Complex Systems in Finance and Econometrics

2011 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Stochastic Volatility

  • Torben G. Andersen
  • Luca Benzoni
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-7701-4_38
How to cite

Article Outline

Glossary

Definition of the Subject

Introduction

Model Specification

Realized Volatility

Applications

Estimation Methods

Future Directions

Acknowledgments

Bibliography

Keywords

Option Price Stochastic Volatility Credit Default Swap Implied Volatility Stochastic Volatility Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgments

We are grateful to Olena Chyruk, Bruce Mizrach (the Section Editor) and Neil Shephard for helpful comments and suggestions. Of course, all errors remain our sole responsibility. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System. The work of Andersen is supported by a grant from the NSF to the NBER and support from CREATES funded by the Danish National Research Foundation.

Bibliography

Primary Literature

  1. 1.
    Ahn DH, Dittmar RF, Gallant AR (2002) Quadratic Term Structure Models: Theory and Evidence. Rev Finance Stud 15:243–288Google Scholar
  2. 2.
    Ahn DH, Dittmar RF, Gallant AR, Gao B (2003) Purebred or hybrid?: Reproducing the volatility in term structure dynamics. J Econometrics 116:147–180Google Scholar
  3. 3.
    Aït‑Sahalia Y (2002) Maximum‐Likelihood Estimation of Discretely‐Sampled Diffusions: A Closed‐Form Approximation Approach. Econometrica 70:223–262Google Scholar
  4. 4.
    Aït‑Sahalia Y (2007) Closed‐Form Likelihood Expansions for Multivariate Diffusions. Annals of Statistics, forthcomingGoogle Scholar
  5. 5.
    Aït‑Sahalia Y, Hansen LP, Scheinkman J (2004) Operator Methods for Continuous‐Time Markov Processes. In: Hansen LP, Aït‑Sahalia Y (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcomingGoogle Scholar
  6. 6.
    Aït‑Sahalia Y, Jacod J (2007) Testing for Jumps in a Discretely Observed Process. Annals of Statistics, forthcomingGoogle Scholar
  7. 7.
    Aït‑Sahalia Y, Kimmel R (2007) Maximum Likelihood Estimation of Stochastic Volatility Models. J Finance Econ 83:413–452Google Scholar
  8. 8.
    Alizadeh S, Brandt MW, Diebold FX (2002) Range-Based Estimation of Stochastic Volatility Models. J Finance 57:1047–1091Google Scholar
  9. 9.
    Almeida CIR, Graveline JJ, Joslin S (2006) Do Options Contain Information About Excess Bond Returns? Working Paper, UMN, Fundação Getulio Vargas, MIT, CambridgeGoogle Scholar
  10. 10.
    Andersen TG (1994) Stochastic Autoregressive Volatility: A Framework for Volatility Modeling. Math Finance 4:75–102Google Scholar
  11. 11.
    Andersen TG (1996) Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility. J Finance 51:169–204Google Scholar
  12. 12.
    Andersen TG, Benzoni L (2006) Do Bonds Span Volatility Risk in the US Treasury Market? A Specification Test for Affine Term Structure Models. Working Paper, KSM and Chicago FED, ChicagoGoogle Scholar
  13. 13.
    Andersen TG, Benzoni L (2007) The Determinants of Volatility in the US Treasury market. Working Paper, KSM and Chicago FED, ChicagoGoogle Scholar
  14. 14.
    Andersen TG, Benzoni L (2007) Realized volatility. In: Andersen TG, Davis RA, Kreiss JP, Mikosch T (eds) Handbook of Financial Time Series. Springer, Berlin (forthcoming)Google Scholar
  15. 15.
    Andersen TG, Benzoni L, Lund J (2002) An Empirical Investigation of Continuous‐Time Equity Return Models. J Finance 57:1239–1284Google Scholar
  16. 16.
    Andersen TG, Benzoni L, Lund J (2004) Stochastic Volatility, Mean Drift and Jumps in the Short Term Interest Rate. Working Paper, Northwestern University, University of Minnesota, and Nykredit Bank, CopenhagenGoogle Scholar
  17. 17.
    Andersen TG, Bollerslev T (1998) Deutsche Mark‐Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies. J Finance 53:219–265Google Scholar
  18. 18.
    Andersen TG, Bollerslev T (1998) Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts. Int Econ Rev 39:885–905Google Scholar
  19. 19.
    Andersen TG, Bollerslev T, Diebold FX (2004) Parametric and nonparametric volatility measurement. In: Hansen LP, Aït‑Sahalia Y (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcomingGoogle Scholar
  20. 20.
    Andersen TG, Bollerslev T, Diebold FX (2007) Roughing It Up: Including Jump Components in Measuring, Modeling and Forecasting Asset Return Volatility. Rev Econ Statist 89:701–720 Google Scholar
  21. 21.
    Andersen TG, Bollerslev T, Diebold FX, Labys P (2003) Modeling and Forecasting Realized Volatility. Econometrica 71:579–625Google Scholar
  22. 22.
    Andersen TG, Bollerslev T, Diebold FX, Vega C (2003) Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange. Ammer Econom Rev 93:38–62Google Scholar
  23. 23.
    Andersen TG, Bollerslev T, Dobrev D (2007) No‐arbitrage semi‐martingale restrictions for continuous‐time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications. J Econome 138:125–180Google Scholar
  24. 24.
    Andersen TG, Bollerslev T, Meddahi N (2004) Analytic Evaluation of Volatility Forecasts. Int Econ Rev 45:1079–1110Google Scholar
  25. 25.
    Andersen TG, Bollerslev T, Meddahi N (2005) Correcting the Errors: Volatility Forecast Evaluation Using High‐Frequency Data and Realized Volatilities. Econometrica 73:279–296Google Scholar
  26. 26.
    Andersen TG, Bondarenko O (2007) Construction and Interpretation of Model-Free Implied Volatility. Working Paper, KSM and UIC, ChicagoGoogle Scholar
  27. 27.
    Andersen TG, Chung HJ, Sørensen BE (1999) Efficient Method of Moments Estimation of a Stochastic Volatility Model: A Monte Carlo Study. J Econom 91:61–87Google Scholar
  28. 28.
    Andersen TG, Lund J (1997) Estimating continuous‐time stochastic volatility models of the short term interest rate diffusion. J Econom 77:343–377Google Scholar
  29. 29.
    Ané T, Geman H (2000) Order Flow, Transaction Clock, and Normality of Asset Returns. J Finance 55:2259–2284Google Scholar
  30. 30.
    Ang A, Hodrick RJ, Xing Y, Zhang X (2006) The Cross‐Section of Volatility and Expected Returns. J Finance 51:259–299Google Scholar
  31. 31.
    Ang A, Hodrick RJ, Xing Y, Zhang X (2008) High idiosyncratic volatility and low returns: international and further U.S. evidence. Finance Econ (forthcoming)Google Scholar
  32. 32.
    Bachelier L (1900) Théorie de la Spéculation. Annales de École Normale Supérieure 3, Gauthier‐Villars, Paris. English translation: Cootner PH (ed) (1964) The Random Character of Stock Market Prices. MIT Press, CambridgeGoogle Scholar
  33. 33.
    Back K (1991) Asset Prices for General Processes. J Math Econ 20:371–395Google Scholar
  34. 34.
    Bakshi G, Cao C, Chen Z (1997) Empirical Performance of Alternative Option Pricing Models. J Finance 52:2003–2049Google Scholar
  35. 35.
    Bakshi G, Cao C, Chen Z (2002) Pricing and hedging long-term options. J Econom 94:277–318Google Scholar
  36. 36.
    Bakshi G, Kapadia N (2003) Delta‐Hedged Gains and the Negative Market Volatility Risk Premium. Rev Finance Stud 16:527–566Google Scholar
  37. 37.
    Bakshi G, Kapadia N, Madan D (2003) Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options. Rev Finance Stud 16:101–143Google Scholar
  38. 38.
    Balduzzi P, Elton EJ, Green TC (2001) Economic News and Bond Prices: Evidence from the US Treasury Market. J Finance Quant Anal 36:523–543Google Scholar
  39. 39.
    Bandi FM (2002) Short-term interest rate dynamics: a spatial approach. J Financ Econ 65:73–110Google Scholar
  40. 40.
    Bandi FM, Moise CE, Russel JR (2008) Market volatility, market frictions, and the cross section of stock returns. Working Paper, University of Chicago, and Case Western Reverse University, ClevelandGoogle Scholar
  41. 41.
    Bandi FM, Nguyen T (2003) On the functional estimation of jump‐diffusion models. J Econom 116:293–328Google Scholar
  42. 42.
    Bandi FM, Phillips PCB (2002) Nonstationary Continuous‐Time Processes. In: Hansen LP, Aït‑Sahalia Y (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcomingGoogle Scholar
  43. 43.
    Bandi FM, Phillips PCB (2003) Fully nonparametric estimation of scalar diffusion models. Econometrica 71:241–283Google Scholar
  44. 44.
    Bandi FM, Phillips PCB (2007) A simple approach to the parametric estimation of potentially nonstationary diffusions. J Econom 137:354–395Google Scholar
  45. 45.
    Bandi FM, Russell J (2006) Separating Microstructure Noise from Volatility. J Finance Econ 79:655–692Google Scholar
  46. 46.
    Bandi FM, Russell J (2007) Volatility. In: Birge J, Linetsky V (eds) Handbook of Financial Engineering. Elsevier, AmsterdamGoogle Scholar
  47. 47.
    Bansal R, Yaron A (2004) Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles. J Finance 59:1481–1509Google Scholar
  48. 48.
    Bartlett MS (1938) The Characteristic Function of a Conditional Statistic. J Lond Math Soc 13:63–67Google Scholar
  49. 49.
    Barndorff‐Nielsen OE, Hansen P, Lunde A, Shephard N (2007) Designing Realized Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise. Working Paper, University of Aarhus, Aarhus. Stanford University, Nuffield College, OxfordGoogle Scholar
  50. 50.
    Barndorff‐Nielsen OE, Shephard N (2001) Non‐Gaussian Ornstein-Uhlenbeckbased models and some of their uses in financial economics. J R Stat Soc B 63:167–241Google Scholar
  51. 51.
    Barndorff‐Nielsen OE, Shephard N (2002) Econometric Analysis of Realised Volatility and its Use in Estimating Stochastic Volatility Models. J R Stat Soc B 64:253–280Google Scholar
  52. 52.
    Barndorff‐Nielsen OE, Shephard N (2002b) Estimating quadratic variation using realized variance. J Appl Econom 17:457–477Google Scholar
  53. 53.
    Barndorff‐Nielsen OE, Shephard N (2004) Power and bipower variation with stochastic volatility and jumps. J Finance Econom 2:1–37Google Scholar
  54. 54.
    Barndorff‐Nielsen OE, Shephard N (2006) Econometrics of testing for jumps in financial economics using bipower variation. J Finance Econom 4:1–30Google Scholar
  55. 55.
    Bates DS (1991) The Crash of '87: Was It Expected? The Evidence from Options Markets. J Finance 46:1009–1044Google Scholar
  56. 56.
    Bates DS (1996) Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options. Rev Finance Stud 9:69–107Google Scholar
  57. 57.
    Bates DS (2000) Post-'87 crash fears in the S&P 500 futures option market. J Econom 94:181–238Google Scholar
  58. 58.
    Bates DS (2006) Maximum Likelihood Estimation of Latent Affine Processes. Rev Finance Stud 19:909–965Google Scholar
  59. 59.
    Benzoni L (2002) Pricing Options under Stochastic Volatility: An Empirical Investigation. Working Paper, Chicago FEDGoogle Scholar
  60. 60.
    Benzoni L, Collin‐Dufresne P, Goldstein RS (2007) Explaining Pre- and Post-1987 Crash Prices of Equity and Options within a Unified General Equilibrium Framework. Working Paper, Chicago FED, UCB, and UMN, MinneapolisGoogle Scholar
  61. 61.
    Bibby BM, Jacobsen M, Sorensen M (2004) Estimating Functions for Discretely Sampled Diffusion‐Type Models. In: Hansen LP, Aït‑Sahalia Y (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcomingGoogle Scholar
  62. 62.
    Bikbov R, Chernov M (2005) Term Structure and Volatility: Lessons from the Eurodollar Markets. Working Paper, LBS, Deutsche Bank, New YorkGoogle Scholar
  63. 63.
    Black F, Scholes M (1973) The Pricing of Options and Corporate Liabilities. J Political Econ 81:637–654Google Scholar
  64. 64.
    Bladt M, Sørensen M (2007) Simple Simulation of Diffusion Bridges with Application to Likelihood Inference for Diffusions. Working Paper, University of Copenhagen, CopenhagenGoogle Scholar
  65. 65.
    Bollen NPB, Whaley RE (2004) Does Net Buying Pressure Affect the Shape of Implied Volatility Functions? J Finance 59:711–753Google Scholar
  66. 66.
    Bollerslev T, Gibson M, Zhou H (2004) Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option‐Implied and Realized Volatilities. Working Paper, Duke University, Federal Reserve Board, Washington D.C.Google Scholar
  67. 67.
    Bollerslev T, Jubinsky PD (1999) Equity Trading vol and Volatility: Latent Information Arrivals and Common Long-Run Dependencies. J Bus Econ Stat 17:9–21Google Scholar
  68. 68.
    Bollerslev T, Zhou H (2002) Estimating stochastic volatility diffusion using conditional moments of integrated volatility. J Econom 109:33–65Google Scholar
  69. 69.
    Bollerslev T, Zhou H (2007) Expected Stock Returns and Variance Risk Premia. Working Paper, Duke University and Federal Reserve Board, Washington D.C.Google Scholar
  70. 70.
    Bondarenko O (2004) Market price of variance risk and performance of hedge funds. Working Paper, UIC, ChicagoGoogle Scholar
  71. 71.
    Brandt MW, Chapman DA (2003) Comparing Multifactor Models of the Term Structure. Working Paper, Duke University and Boston College, Chestnut HillGoogle Scholar
  72. 72.
    Brandt MW, Diebold FX (2006) A No‐Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations. J Bus 79:61–73Google Scholar
  73. 73.
    Brandt MW, Jones CS (2006) Volatility Forecasting with Range-Based EGARCH Models. J Bus Econ Stat 24:470–486Google Scholar
  74. 74.
    Brandt MW, Kavajecz KA (2004) Price Discovery in the US Treasury Market: The Impact of Orderflow and Liquidity on the Yield Curve. J Finance 59:2623–2654Google Scholar
  75. 75.
    Brandt MW, Santa-Clara P (2002) Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets. J Finance Econ 63:161–210Google Scholar
  76. 76.
    Breidt FJ, Crato N, de Lima P (1998) The detection and estimation of long memory in stochastic volatility. J Econom 83:325–348Google Scholar
  77. 77.
    Britten‐Jones M, Neuberger A (2000) Option Prices, Implied Price Processes, and Stochastic Volatility. J Finance 55:839–866Google Scholar
  78. 78.
    Broadie M, Chernov M, Johannes MJ (2007) Model Specification and Risk Premia: Evidence from Futures Options. J Finance 62:1453–1490Google Scholar
  79. 79.
    Buraschi A, Jackwerth J (2001) The price of a smile: hedging and spanning in option markets. Rev Finance Stud 14:495–527Google Scholar
  80. 80.
    Campbell JY, Cochrane JH (1999) By Force of Habit: A Consumption‐Based Explanation of Aggregate Stock Market Behavior. J Polit Economy 107:205–251Google Scholar
  81. 81.
    Campbell JY, Viceira LM (2001) Who Should Buy Long-Term Bonds? Ammer Econ Rev 91:99–127Google Scholar
  82. 82.
    Carr P, Lee R (2007) Robust Replication of Volatility Derivatives. Working Paper, NYU and Uinversity of Chicago, ChicagoGoogle Scholar
  83. 83.
    Carr P, Madan D (1998) Towards a theory of volatility trading. In: Jarrow R (ed) Volatility. Risk Publications, LondonGoogle Scholar
  84. 84.
    Carr P, Wu L (2004) Time‐changed Lévy processes and option pricing. J Finance Econ 71:113–141Google Scholar
  85. 85.
    Carr P, Wu L (2007) Variance Risk Premia. Rev Finance Stud, forthcomingGoogle Scholar
  86. 86.
    Carrasco M, Chernov M, Florens JP, Ghysels E (2007) Efficient estimation of general dynamic models with a continuum of moment conditions. J Econom 140:529–573Google Scholar
  87. 87.
    Carrasco M, Florens JP (2000) Generalization of GMM to a continuum of moment conditions. Econom Theory 16:797–834Google Scholar
  88. 88.
    Chacko G, Viceira LM (2003) Spectral GMM estimation of continuous‐time processes. J Econom 116:259–292Google Scholar
  89. 89.
    Chan KC, Karolyi GA, Longstaff FA, Sanders AB (1992) An Empirical Comparison of Alternative Models of the Short-Term Interest Rate. J Finance 47:1209–1227Google Scholar
  90. 90.
    Chen J (2003) Intertemporal CAPM and the Cross‐Section of Stock Return. Working Paper, USC, Los AngelesGoogle Scholar
  91. 91.
    Chen RR, Scott L (1993) Maximum likelihood estimation for a multifactor equilibrium model of the term structure of interest rates. J Fixed Income 3:14–31Google Scholar
  92. 92.
    Cheridito P, Filipović D, Kimmel RL (2007) Market Price of Risk Specifications for Affine Models: Theory and Evidence. J Finance Econ, 83(1):123–170Google Scholar
  93. 93.
    Chernov M, Ghysels E (2002) A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation. J Finance Econ 56:407–458Google Scholar
  94. 94.
    Chernov M, Gallant AR, Ghysels E, Tauchen G (1999) A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation. Working Paper, London Business School, Duke University, University of Northern CarolinaGoogle Scholar
  95. 95.
    Chernov M, Gallant AR, Ghysels E, Tauchen G (2003) Alternative models for stock price dynamics. J Econom 116:225–257Google Scholar
  96. 96.
    Chib S, Nardari F, Shephard N (2002) Markov chain Monte Carlo methods for stochastic volatility models. J Econom 108:281–316Google Scholar
  97. 97.
    Chib S, Nardari F, Shephard N (2006) Analysis of high dimensional multivariate stochastic volatility models. J Econom 134:341–371Google Scholar
  98. 98.
    Christoffersen PF, Jacobs K (2004) The importance of the loss function in option valuation. J Finance Econ 72:291–318Google Scholar
  99. 99.
    Christoffersen PF, Jacobs K, Karoui L, Mimouni K (2007) Estimating Term Structure Models Using Swap Rates. Working Paper, McGill University, MontrealGoogle Scholar
  100. 100.
    Christoffersen PF, Jacobs K, Mimouni K (2006a) Models for S&P 500 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices. Working Paper, McGill University, MontrealGoogle Scholar
  101. 101.
    Christoffersen PF, Jacobs K, Wang Y (2006b) Option Valuation with Long-run and Short-run Volatility Components. Working Paper, McGill University, MontrealGoogle Scholar
  102. 102.
    Clark PK (1973) A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices. Econometrica 41:135–156Google Scholar
  103. 103.
    Collin‐Dufresne P, Goldstein RS (2002) Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility. J Finance 57:1685–1730Google Scholar
  104. 104.
    Collin‐Dufresne P, Goldstein R, Jones CS (2008) Identification of Maximal Affine Term Structure Models. J Finance 63(2):743–795 Google Scholar
  105. 105.
    Collin‐Dufresne P, Goldstein R, Jones CS (2007b) Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility. Working Paper, UCB, USC, UMN, MinneapolisGoogle Scholar
  106. 106.
    Collin‐Dufresne P, Solnik B (2001) On the Term Structure of Default Premia in the Swap and LIBOR Markets. J Finance 56:1095–1115Google Scholar
  107. 107.
    Comte F, Coutin L, Renault E (2003) Affine Fractional Stochastic Volatility Models with Application to Option Pricing. Working Paper, CIRANO, MontrealGoogle Scholar
  108. 108.
    Comte F, Renault E (1998) Long memory in continuous‐time stochastic volatility models. Math Finance 8:291–323Google Scholar
  109. 109.
    Conley TG, Hansen LP, Luttmer EGJ, Scheinkman JA (1997) Short-term interest rates as subordinated diffusions. Rev Finance Stud 10:525–577Google Scholar
  110. 110.
    Corsi F (2003) A Simple Long Memory Model of realized Volatility. Working paper, University of Southern Switzerland, LuganoGoogle Scholar
  111. 111.
    Coval JD, Shumway T (2001) Expected Option Returns. J Finance 56:983–1009Google Scholar
  112. 112.
    Cox JC, Ingersoll JE, Ross SA (1985) An Intertemporal General Equilibrium Model of Asset Prices. Econometrica 53:363–384Google Scholar
  113. 113.
    Cox JC, Ingersoll JE, Ross SA (1985) A Theory of the Term Structure of Interest Rates. Econometrica 53:385–407Google Scholar
  114. 114.
    Dai Q, Singleton KJ (2000) Specification Analysis of Affine Term Structure Models. J Finance 55:1943–1978Google Scholar
  115. 115.
    Dai Q, Singleton KJ (2003) Term Structure Dynamics in Theory and Reality. Rev Finance Stud 16:631–678Google Scholar
  116. 116.
    Danielsson J (1994) Stochastic Volatility in Asset Prices: Estimation by Simulated Maximum Likelihood. J Econom 64:375–400Google Scholar
  117. 117.
    Danielsson J, Richard JF (1993) Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models. J Appl Econom 8:S153–S173Google Scholar
  118. 118.
    Deo R, Hurvich C (2001) On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models. Econom Theory 17:686–710Google Scholar
  119. 119.
    Derman E, Kani I (1994) The volatility smile and its implied tree. Quantitative Strategies Research Notes, Goldman Sachs, New YorkGoogle Scholar
  120. 120.
    Diebold FX, Nerlove M (1989) The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model. J Appl Econom 4:1–21Google Scholar
  121. 121.
    Diebold FX, Strasser G (2007) On the Correlation Structure of Microstructure Noise in Theory and Practice. Working Paper, University of Pennsylvania, PhiladelphiaGoogle Scholar
  122. 122.
    Dobrev D (2007) Capturing Volatility from Large Price Moves: Generalized Range Theory and Applications. Working Paper, Federal Reserve Board, Washington D.C.Google Scholar
  123. 123.
    Driessen J, Maenhout P, Vilkov G (2006) Option‐Implied Correlations and the Price of Correlation Risk. Working Paper, University of Amsterdam and INSEAD, AmsterdamGoogle Scholar
  124. 124.
    Duarte J (2004) Evaluating An Alternative Risk Preference in Affine Term Structure Models. Rev Finance Stud 17:370–404Google Scholar
  125. 125.
    Duarte J (2007) The Causal Effect of Mortgage Refinancing on Interest‐Rate Volatility: Empirical Evidence and Theoretical Implications. Rev Finance Stud, forthcomingGoogle Scholar
  126. 126.
    Duarte J, Jones CS (2007) The Price of Market Volatility Risk. Working Paper, University of Washington and USC, WashingtonGoogle Scholar
  127. 127.
    Duffee GR (2002) Term Premia and Interest Rate Forecasts in Affine Models. J Finance 57:405–443Google Scholar
  128. 128.
    Duffee G, Stanton R (2008) Evidence on simulation inference for near unit-root processes with implications for term structure estimation. J Finance Econom 6:108–142Google Scholar
  129. 129.
    Duffie D, Kan R (1996) A yield‐factor model of interest rates. Math Finance 6:379–406Google Scholar
  130. 130.
    Duffie D, Pan J, Singleton KJ (2000) Transform Analysis and Asset Pricing for Affine Jump‐Diffusions. Econometrica 68:1343–1376Google Scholar
  131. 131.
    Duffie D, Singleton KJ (1993) Simulated Moments Estimation of Markov Models of Asset Prices. Econometrica 61:929–952Google Scholar
  132. 132.
    Duffie D, Singleton KJ (1997) An Econometric Model of the Term Structure of Interest‐Rate Swap Yields. J Finance 52:1287–1321Google Scholar
  133. 133.
    Dumas B, Fleming J, Whaley RE (1996) Implied Volatility Functions: Empirical Tests. J Finance 53:2059–2106Google Scholar
  134. 134.
    Dupire B (1994) Pricing with a smile. Risk 7:18–20Google Scholar
  135. 135.
    Elerian O, Chib S, Shephard N (2001) Likelihood Inference for Discretely Observed Nonlinear Diffusions. Econometrica 69:959–994Google Scholar
  136. 136.
    Engle RF (2002) New frontiers for ARCH models. J Appl Econom 17:425–446Google Scholar
  137. 137.
    Engle RF, Gallo GM (2006) A multiple indicators model for volatility using intra-daily data. J Econom 131:3–27Google Scholar
  138. 138.
    Engle RF, Ghysels E, Sohn B (2006) On the Economic Sources of Stock Market Volatility. Working Paper, NYU and UNC, Chapel HillGoogle Scholar
  139. 139.
    Engle RF, Rangel JG (2006) The Spline‐GARCH Model for Low Frequency Volatility and Its Global Macroeconomic Causes. Working Paper, NYU, New YorkGoogle Scholar
  140. 140.
    Eraker B (2001) MCMC Analysis of Diffusions with Applications to Finance. J Bus Econ Stat 19:177–191Google Scholar
  141. 141.
    Eraker B (2004) Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices. J Finance 59:1367–1404Google Scholar
  142. 142.
    Eraker B, Johannes MS, Polson N (2003) The Impact of Jumps in Volatility and Returns. J Finance 58:1269–1300Google Scholar
  143. 143.
    Fan R, Gupta A, Ritchken P (2003) Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets. J Finance 58:2219–2248Google Scholar
  144. 144.
    Fiorentina G, Sentana E, Shephard N (2004) Likelihood‐Based Estimation of Latent Generalized ARCH Structures. Econometrica 72:1481–1517Google Scholar
  145. 145.
    Fisher M, Gilles C (1996) Estimating exponential‐affine models of the term structure. Working Paper, Atlanta FED, AtlantaGoogle Scholar
  146. 146.
    Fleming MJ, Remolona EM (1999) Price Formation and Liquidity in the US Treasury Market: The Response to Public Information. J Finance 54:1901–1915Google Scholar
  147. 147.
    Forsberg L, Ghysels E (2007) Why Do Absolute Returns Predict Volatility So Well? J Finance Econom 5:31–67Google Scholar
  148. 148.
    French KR, Schwert GW, Stambaugh RF (1987) Expected stock returns and volatility. J Finance Econ 19:3–29Google Scholar
  149. 149.
    Fridman M, Harris L (1998) A Maximum Likelihood Approach for Non‐Gaussian Stochastic Volatility Models. J Bus Econ Stat 16:284–291Google Scholar
  150. 150.
    Gallant AR, Hsieh DA, Tauchen GE (1997) Estimation of Stochastic Volatility Models with Diagnostics. J Econom 81:159–192Google Scholar
  151. 151.
    Gallant AR, Hsu C, Tauchen GE (1999) Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance. Rev Econ Stat 81:617–631Google Scholar
  152. 152.
    Gallant AR, Long JR (1997) Estimating stochastic differential equations efficiently by minimum chi‐squared. Biometrika 84:125–141Google Scholar
  153. 153.
    Gallant AR, Rossi PE, Tauchen GE (1992) Stock Prices and Volume. Rev Finance Stud 5:199–242Google Scholar
  154. 154.
    Gallant AR, Tauchen GE (1996) Which Moments to Match. Econ Theory 12:657–681Google Scholar
  155. 155.
    Gallant AR, Tauchen G (1998) Reprojecting Partially Observed Systems With Application to Interest Rate Diffusions. J Ammer Stat Assoc 93:10–24Google Scholar
  156. 156.
    Garcia R, Lewis MA, Pastorello S, Renault E (2001) Estimation of Objective and Risk‐neutral Distributions based on Moments of Integrated Volatility, Working Paper. Université de Montréal, Banque Nationale du Canada, Università di Bologna, UNCGoogle Scholar
  157. 157.
    Garman MB, Klass MJ (1980) On the Estimation of Price Volatility From Historical Data. J Bus 53:67–78Google Scholar
  158. 158.
    Ghysels E, Harvey AC, Renault E (1996) Stochastic Volatility. In: Maddala GS, Rao CR (eds) Handbook of Statistics, vol 14. North Holland, AmsterdamGoogle Scholar
  159. 159.
    Ghysels E, Santa-Clara P, Valkanov R (2006) Predicting Volatility: How to Get the Most Out of Returns Data Sampled at Different Frequencies. J Econom 131:59–95Google Scholar
  160. 160.
    Glosten LR, Jagannathan R, Runkle D (1993) On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. J Finance 48:1779–1801Google Scholar
  161. 161.
    Gong FF, Remolona EM (1996) A three‐factor econometric model of the US term structure. Working paper, Federal Reserve Bank of New York, New YorkGoogle Scholar
  162. 162.
    Gouriéroux C, Monfort A, Renault E (1993) Indirect Inference. J Appl Econom 8:S85–S118Google Scholar
  163. 163.
    Guo H, Neely CJ, Higbee J (2007) Foreign Exchange Volatility Is Priced in Equities. Finance Manag, forthcomingGoogle Scholar
  164. 164.
    Han B (2007) Stochastic Volatilities and Correlations of Bond Yields. J Finance 62:1491–1524Google Scholar
  165. 165.
    Hansen PR, Lunde A (2006) Realized Variance and Market Microstructure Noise. J Bus Econ Stat 24:127–161Google Scholar
  166. 166.
    Harvey AC (1998) Long memory in stochastic volatility. In: Knight J, Satchell S (eds) Forecasting Volatility in Financial Markets. Butterworth‐Heinemann, LondonGoogle Scholar
  167. 167.
    Harvey AC, Ruiz E, Shephard N (1994) Multivariate Stochastic Variance Models. Rev Econ Stud 61:247–264Google Scholar
  168. 168.
    Harvey AC, Shephard N (1996) Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns. J Bus Econ Stat 14:429–434Google Scholar
  169. 169.
    Heidari M, Wu L (2003) Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates? J Fixed Income 13:75–86Google Scholar
  170. 170.
    Heston SL (1993) A closed‐form solution for options with stochastic volatility with applications to bond and currency options. Rev Finance Stud 6:327–343Google Scholar
  171. 171.
    Ho M, Perraudin W, Sørensen BE (1996) A Continuous Time Arbitrage Pricing Model with Stochastic Volatility and Jumps. J Bus Econ Stat 14:31–43Google Scholar
  172. 172.
    Huang X, Tauchen G (2005) The relative contribution of jumps to total price variation. J Finance Econom 3:456–499Google Scholar
  173. 173.
    Huang J, Wu L (2004) Specification Analysis of Option Pricing Models Based on Time‐Changed Levy Processes. J Finance 59:1405–1440Google Scholar
  174. 174.
    Hull J, White A (1987) The Pricing of Options on Assets with Stochastic Volatilities. J Finance 42:281–300Google Scholar
  175. 175.
    Hurvich CM, Soulier P (2007) Stochastic Volatility Models with Long Memory. In: Andersen TG, Davis RA, Kreiss JP, Mikosch T (eds) Handbook of Financial Time Series. Springer,Berlin Google Scholar
  176. 176.
    Jung J (2006) Vexed by variance. Risk AugustGoogle Scholar
  177. 177.
    Jackwerth JC, Rubinstein M (1996) Recovering Probability Distributions from Option Prices. J Finance 51:1611–1631Google Scholar
  178. 178.
    Jacobs K, Karoui L (2007) Conditional Volatility in Affine Term Structure Models: Evidence from Treasury and Swap Markets. Working Paper, McGill University, MontrealGoogle Scholar
  179. 179.
    Jacobs K, Li X (2008) Modeling the Dynamics of Credit Spreads with Stochastic Volatility. Manag Sci 54:1176–1188Google Scholar
  180. 180.
    Jacquier E, Polson NG, Rossi PE (1994) Bayesian Analysis of Stochastic Volatility Models. J Bus Econ Stat 12:371–389Google Scholar
  181. 181.
    Jacquier E, Polson NG, Rossi PE (2004) Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. J Econom 122:185–212Google Scholar
  182. 182.
    Jagannathan R, Kaplin A, Sun S (2003) An evaluation of multi‐factor CIR models using LIBOR, swap rates, and cap and swaption prices. J Econom 116:113–146Google Scholar
  183. 183.
    Jarrow R, Li H, Zhao F (2007) Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile? J Finance 62:345–382Google Scholar
  184. 184.
    Jiang GJ, Knight JL (2002) Efficient Estimation of the Continuous Time Stochastic Volatility Model via the Empirical Characteristic Function. J Bus Econ Stat 20:198–212Google Scholar
  185. 185.
    Jiang GJ, Tian YS (2005) The Model-Free Implied Volatility and Its Information Content. Rev Finance Stud 18:1305–1342Google Scholar
  186. 186.
    Johannes MS, Polson N (2003) MCMC Methods for Continuous‐Time Financial Econometrics. In: Hansen LP, Aït‑Sahalia I (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcomingGoogle Scholar
  187. 187.
    Johannes MS, Polson N (2006) Particle Filtering. In: Andersen TG, Davis RA, Kreiss JP, Mikosch T (eds) Handbook of Financial Time Series. Springer, BerlinGoogle Scholar
  188. 188.
    Johnson H, Shanno D (1987) Option Pricing when the Variance Is Changing. J Finance Quant Anal 22:143–152Google Scholar
  189. 189.
    Jones CS (2003) Nonlinear Mean Reversion in the Short-Term Interest Rate. Rev Finance Stud 16:793–843Google Scholar
  190. 190.
    Jones CS (2003) The dynamics of stochastic volatility: evidence from underlying and options markets. J Econom 116:181–224Google Scholar
  191. 191.
    Joslin S (2006) Can Unspanned Stochastic Volatility Models Explain the Cross Section of Bond Volatilities? Working Paper, MIT, CambridgeGoogle Scholar
  192. 192.
    Joslin S (2007) Pricing and Hedging Volatility Risk in Fixed Income Markets. Working Paper, MIT, CambridgeGoogle Scholar
  193. 193.
    Kim SN, Shephard N, Chib S (1998) Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models. Rev Econ Stud 65:361–393Google Scholar
  194. 194.
    Lamoureux CG, Lastrapes WD (1994) Endogenous Trading vol and Momentum in Stock‐Return Volatility. J Bus Econ Stat 14:253–260Google Scholar
  195. 195.
    Lee SS, Mykland PA (2006) Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics. Working Paper, Georgia Institute of Technology and University of Chicago, ChicagoGoogle Scholar
  196. 196.
    Li H, Wells MT, Yu CL (2006) A Bayesian Analysis of Return Dynamics with Lévy Jumps. Rev Finance Stud, forthcomingGoogle Scholar
  197. 197.
    Li H, Zhao F (2006) Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate Derivatives. J Finance 61:341–378Google Scholar
  198. 198.
    Liesenfeld R (1998) Dynamic Bivariate Mixture Models: Modeling the Behavior of Prices and Trading Volume. J Bus Econ Stat 16:101–109Google Scholar
  199. 199.
    Liesenfeld R (2001) A Generalized Bivariate Mixture Model for Stock Price Volatility and Trading Volume. J Econom 104:141–178Google Scholar
  200. 200.
    Liesenfeld R, Richard J-F (2003) Univariate and Multivariate Stochastic Volatility Models: Estimation and Diagnostics. J Empir Finance 10:505–531Google Scholar
  201. 201.
    Litterman R, Scheinkman JA (1991) Common Factors Affecting Bond Returns. J Fixed Income 1:54–61Google Scholar
  202. 202.
    Liu C, Maheu JM (2007) Forecasting Realized Volatility: A Bayesian Model Averaging Approach. Working Paper, University of Toronto, TorontoGoogle Scholar
  203. 203.
    Lo AW (1988) Maximum likelihood estimation of generalized Itô processes with discretely‐sampled data. Econom Theory 4:231–247Google Scholar
  204. 204.
    Longstaff FA, Schwartz ES (1992) Interest Rate Volatility and the Term Structure: A Two‐Factor General Equilibrium Model. J Finance 47:1259–1282Google Scholar
  205. 205.
    McAleer M, Medeiros MC (2007) Realized Volatility: A Review. Econom Rev, forthcomingGoogle Scholar
  206. 206.
    McFadden D (1989) A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration. Econometrica 57:995–1026Google Scholar
  207. 207.
    McQueen G, Vorkink K (2004) Whence GARCH? A Preference‐Based Explanation for Conditional Volatility. Rev Finance Stud 17:915–949Google Scholar
  208. 208.
    Meddahi N (2001) An Eigenfunction Approach for Volatility Modeling. Working Paper, Imperial College, LondonGoogle Scholar
  209. 209.
    Meddahi N (2002) A Theoretical Comparison Between Integrated and Realized Volatility. J Appl Econom 17:475–508Google Scholar
  210. 210.
    Meddahi N (2002) Moments of Continuous Time Stochastic Volatility Models. Working Paper, Imperial College, LondonGoogle Scholar
  211. 211.
    Melino A, Turnbull SM (1990) Pricing foreign currency options with stochastic volatility. J Econom 45:239–265Google Scholar
  212. 212.
    Merton RC (1969) Lifetime portfolio selection under uncertainty: the continuous‐time case. Rev Econ Stat 51:247–257Google Scholar
  213. 213.
    Merton RC (1973) An Intertemporal Capital Asset Pricing Model. Econometrica 41:867–887Google Scholar
  214. 214.
    Merton RC (1976) Option pricing when underlying stock returns are discontinuous. J Finance Econs 3:125–144Google Scholar
  215. 215.
    Merton RC (1980) On estimating the expected return on the market: An exploratory investigation. J Finance Econ 8:323–361Google Scholar
  216. 216.
    Mizrach B (2006) The Enron Bankruptcy: When Did The Options Market Lose Its Smirk. Rev Quant Finance Acc 27:365–382Google Scholar
  217. 217.
    Mizrach B (2007) Recovering Probabilistic Information From Options Prices and the Underlying. In: Lee C, Lee AC (eds) Handbook of Quantitative Finance. Springer, New YorkGoogle Scholar
  218. 218.
    Nelson DB (1991) Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica 59:347–370Google Scholar
  219. 219.
    Nelson DB, Foster DP (1994) Asymptotic Filtering Theory for Univariate ARCH Models. Econometrica 62:1–41Google Scholar
  220. 220.
    Pan J (2002) The jump-risk premia implicit in options: evidence from an integrated time‐series study. J Finance Econ 63:3–50Google Scholar
  221. 221.
    Parkinson M (1980) The Extreme ValueMethod for Estimating the Variance of the Rate of Return. J Bus 53:61–65Google Scholar
  222. 222.
    Pasquariello P, Vega C (2007) Informed and Strategic Order Flow in the Bond Markets. Rev Finance Stud 20:1975–2019Google Scholar
  223. 223.
    Pearson ND, Sun TS (1994) Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model. J Finance 49:1279–1304Google Scholar
  224. 224.
    Pedersen AR (1995) A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scand J Stat 22:55–71Google Scholar
  225. 225.
    Pennacchi GG (1991) Identifying the Dynamics of Real Interest Rates and Inflation: Evidence Using Survey Data. Rev Finance Stud 4:53–86Google Scholar
  226. 226.
    Piazzesi M (2003) Affine Term Structure Models. In: Hansen LP, Aït‑Sahalia I (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcoming Google Scholar
  227. 227.
    Piazzesi M (2005) Bond Yields and the Federal Reserve. J Political Econ 113:311–344Google Scholar
  228. 228.
    Pitt MK, Shephard N (1999) Filtering via simulation: auxiliary particle filter. J Ammer Stat Assoc 94:590–599Google Scholar
  229. 229.
    Protter P (1992) Stochastic Integration and Differential Equations: A New Approach. Springer, New YorkGoogle Scholar
  230. 230.
    Renault E (1997) Econometric models of option pricing errors. In: Kreps D, Wallis K (eds) Advances in Economics and Econometrics, Seventh World Congress. Cambridge University Press, New York, pp 223–278Google Scholar
  231. 231.
    Richardson M, Smith T (1994) A Direct Test of the Mixture of Distributions Hypothesis: Measuring the Daily Flow of Information. J Financ Quant Anal 29:101–116Google Scholar
  232. 232.
    Rosenberg B (1972) The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices. working Paper, UCB, BerkleyGoogle Scholar
  233. 233.
    Rubinstein M (1994) Implied Binomial Trees. J Financ 49:771–818Google Scholar
  234. 234.
    Santa-Clara P (1995) Simulated likelihood estimation of diffusions with an application to the short term interest rate. Dissertation, INSEADGoogle Scholar
  235. 235.
    Schaumburg E (2005) Estimation of Markov processes with Levy type generators. Working Paper, KSM, EvanstonGoogle Scholar
  236. 236.
    Schwert GW (1989) Why Does Stock Market Volatility Change Over Time? J Financ 44:1115–1153Google Scholar
  237. 237.
    Schwert GW (1990) Stock Volatility and the Crash of '87. Rev Financ Stud 3:77–102Google Scholar
  238. 238.
    Scott LO (1987) Option Pricing when the Variance Changes Randomly: Theory, Estimation and an Application. J Financ Quant Anal 22:419–438Google Scholar
  239. 239.
    Shephard N (1996) Statistical Aspects of ARCH and Stochastic Volatility Models. In: Cox DR, Hinkley DV, Barndorff‐Nielsen OE (eds) Time Series Models in Econometrics, Finance and Other Fields. Chapman & Hall, London, pp 1–67Google Scholar
  240. 240.
    Shephard N (2004) Stochastic Volatility: Selected Readings. Oxford University Press, OxfordGoogle Scholar
  241. 241.
    Shiller RJ (1981) Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends? Ammer Econ Rev 71:421–436Google Scholar
  242. 242.
    Singleton KJ (2001) Estimation of affine asset pricing models using the empirical characteristic function. J Econom 102:111–141Google Scholar
  243. 243.
    Smith AA Jr (1993) Estimating Nonlinear Time‐series Models using Simulated Vector Autoregressions. J Appl Econom 8:S63–S84Google Scholar
  244. 244.
    Stein JC (1989) Overreactions in the Options Market. J Finance 44:1011–1023Google Scholar
  245. 245.
    Stein EM, Stein JC (1991) Stock price distributions with stochastic volatility: an analytic approach. Rev Finance Stud 4:727–752Google Scholar
  246. 246.
    Tauchen GE (2005) Stochastic Volatility in General Equilibrium. Working Paper, Duke, University DurhamGoogle Scholar
  247. 247.
    Tauchen GE, Pitts M (1983) The Price Variability‐Volume Relationship on Speculative Markets. Econometrica 51:485–505Google Scholar
  248. 248.
    Tauchen GE, Zhou H (2007) Realized Jumps on Financial Markets and Predicting Credit Spreads. Working Paper, Duke University and Board of Governors, Washington D.C.Google Scholar
  249. 249.
    Taylor SJ (1986) Modeling Financial Time Series. Wiley, ChichesterGoogle Scholar
  250. 250.
    Thompson S (2004) Identifying Term Structure Volatility from the LIBOR-Swap Curve. Working Paper, Harvard University, BostonGoogle Scholar
  251. 251.
    Todorov V (2006) Variance Risk Premium Dynamics. Working Paper, KSM, EvanstonGoogle Scholar
  252. 252.
    Todorov V (2006) Estimation of Continuous‐time Stochastic Volatility Models with Jumps using High‐Frequency Data. Working Paper, KSM, EvanstonGoogle Scholar
  253. 253.
    Trolle AB, Schwartz ES (2007) Unspanned stochastic volatility and the pricing of commodity derivatives. Working Paper, Copenhagen Business School and UCLA, CopenhagenGoogle Scholar
  254. 254.
    Trolle AB, Schwartz ES (2007) A general stochastic volatility model for the pricing of interest rate derivatives. Rev Finance Stud, forthcomingGoogle Scholar
  255. 255.
    Vasicek OA (1977) An equilibrium characterization of the term structure. J Finance Econ 5:177–188Google Scholar
  256. 256.
    Wiggins JB (1987) Option Values under Stochastic Volatility: Theory and Empirical Estimates. J Finance Econ 19:351–372Google Scholar
  257. 257.
    Whaley RE (1993) Derivatives on Market Volatility: Hedging Tools Long Overdue. J Deriv 1:71–84Google Scholar
  258. 258.
    Wright J, Zhou H (2007) Bond Risk Premia and Realized Jump Volatility. Working Paper, Board of Governors, Washington D.C.Google Scholar
  259. 259.
    Yang D, Zhang Q (2000) Drift‐Independent Volatility Estimation Based on High, Low, Open, and Close Prices. J Bus 73:477–491Google Scholar
  260. 260.
    Zhang BY, Zhou H, Zhu H (2005) Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms. Working Paper, Fitch Ratings, Federal Reserve Board, BISGoogle Scholar
  261. 261.
    Zhang L (2007) What you don't know cannot hurt you: On the detection of small jumps. Working Paper, UIC, ChicagoGoogle Scholar
  262. 262.
    Zhang L, Mykland PA, Aït‑Sahalia Y (2005) A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data. J Ammer Stat Assoc 100:1394–1411Google Scholar

Books and Reviews

  1. 263.
    Asai M, McAleer M, Yu J (2006) Multivariate Stochastic Volatility: A Review. Econom Rev 25:145–175Google Scholar
  2. 264.
    Bates DS (2003) Empirical option pricing: a retrospection. J Econom 116:387–404Google Scholar
  3. 265.
    Campbell JY, Lo AW, MacKinlay AC (1996) The Econometrics of Financial Markets. Princeton University Press, PrincetonGoogle Scholar
  4. 266.
    Chib S, Omori Y, Asai M (2007) Multivariate Stochastic Volatility. Working Paper, Washington UniversityGoogle Scholar
  5. 267.
    Duffie D (2001) Dynamic Asset Pricing Theory. Princeton University Press, PrincetonGoogle Scholar
  6. 268.
    Gallant AR, Tauchen G (2002) Simulated Score Methods and Indirect Inference for Continuous‐time Models. In: Hansen LP, Aït‑Sahalia Y (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcomingGoogle Scholar
  7. 269.
    Garcia R, Ghysels E, Renault E (2003) The Econometrics of Option Pricing. In: Hansen LP, Aït‑Sahalia Y (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcomingGoogle Scholar
  8. 270.
    Gouriéroux C, Jasiak J (2001) Financial Econometrics. Princeton University Press, PrincetonGoogle Scholar
  9. 271.
    Johannes MS, Polson N (2006) Markov Chain Monte Carlo. In: Andersen TG, Davis RA, Kreiss JP, Mikosch T (eds) Handbook of Financial Time Series. Springer, BerlinGoogle Scholar
  10. 272.
    Jungbacker B, Koopman SJ (2007) Parameter Estimation and Practical Aspect of Modeling Stochastic Volatility. Working Paper, Vrije Universiteit, AmsterdamGoogle Scholar
  11. 273.
    Mykland PA (2003) Option Pricing Bounds and Statistical Uncertainty. In: Hansen LP, Aït‑Sahalia Y (eds) Handbook of Financial Econometrics. North‐Holland, Amsterdam, forthcomingGoogle Scholar
  12. 274.
    Renault E (2007) Moment‐Based Estimation of Stochastic Volatility Models. In: Andersen TG, Davis RA, Kreiss JP, Mikosch T (eds) Handbook of Financial Time Series. Springer, BerlinGoogle Scholar
  13. 275.
    Singleton KJ (2006) Empirical Dynamic Asset Pricing: Model Specification and Econometric Assessment. Princeton University Press, PrincetonGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Torben G. Andersen
    • 1
    • 2
    • 3
  • Luca Benzoni
    • 4
  1. 1.Kellogg School of ManagementNorthwestern UniversityEvanstonUSA
  2. 2.NBERCambridgeUSA
  3. 3.CREATESAarhusDenmark
  4. 4.Federal Reserve Bank of ChicagoChicagoUSA