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The Moment Formula For Implied Volatility At Extreme Strikes

Citations

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Cited by:

  1. Andrew Papanicolaou, 2021. "Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options," Papers 2101.00299, arXiv.org, revised Mar 2021.
  2. Ankush Agarwal & Stefano de Marco & Emmanuel Gobet & Gang Liu, 2017. "Rare event simulation related to financial risks: efficient estimation and sensitivity analysis," Working Papers hal-01219616, HAL.
  3. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
  4. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
  5. Andrey Itkin & Alexander Lipton, 2016. "Filling the gaps smoothly," Papers 1608.05145, arXiv.org.
  6. Martin Keller-Ressel, 2008. "Moment Explosions and Long-Term Behavior of Affine Stochastic Volatility Models," Papers 0802.1823, arXiv.org, revised Oct 2008.
  7. Emmanuel Gobet & Ali Suleiman, 2013. "New approximations in local volatility models," Post-Print hal-00523369, HAL.
  8. Andrew Papanicolaou, 2015. "Introduction to Stochastic Differential Equations (SDEs) for Finance," Papers 1504.05309, arXiv.org, revised Jan 2019.
  9. David Berger & Ian Dew-Becker & Stefano Giglio, 2020. "Uncertainty Shocks as Second-Moment News Shocks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(1), pages 40-76.
  10. Stefan Gerhold & I. Cetin Gulum & Arpad Pinter, 2013. "Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models," Papers 1310.3061, arXiv.org, revised May 2016.
  11. Liang, J. & Gao, Y., 2012. "Calibration of implied volatility for the exchange rate for the Chinese Yuan from its derivatives," Economic Modelling, Elsevier, vol. 29(4), pages 1278-1285.
  12. Mario Dell’Era, 2014. "Closed Form Solution for Heston PDE By Geometrical Transformations," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 4(6), pages 793-807, June.
  13. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020, arXiv.org, revised May 2017.
  14. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2021. "A Black-Scholes user's guide to the Bachelier model," Papers 2104.08686, arXiv.org, revised Feb 2022.
  15. Choi, Jaehyuk & Wu, Lixin, 2021. "The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
  16. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
  17. Zhenyu Cui & J. Lars Kirkby & Guanghua Lian & Duy Nguyen, 2017. "Integral Representation Of Probability Density Of Stochastic Volatility Models And Timer Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
  18. Cyril Grunspan & Joris van der Hoeven, 2017. "Effective asymptotic analysis for finance," Working Papers hal-01573621, HAL.
  19. Emanuele Nastasi & Andrea Pallavicini & Giulio Sartorelli, 2020. "Smile Modeling In Commodity Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-28, May.
  20. H. Peter Boswijk & Roger J. A. Laeven & Evgenii Vladimirov, 2022. "Estimating Option Pricing Models Using a Characteristic Function-Based Linear State Space Representation," Papers 2210.06217, arXiv.org.
  21. Akihiko Takahashi & Yukihiro Tsuzuki, 2014. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-341, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  22. Antonie Kotzé & Rudolf Oosthuizen & Edson Pindza, 2015. "Implied and Local Volatility Surfaces for South African Index and Foreign Exchange Options," JRFM, MDPI, vol. 8(1), pages 1-40, January.
  23. Akihiko Takahashi & Yukihiro Tsuzuki, 2013. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CIRJE F-Series CIRJE-F-874, CIRJE, Faculty of Economics, University of Tokyo.
  24. Kein Joe Lau & Yong Kheng Goh & An Chow Lai, 2019. "An empirical study on asymmetric jump diffusion for option and annuity pricing," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-18, May.
  25. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
  26. Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
  27. Lan Zhang, 2012. "Implied and realized volatility: empirical model selection," Annals of Finance, Springer, vol. 8(2), pages 259-275, May.
  28. Florence Guillaume & Wim Schoutens, 2014. "Heston Model: The Variance Swap Calibration," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 76-89, April.
  29. Antoine Jacquier & Fangwei Shi, 2016. "The randomised Heston model," Papers 1608.07158, arXiv.org, revised Dec 2018.
  30. Francesco Caravenna & Jacopo Corbetta, 2015. "The asymptotic smile of a multiscaling stochastic volatility model," Papers 1501.03387, arXiv.org, revised Jul 2017.
  31. Akihiko Takahashi & Yukihiro Tsuzuki, 2013. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-305, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  32. Archil Gulisashvili & Peter Tankov, 2014. "Implied volatility of basket options at extreme strikes," Papers 1406.0394, arXiv.org.
  33. Aleksandar Mijatovi'c & Martijn Pistorius, 2009. "Exotic derivatives under stochastic volatility models with jumps," Papers 0912.2595, arXiv.org, revised Oct 2010.
  34. P. Friz & S. Gerhold & A. Gulisashvili & S. Sturm, 2010. "On refined volatility smile expansion in the Heston model," Papers 1001.3003, arXiv.org, revised Nov 2010.
  35. Sergey Badikov & Mark H.A. Davis & Antoine Jacquier, 2021. "Perturbation analysis of sub/super hedging problems," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1240-1274, October.
  36. Cyril Grunspan & Joris Van Der Hoeven, 2020. "Effective Asymptotics Analysis For Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-23, March.
  37. Antoine Jacquier, 2007. "Asymptotic skew under stochastic volatility," Birkbeck Working Papers in Economics and Finance 0703, Birkbeck, Department of Economics, Mathematics & Statistics.
  38. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
  39. Jurek, Jakub W., 2014. "Crash-neutral currency carry trades," Journal of Financial Economics, Elsevier, vol. 113(3), pages 325-347.
  40. Andrey Itkin, 2013. "New solvable stochastic volatility models for pricing volatility derivatives," Review of Derivatives Research, Springer, vol. 16(2), pages 111-134, July.
  41. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
  42. Kun Gao & Roger Lee, 2014. "Asymptotics of implied volatility to arbitrary order," Finance and Stochastics, Springer, vol. 18(2), pages 349-392, April.
  43. Peters, R. & van der Weide, R., 2012. "Volatility: Expectations and Realizations," CeNDEF Working Papers 12-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  44. Bedendo, Mascia & Hodges, Stewart D., 2009. "The dynamics of the volatility skew: A Kalman filter approach," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1156-1165, June.
  45. Shuzhen Yang & Wenqing Zhang, 2023. "Fixed-point iterative algorithm for SVI model," Papers 2301.07830, arXiv.org.
  46. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.
  47. Michael R. Tehranchi, 2015. "Uniform bounds for Black--Scholes implied volatility," Papers 1512.06812, arXiv.org, revised Aug 2016.
  48. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
  49. Antoine Jacquier & Patrick Roome, 2013. "The Small-Maturity Heston Forward Smile," Papers 1303.4268, arXiv.org, revised Aug 2013.
  50. Peter Carr & Sander Willems, 2019. "A lognormal type stochastic volatility model with quadratic drift," Papers 1908.07417, arXiv.org.
  51. Itkin, Andrey, 2015. "To sigmoid-based functional description of the volatility smile," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 264-291.
  52. Leif Döring & Blanka Horvath & Josef Teichmann, 2017. "Functional Analytic (Ir-)Regularity Properties Of Sabr-Type Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-48, May.
  53. Peter Carr & Andrey Itkin & Sasha Stoikov, 2019. "A model-free backward and forward nonlinear PDEs for implied volatility," Papers 1907.07305, arXiv.org.
  54. Bo Zhao & Stewart Hodges, 2013. "Parametric modeling of implied smile functions: a generalized SVI model," Review of Derivatives Research, Springer, vol. 16(1), pages 53-77, April.
  55. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
  56. Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.
  57. Bastien Baldacci, 2020. "High-frequency dynamics of the implied volatility surface," Papers 2012.10875, arXiv.org.
  58. Stefan Gerhold & Johannes F. Morgenbesser & Axel Zrunek, 2014. "Refined wing asymptotics for the Merton and Kou jump diffusion models," Papers 1401.1954, arXiv.org.
  59. Stefano De Marco & Claude Martini, 2017. "Moment generating functions and Normalized implied volatilities: unification and extension via Fukasawa's pricing formula," Papers 1703.00957, arXiv.org, revised May 2017.
  60. Aleksandar Mijatovi'c & Peter Tankov, 2012. "A new look at short-term implied volatility in asset price models with jumps," Papers 1207.0843, arXiv.org, revised Jul 2012.
  61. Nian Yao & Zhiqiu Li & Zhichao Ling & Junfeng Lin, 2020. "Asymptotic Smiles for an Affine Jump-Diffusion Model," Papers 2003.00334, arXiv.org, revised May 2020.
  62. Martin Keller-Ressel, 2022. "W-shaped implied volatility curves in a variance-gamma mixture model," Papers 2209.14726, arXiv.org.
  63. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2017. "Shapes of implied volatility with positive mass at zero," Working Papers 2017-77, Center for Research in Economics and Statistics.
  64. Carol Alexander & Alexander Rubinov & Markus Kalepky & Stamatis Leontsinis, 2012. "Regime‐dependent smile‐adjusted delta hedging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(3), pages 203-229, March.
  65. Frédéric Abergel & Riadh Zaatour, 2012. "What drives option prices ?," Post-Print hal-00687675, HAL.
  66. Antoine Jacquier & Martin Keller-Ressel, 2015. "Implied volatility in strict local martingale models," Papers 1508.04351, arXiv.org.
  67. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
  68. Francesco Caravenna & Jacopo Corbetta, 2014. "General smile asymptotics with bounded maturity," Papers 1411.1624, arXiv.org, revised Jul 2016.
  69. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2019. "Extreme-strike asymptotics for general Gaussian stochastic volatility models," Annals of Finance, Springer, vol. 15(1), pages 59-101, March.
  70. Archil Gulisashvili & Elias M. Stein, 2009. "Implied Volatility In The Hull–White Model," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 303-327, April.
  71. Bender Christian & Thiel Matthias, 2020. "Arbitrage-free interpolation of call option prices," Statistics & Risk Modeling, De Gruyter, vol. 37(1-2), pages 55-78, January.
  72. Madan, Dilip B. & Wang, King, 2018. "Strike asymptotics for Laplace implied volatilities," Finance Research Letters, Elsevier, vol. 25(C), pages 183-189.
  73. Michael R. Tehranchi, 2020. "A Black–Scholes inequality: applications and generalisations," Finance and Stochastics, Springer, vol. 24(1), pages 1-38, January.
  74. Stefano Giglio & Ian Dew-Becker & David Berger, 2016. "Contractionary Volatility or Volatile Contractions?," 2016 Meeting Papers 673, Society for Economic Dynamics.
  75. Arianna Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Papers 2204.00312, arXiv.org.
  76. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Extreme-Strike Asymptotics for General Gaussian Stochastic Volatility Models," Papers 1502.05442, arXiv.org, revised Feb 2017.
  77. Cyril Grunspan & Joris van der Hoeven, 2020. "Effective asymptotic analysis for finance," Post-Print hal-01573621, HAL.
  78. Andreas Kunz, 2012. "Robust Hedging of Withdrawal Guarantees (Extended Version)," Papers 1202.0175, arXiv.org, revised Sep 2012.
  79. A. Gulisashvili, 2009. "Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes," Papers 0906.0394, arXiv.org.
  80. Akihiko Takahashi & Yukihiro Tsuzuki, 2014. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CIRJE F-Series CIRJE-F-917, CIRJE, Faculty of Economics, University of Tokyo.
  81. Andrey Itkin, 2020. "Geometric Local Variance Gamma Model," World Scientific Book Chapters, in: Fitting Local Volatility Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, chapter 6, pages 137-173, World Scientific Publishing Co. Pte. Ltd..
  82. Xiaowei Zhang & Peter W. Glynn, 2018. "Affine Jump-Diffusions: Stochastic Stability and Limit Theorems," Papers 1811.00122, arXiv.org.
  83. Akihiko Takahashi & Yukihiro Tsuzuki, 2014. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-350, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  84. Dan Pirjol & Lingjiong Zhu, 2020. "Asymptotics of the time-discretized log-normal SABR model: The implied volatility surface," Papers 2001.09850, arXiv.org, revised Mar 2020.
  85. Tahar Ferhati, 2020. "Robust Calibration For SVI Model Arbitrage Free," Working Papers hal-02490029, HAL.
  86. Tahar Ferhati, 2020. "SVI Model Free Wings," Working Papers hal-02517572, HAL.
  87. Sidi Mohamed Aly, 2016. "Moment explosions, implied volatility and local volatility at extreme strikes," Papers 1601.06995, arXiv.org, revised Aug 2016.
  88. S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12, January.
  89. Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2021. "The Alpha‐Heston stochastic volatility model," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 943-978, July.
  90. Vimal Raval & Antoine Jacquier, 2021. "The Log Moment formula for implied volatility," Papers 2101.08145, arXiv.org.
  91. Gaoyue Guo & Antoine Jacquier & Claude Martini & Leo Neufcourt, 2012. "Generalised arbitrage-free SVI volatility surfaces," Papers 1210.7111, arXiv.org, revised May 2016.
  92. repec:hal:wpaper:hal-00687675 is not listed on IDEAS
  93. Archil Gulisashvili, 2013. "Left-wing asymptotics of the implied volatility in the presence of atoms," Papers 1311.6027, arXiv.org.
  94. Peter Friz & Stefan Gerhold, 2011. "Don't stay local - extrapolation analytics for Dupire's local volatility," Papers 1105.1267, arXiv.org.
  95. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Small-time asymptotics for Gaussian self-similar stochastic volatility models," Papers 1505.05256, arXiv.org, revised Mar 2016.
  96. Cyril Grunspan, 2011. "A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach," Papers 1112.1782, arXiv.org.
  97. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2022. "CBI-time-changed Lévy processes," Working Papers 05/2022, University of Verona, Department of Economics.
  98. Peter Van Tassel, 2016. "Merger options and risk arbitrage," Staff Reports 761, Federal Reserve Bank of New York.
  99. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
  100. A. Gulisashvili & E. M. Stein, 2009. "Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models," Papers 0906.0392, arXiv.org.
  101. J. D. Deuschel & P. K. Friz & A. Jacquier & S. Violante, 2013. "Marginal density expansions for diffusions and stochastic volatility, part II: Applications [to the Stein--Stein model]," Papers 1305.6765, arXiv.org.
  102. Caravenna, Francesco & Corbetta, Jacopo, 2018. "The asymptotic smile of a multiscaling stochastic volatility model," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1034-1071.
  103. Philip Stahl, 2022. "Asymptotic extrapolation of model-free implied variance: exploring structural underestimation in the VIX Index," Review of Derivatives Research, Springer, vol. 25(3), pages 315-339, October.
  104. Arianna Mingone, 2022. "Smiles in delta," Papers 2209.00406, arXiv.org.
  105. del Baño Rollin, Sebastian & Ferreiro-Castilla, Albert & Utzet, Frederic, 2010. "On the density of log-spot in the Heston volatility model," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2037-2063, September.
  106. Stefan Gerhold & Christoph Gerstenecker & Arpad Pinter, 2018. "Moment Explosions in the Rough Heston Model," Papers 1801.09458, arXiv.org, revised Apr 2018.
  107. Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2018. "The Alpha-Heston Stochastic Volatility Model," Papers 1812.01914, arXiv.org.
  108. J. D. Deuschel & P. K. Friz & A. Jacquier & S. Violante, 2011. "Marginal density expansions for diffusions and stochastic volatility, part I: Theoretical Foundations," Papers 1111.2462, arXiv.org, revised May 2013.
  109. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
  110. Stefano De Marco & Peter Friz, 2013. "Varadhan's formula, conditioned diffusions, and local volatilities," Papers 1311.1545, arXiv.org, revised Jun 2016.
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