience , 1984 .

[74]  Douglas T. Breeden,et al.  Prices of State-Contingent Claims Implicit in Option Prices , 1978 .

[75]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[76]  F Escher,et al.  On the probability function in the collective theory of risk , 1932 .

[77]  O. Nikodým.  Sur une généralisation des intégrales de M. J. Radon , 1930 .