Tempered stable Ornstein– Uhlenbeck processes: A practical view

ABSTRACT We study the one-dimensional Ornstein–Uhlenbeck (OU) processes with marginal law given by tempered stable and tempered infinitely divisible distributions. We investigate the transition law between consecutive observations of these processes and evaluate the characteristic function of integrated tempered OU processes with a view toward practical applications. We then analyze how to draw a random sample from this class of processes by considering both the classical inverse transform algorithm and an acceptance–rejection method based on simulating a stable random sample. Using a maximum likelihood estimation method based on the fast Fourier transform, we empirically assess the simulation algorithm performance.

[1]  Andrea Nobili,et al.  Oil and the Macroeconomy: A Quantitative Structural Analysis , 2009 .

[2]  Ioannis Kyriakou,et al.  Monte Carlo Simulation of the CGMY Process and Option Pricing , 2013 .

[3]  R. Kawai,et al.  On finite truncation of infinite shot noise series representation of tempered stable laws , 2011 .

[4]  J. Teichmann,et al.  THE AFFINE LIBOR MODELS , 2009, 0904.0555.

[5]  Riccardo Cristadoro,et al.  Household savings in China , 2012 .

[6]  Massimiliano Marcellino,et al.  Short-Term GDP Forecasting With a Mixed-Frequency Dynamic Factor Model With Stochastic Volatility , 2013 .

[7]  Stefano Federico,et al.  Headquarter intensity and the choice between outsourcing versus integration at home or abroad , 2012 .

[8]  Reiichiro Kawai,et al.  On simulation of tempered stable random variates , 2010, J. Comput. Appl. Math..

[9]  S. Rachev,et al.  Tempered stable distributions and processes in finance: numerical analysis , 2010 .

[10]  J. Rosínski.  Tempering stable processes , 2007 .

[11]  Luisa Carpinelli,et al.  Credit Supply During a Sovereign Debt Crisis , 2013 .

[12]  Andrea Nobili,et al.  Futures Contract Rates as Monetary Policy Forecasts , 2008, SSRN Electronic Journal.

[13]  Reiichiro Kawai,et al.  Exact discrete sampling of finite variation tempered stable Ornstein–Uhlenbeck processes , 2011, Monte Carlo Methods Appl..

[14]  Dawn Hunter,et al.  A public guarantee of a minimum return to defined contribution pension scheme members , 2011 .

[15]  Matteo Bugamelli,et al.  Do Workers' Remittances Reduce the Probability of Current Account Reversals? , 2005 .

[16]  Frank J. Fabozzi,et al.  Financial Models with Levy Processes and Volatility Clustering , 2011 .

[17]  F. Cingano,et al.  Politicians at Work: The Private Returns and Social Costs of Political Connections , 2009 .

[18]  F. Tricomi.  Funzioni ipergeometriche confluenti , 1954 .

[19]  Libero Monteforte,et al.  The General Equilibrium Effects of Fiscal Policy: Estimates for the Euro Area , 2007 .

[20]  Andrea Neri,et al.  Asking Income and Consumption Questions in the Same Survey: What are the Risks? , 2013 .

[21]  Jennifer L. Sinclair,et al.  Generalized tempered stable processes , 2010 .

[22]  Leandro D'Aurizio,et al.  Family Firms and the Great Recession: Out of Sight, Out of Mind? , 2012 .

[23]  Silvia Magri,et al.  The financing of small innovative firms: the Italian case , 2007 .

[24]  Marcello Pericoli,et al.  The CAPM and the Risk Appetite Index: Theoretical Differences, Empirical Similarities, and Implementation Problems , 2009 .

[25]  Neil Shephard,et al.  Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models , 2003 .

[26]  Paolo Piselli,et al.  Determinants of long-run regional productivity with geographical spillovers: The role of R&D, human capital and public infrastructure , 2009 .

[27]  A. Calza,et al.  NONLINEARITIES IN THE DYNAMICS OF THE EURO AREA DEMAND FOR M1 , 2008, Macroeconomic Dynamics.

[28]  Valter Di Giacinto,et al.  Local and Global Agglomeration Patterns: Two Econometrics-Based Indicators , 2011 .

[29]  Raffaela Giordano,et al.  What Determines Debt Intolerance? The Role of Political and Monetary Institutions , 2009 .

[30]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[31]  E. Nicolato,et al.  Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type , 2003 .

[32]  Stefano Federico,et al.  Industry Dynamics and Competition from Low‐Wage Countries: Evidence on Italy , 2014 .

[33]  Svetlozar T. Rachev,et al.  Approximation of skewed and leptokurtic return distributions , 2012 .

[34]  Reiichiro Kawai,et al.  Infinite Variation Tempered Stable Ornstein–Uhlenbeck Processes with Discrete Observations , 2010, Commun. Stat. Simul. Comput..

[35]  Juri Marcucci,et al.  The Predictive Power of Google Searches in Forecasting Unemployment , 2012 .

[36]  Eugenio Gaiotti,et al.  Credit availability and investment: Lessons from the “great recession” , 2013 .

[37]  Xinsheng Zhang,et al.  Exact Simulation of IG-OU Processes , 2008 .

[38]  Alessandro Girardi,et al.  Price Discovery in the Italian Sovereign Bonds Market: The Role of Order Flow , 2013 .

[39]  Sauro Mocetti,et al.  Tax morale and public spending inefficiency , 2009 .

[40]  Ernst Eberlein,et al.  Term Structure Models Driven by General Lévy Processes , 1999 .

[41]  Silvia Fabiani,et al.  What's Behind 'Inflation Perceptions'? A Survey-Based Analysis of Italian Consumers , 2008 .

[42]  Emanuela Ciapanna,et al.  Directed Matching with Endogenous Markov Probability: Clients or Competitors? , 2010 .

[43]  Paolo Piselli,et al.  Emerging Markets Spreads and Global Financial Conditions , 2007 .

[44]  Andrea Nobili,et al.  The Transmission of US Monetary Policy to the Euro Area , 2010 .

[45]  Antonio Accetturo,et al.  Geography, Productivity, and Trade: Does Selection Explain Why Some Locations are More Productive than Others? , 2013, Journal of Regional Science.

[46]  M. S. Ridout,et al.  Generating random numbers from a distribution specified by its Laplace transform , 2009, Stat. Comput..

[47]  Piotr Jelonek,et al.  Generating Tempered Stable Random Variates from Mixture Representation , 2012 .

[48]  Mario Quagliariello,et al.  Incentives Through the Cycle: Microfounded Macroprudential Regulation , 2011 .

[49]  Elisa Nicolato,et al.  Sato Processes in Default Modelling , 2010 .

[50]  Shibin Zhang,et al.  Exact simulation of tempered stable Ornstein–Uhlenbeck processes , 2011 .

[51]  Fabio Fornari,et al.  Macroeconomic Determinants of Carry Trade Activity , 2010 .

[52]  A. Calza,et al.  Sectoral Money Demand and the Great Disinflation in the US , 2010, SSRN Electronic Journal.

[53]  Yener Altunbas,et al.  Securitisation and the Bank Lending Channel , 2007 .

[54]  Luc Devroye,et al.  Random variate generation for exponentially and polynomially tilted stable distributions , 2009, TOMC.

[55]  M. Affinito,et al.  Do Interbank Customer Relationships Exist? And How Did They Function Over the Crisis? Learning from Italy , 2011 .

[56]  Giacinto Micucci,et al.  The Producer Service Sector in Italy: Long-term Growth and its Local Determinants , 2007 .

[57]  M. Pisani,et al.  The EAGLE: A Model for Policy Analysis of Macroeconomic Interdependence in the Euro Area , 2010, SSRN Electronic Journal.

[58]  M. Affinito,et al.  What are Borders Made of? An Analysis of Barriers to European Banking Integration , 2008 .

[59]  Stefano Federico,et al.  Measuring the Price Elasticity of Import Demand in the Destination Markets of Italian Export , 2010 .

[60]  Filippo Altissimo,et al.  New Eurocoin: Tracking Economic Growth in Real Time , 2006, The Review of Economics and Statistics.

[61]  Ines Buono,et al.  The Effect of the Uruguay Round on the Intensive and Extensive Margins of Trade , 2010 .

[62]  Francesco D'Amuri,et al.  Immigration, Jobs and Employment Protection: Evidence from Europe before and during the Great Recession , 2012 .

[63]  J. Rosínski.  Series Representations of Lévy Processes from the Perspective of Point Processes , 2001 .

[64]  N. Shephard,et al.  Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics , 2001 .

[65]  Elisabetta Allevi,et al.  A Spatial Competitive Analysis: The Carbon Leakage Effect on the Cement Industry Under the European Emissions Trading Scheme , 2013 .

[66]  Frank J. Fabozzi,et al.  Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads , 2015 .

[67]  Antonio Accetturo,et al.  Policies for Local Development: An Evaluation of Italy's 'Patti Territoriali' , 2011 .

[68]  Antonio Di Cesare,et al.  An Analysis of the Determinants of Credit Default Swap Spread Changes Before and During the Subprime Financial Turmoil , 2010 .

[69]  Michael Grabchak.  On a new Class of Tempered Stable Distributions: Moments and Regular Variation , 2012, J. Appl. Probab..

[70]  Svetlozar T. Rachev,et al.  Tempered stable and tempered infinitely divisible GARCH models , 2010 .

[71]  Domenico Depalo,et al.  Public–private wage differentials in euro-area countries: evidence from quantile decomposition analysis , 2015 .

[72]  G. Gobbi,et al.  Does the Underground Economy Hold Back Financial Deepening? Evidence from the Italian Credit Market , 2007 .

[73]  W. Schoutens.  Lévy Processes in Finance: Pricing Financial Derivatives , 2003 .

[74]  Daniele Franco,et al.  The Reliability of EMU Fiscal Indicators: Risks and Safeguards , 2007 .

[75]  Xinsheng Zhang,et al.  On the Transition Law of Tempered Stable Ornstein–Uhlenbeck Processes , 2009, Journal of Applied Probability.

[76]  Silvia Magri,et al.  The Rise of Risk-Based Pricing of Mortgage Interest Rates in Italy , 2010 .

[77]  Giancarlo Spagnolo,et al.  Limited Credit Records and Market Outcomes , 2013 .

[78]  Marcello Pericoli,et al.  " Pure " or " wake-up-call " contagion ? Another look at the EMU sovereign debt crisis Ra ¤ , 2012 .

[79]  W. Schoutens,et al.  Jumps in intensity models: investigating the performance of Ornstein-Uhlenbeck processes in credit risk modeling , 2009 .

[80]  Stefano Federico,et al.  Outsourcing versus integration at home or abroad and firm heterogeneity , 2010 .

[81]  Alessandro Staino.  Financial models with Lévy processes , 2008 .

[82]  Antonio Accetturo,et al.  Agglomeration and Growth: The Effects of Commuting Costs , 2008 .

[83]  Nico M. Temme,et al.  Numerical methods for special functions , 2007 .

[84]  Stoyan V. Stoyanov,et al.  Numerical Methods for Stable Modeling in Financial Risk Management , 2004 .

[85]  S. Rachev,et al.  Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models , 2014 .

[86]  Andrea Nobili,et al.  " Liquidity and Liquidity Risks ": What Has Changed, and Why ? " the Interbank Market after August 2007: What Has Changed, and Why? , 2022 .

[87]  Guido Ascari,et al.  Trend Inflation, Taylor Principle and Indeterminacy , 2009 .

[88]  Marco Taboga,et al.  Under/Over-Valuation of the Stock Market and Cyclically Adjusted Earnings , 2010 .

[89]  Michele Leonardo Bianchi.  Are the log-returns of Italian open-end mutual funds normally distributed? A risk assessment perspective , 2015 .

[90]  Giuliana Palumbo,et al.  Over-Optimism and Lender Liability in the Consumer Credit Market , 2010 .

[91]  Giuseppe Cappelletti,et al.  A Note on Rationalizability and Restrictions on Belief , 2010 .

[92]  Davide Fantino,et al.  Evaluating the Efficacy of European Regional Funds for R&D , 2013 .

[93]  Stefano Nobili,et al.  Explaining and Forecasting Bond Risk Premiums , 2010 .

[94]  I. J. Schoenberg.  Metric spaces and completely monotone functions , 1938 .

[95]  Enrico Beretta,et al.  Banking Consolidation and Bank-Firm Credit Relationships: The Role of Geographical Features and Relationship Characteristics , 2013 .

[96]  Craig B. Borkowf,et al.  Random Number Generation and Monte Carlo Methods , 2000, Technometrics.

[97]  Leonardo Gambacorta,et al.  Mutual Guarantee Institutions and Small Business Finance , 2009 .

[98]  Olivier J. Blanchard,et al.  Why are the 2000s so Different from the 1970s? A Structural Interpretation of Changes in the Macroeconomic Effects of Oil Prices , 2009 .

[99]  M. L. Bianchi,et al.  An Empirical Comparison of Alternative Credit Default Swap Pricing Models , 2012 .

[100]  Agnieszka Wyłomańska,et al.  Measures of dependence for Ornstein–Uhlenbeck processes with tempered stable distribution , 2010 .

[101]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[102]  Giuseppe Cappelletti,et al.  What Determines Annuity Demand at Retirement? , 2013 .

[103]  Paolo Piselli,et al.  Testing for East-West Contagion in the European Banking Sector During the Financial Crisis , 2011 .

[104]  Vincenzo Cuciniello,et al.  The Welfare Effect of Foreign Monetary Conservatism with Non-Atomistic Wage Setters , 2009 .

[105]  Svetlozar T. Rachev,et al.  Tempered Infinitely Divisible Distributions and Processes , 2011 .