Review of Quantitative Finance and Accounting

, Volume 43, Issue 4, pp 751–779 | Cite as

A noise-robust estimator of volatility based on interquantile ranges

  • Jin-Huei Yeh
  • Jying-Nan Wang
  • Chung-Ming Kuan
Original Research


This paper proposes a new class of estimators based on the interquantile range of intraday returns, referred to as interquantile range based volatility (IQRBV), to estimate the integrated daily volatility. More importantly and intuitively, it is shown that a properly chosen IQRBV is jump-free for its trimming of the intraday extreme two tails that utilize the range between symmetric quantiles. We exploit its approximation optimality by examining a general class of distributions from the Pearson type IV family and recommend using IQRBV.04 as the integrated variance estimate. Both our simulation and the empirical results highlight interesting features of the easy-to-implement and model-free IQRBV over the other competing estimators that are seen in the literature.


Inter quantile range Price jump Realized volatility Range-based volatility Bi-power variation Market microstructure noise 

JEL Classification

G10 G12 C58 


  1. Aït-Sahalia Y, Mykland PA, Zhang L (2005) How often to sample a continuous-time process in the presence of market microstructure noise. Rev Financ Stud 18:351–416CrossRefGoogle Scholar
  2. Alizadeh S, Brandt MW, Diebold FX (2002) Range-based estimation of stochastic volatility models. J Financ 57:1047–1091CrossRefGoogle Scholar
  3. Andersen T, Bollerslev T (1998) Answering the skeptics: yes, standard volatility models do provide accurate forecasts. Int Econ Rev 39:885–905CrossRefGoogle Scholar
  4. Andersen TG, Bollerslev T, Diebold FX, Labys P (2001) The distribution of exchange rate volatility. J Am Stat Assoc 96:42–55, correction published in 2003, 98, p 501Google Scholar
  5. Andersen TG, Benzoni L, Lund J (2002) An empirical investigation of continuous-time equity return models. J Financ 57:1239–1284CrossRefGoogle Scholar
  6. Andersen TG, Bollerslev T, Diebold FX, Labys P (2003) Modeling and forecasting realized volatility. Econometrica 71:579–625CrossRefGoogle Scholar
  7. Andersen TG, Bollerslev T, Diebold FX (2007a) Roughing it up: including jump components in the measurement, modeling, and forecasting of return volatility. Rev Econ Stat 89:701–720CrossRefGoogle Scholar
  8. Andersen TG, Bollerslev T, Dobrev D (2007b) 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 Econ 138:125–180CrossRefGoogle Scholar
  9. Andersen TG, Bollerslev T, Diebold FX (2010) Parametric and nonparametric measurements of volatility. In: Aït-Sahalia Y, Hansen LP (eds) Handbook of financial econometrics, vol 1. North-Holland, Oxford, pp 67–128Google Scholar
  10. Ball CA, Torous WN (1984) The maximum likelihood estimation of security price volatility: theory, evidence, and application to option pricing. J Bus 57:97–112CrossRefGoogle Scholar
  11. Bandi FM, Russell JR (2006) Separating microstructure noise from volatility. J Financ Econ 79:655–692CrossRefGoogle Scholar
  12. Bandi FM, Russell JR (2008) Microstructure noise, realized variance, and optimal sampling. Rev Econ Stud 75:339–369CrossRefGoogle Scholar
  13. Barndorff-Nielsen OE, Shephard N (2002a) Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J R Stat Soc B 63:253–280CrossRefGoogle Scholar
  14. Barndorff-Nielsen OE, Shephard N (2002b) Estimating quadratic variation using realized variance. J Appl Econ 17:457–477CrossRefGoogle Scholar
  15. Barndorff-Nielsen OE, Shephard N (2004) Power and bipower variation with stochastic volatility and jumps. J Financ Econ 2:1–37Google Scholar
  16. Barndorff-Nielsen OE, Shephard N (2006) Econometrics of testing for jumps in financial economics using bipower variation. J Financ Econ 4:1–30Google Scholar
  17. Barndorff-Nielsen OE, Hansen PR, Lunde A, Shephard N (2008) Designing realized kernels to measure the ex post variation of equity prices in the presence of noise. Econometrica 76:1481–1536CrossRefGoogle Scholar
  18. Bates DS (1996) Jumps and stochastic volatility: exchange rate processes implicit in deutsch mark options. Rev Financ Stud 9:69–107CrossRefGoogle Scholar
  19. Bates DS (2000) Post-“87" crash fears in the s&p 500 futures option market. J Econ 94:181–238CrossRefGoogle Scholar
  20. Beckers S (1983) Variance of security price returns based on high, low, and closing prices. J Bus 56:97–112CrossRefGoogle Scholar
  21. Bessembinder H (2003) Trade execution costs and market quality after decimalization. J Financ Quant Anal 38:747–777CrossRefGoogle Scholar
  22. Bollen B, Inder B (2002) Estimating daily volatility in financial markets utilizing intraday data. J Empir Financ 9:551–562CrossRefGoogle Scholar
  23. Brandt MW, Diebold FX (2006) A no-arbitrage approach to range-based estimation of return covariances and correlations. J Bus 79:61–73CrossRefGoogle Scholar
  24. Brandt MW, Jones CS (2006) Volatility forecasting with range-based egarch models. J Bus Econ Stat 24:470–486CrossRefGoogle Scholar
  25. Chernov M, Gallant AR, Ghysels E, Tauchen G (2003) Alternative models for stock price dynamics. J Econ 116:225–257CrossRefGoogle Scholar
  26. Chou RY (2005) Forecasting financial volatilities with extreme values: the conditional autoregressive range (carr) model. J Money Credit Bank 37:561–582CrossRefGoogle Scholar
  27. Christensen K, Podolskij M (2007) Realized range-based estimation of integrated variance. J Econ 141:323–349CrossRefGoogle Scholar
  28. Christensen K, Oomen R, Podolskij M (2010) Realised quantile-based estimation of the integrated variance. J Econ 159:74–98CrossRefGoogle Scholar
  29. Comte F, Renault E (1998) Long memory in continuous-time stochastic volatility models. Math Financ 8:291–323CrossRefGoogle Scholar
  30. Corsi F, Zumbach G, Muller UA, Dacorogna MM (2001) Consistent high-precision volatility from high-frequency data. Econ Notes 30:183–204CrossRefGoogle Scholar
  31. Dobrev D (2007) Capturing volatility from large price moves, generalized range theory and applications, unpublished working paper, Northwestern UniversityGoogle Scholar
  32. Dungey M, Hvozdyk L (2012) Cojumping: Evidence from the us treasury bond and futures markets. J Bank Financ 36:1563–1575CrossRefGoogle Scholar
  33. Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica 50:987–1007CrossRefGoogle Scholar
  34. Eraker B (2001) Markov chain monte carlo analysis of diffusion models with application to finance. J Bus Econ Stat 19:177–191CrossRefGoogle Scholar
  35. Eraker B, Johannes MS, Polson NG (2003) The impact of jumps in volatility and returns. J Financ 58:1269–1300CrossRefGoogle Scholar
  36. Evans KP (2011) Intraday jumps and us macroeconomic news announcements. J Bank Financ 35:2511–2527CrossRefGoogle Scholar
  37. Feller W (1951) The asymptotic distribution of the range of sums of independent random variables. Ann Math Stat 22:427–432CrossRefGoogle Scholar
  38. Hansen PR, Lunde A (2006) Realized variance and market microstructure noise. J Bus Econ Stat 24:127–161CrossRefGoogle Scholar
  39. Hausman JA (1978) Specification tests in econometrics. Econometrica 46:1251–1271CrossRefGoogle Scholar
  40. He Y, Wu C (2005) The effects of decimalization on return volatility components, serial correlation, and trading costs. J Financ Res 28:77–96CrossRefGoogle Scholar
  41. Huang X, Tauchen G (2005) The relative contribution of jumps to total price variance. J Financ Econ 3:456–499Google Scholar
  42. Jacod J (1994) Limit of random measures associated with the increments of a brownian semimartingale, preprint number 120, Laboratoire de Probabilitiés, Université Pierre et Marie Curie, ParisGoogle Scholar
  43. Johannes M (2004) The statistical and economic role of jumps in interest rates. J Financ 59:227–260CrossRefGoogle Scholar
  44. Keefer DL (1994) Certainty equivalents for three-point discrete-distribution approximations. Manag Sci 40:760–773CrossRefGoogle Scholar
  45. Keefer DL, Bodily SE (1983) Three-point approximations for continuous random variables. Manag Sci 29:595–609CrossRefGoogle Scholar
  46. Keefer DL, Verdini WA (1993) Better estimation of pert activity time parameters. Manag Sci 39:1086–1091CrossRefGoogle Scholar
  47. Kim I, Baek IS, Noh J, Kim S (2007) The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the kospi 200 returns dynamics. Rev Quant Financ Acc 29:69–110CrossRefGoogle Scholar
  48. Madhavan A (2000) Market microstructure: a survey. J Financ Mark 3:205–258CrossRefGoogle Scholar
  49. McAleer M, Medeiros MC (2008) Realized volatility: A review. Econ Rev 27:10–45CrossRefGoogle Scholar
  50. Merton RC (1976) Option pricing when underlying stock returns are discontinuous. J Financ Econ 3:125–144CrossRefGoogle Scholar
  51. Moder JJ, Rodgers EG (1968) Judgment estimates of the moments of pert type distributions. Manag Sci 15:B76–B83CrossRefGoogle Scholar
  52. Oomen RCA (2006) Properties of realized variance under alternative sampling schemes. J Bus Econ Stat 24:219–237CrossRefGoogle Scholar
  53. Oppenheimer HR, Sabherwal S (2003) The competitive effects of us decimalization: evidence from the us-listed canadian stocks. J Bank Financ 27:1883–1910CrossRefGoogle Scholar
  54. Pan J (2002) The jump-risk premia implicit in options: evidence from an integrated time-series study. J Financ Econ 63:3–50CrossRefGoogle Scholar
  55. Parkinson M (1980) The extreme value method for estimating the variance of the rate of return. J Bus 53:61–65CrossRefGoogle Scholar
  56. Pearson ES, Tukey JW (1965) Approximate means and standard deviations based on distances between percentage points of frequency curves. Biometrika 52:533–546CrossRefGoogle Scholar
  57. Psychoyios D, Dotsis G, Markellos R (2010) A jump diffusion model for vix volatility options and futures. Rev Quant Financ Acc 35:245–269CrossRefGoogle Scholar
  58. Rangel JG (2011) Macroeconomic news, announcements, and stock market jump intensity dynamics. J Bank Financ 35:1263–1276CrossRefGoogle Scholar
  59. Rogers LCG, Satchell SE (1991) Estimating variance from high, low, and closing price. Ann Appl Probab 1:504–512CrossRefGoogle Scholar
  60. Taylor JW (2005) Generating volatility forecasts from value at risk estimates. Manag Sci 51:712–725CrossRefGoogle Scholar
  61. Wright JH, Zhou H (2009) Bond risk premia and realized jump risk. J Bank Financ 33:2333–2345CrossRefGoogle Scholar
  62. Wu L (2003) Jumps and dynamic asset allocation. Rev Quant Financ Acc 20:207–243CrossRefGoogle Scholar
  63. Yang D, Zhang Q (2000) Drift-independent volatility estimation based on high, low, open, and close prices. J Bus 73:477–491CrossRefGoogle Scholar
  64. Zhang L, Mykland P, Aït-Sahalia Y (2005) A tale of two time scales: determining integrated volatility with noisy high-frequency data. J Am Stat Assoc 100:1394–1411CrossRefGoogle Scholar
  65. Zhou B (1996) High frequency data and volatility in foreign-exchange rates. J Bus Econ Stat 14:45–52Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of FinanceNational Central UniversityTaoyuanTaiwan
  2. 2.Department of FinanceMinghsin University of Science and TechnologyHsinchuTaiwan
  3. 3.Department of FinanceNational Taiwan UniversityTaipeiTaiwan

Personalised recommendations