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Volatility models in practice: Rough, Path-dependent or Markovian? (2401.03345v2)

Published 7 Jan 2024 in q-fin.MF, q-fin.CP, and q-fin.PR

Abstract: We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter $H \in (0,1/2)$ are inconsistent with the global shape of SPX smiles. In particular, the at-the-money SPX skew is incompatible with the power-law shape generated by these models, which increases too fast for short maturities and decays too slowly for longer maturities. For maturities between one week and three months, rough volatility models underperform one-factor Markovian models with the same number of parameters. When extended to longer maturities, rough volatility models do not consistently outperform one-factor Markovian models. Our study identifies a non-rough path-dependent model and a two-factor Markovian model that outperform their rough counterparts in capturing SPX smiles between one week and three years, with only 3 to 4 parameters.

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References (51)
  1. Eduardo Abi Jaber. Lifting the Heston model. Quantitative Finance, 19(12):1995–2013, 2019.
  2. Reconciling rough volatility with jumps. Available at SSRN 4387574, 2023.
  3. Markovian structure of the Volterra Heston model. Statistics & Probability Letters, 149:63–72, 2019.
  4. Affine Volterra processes. The Annals of Applied Probability, 29(5):3155–3200, 2019.
  5. A weak solution theory for stochastic volterra equations of convolution type. The Annals of Applied Probability, 31(6):2924–2952, 2021a.
  6. Linear-quadratic control for a class of stochastic volterra equations: solvability and approximation. The Annals of Applied Probability, 31(5):2244–2274, 2021b.
  7. Joint SPX–VIX calibration with gaussian polynomial volatility models: deep pricing with quantization hints. Available at SSRN 4292544, 2022.
  8. The quintic ornstein-uhlenbeck volatility model that jointly calibrates spx & vix smiles. Risk Magazine, Cutting Edge Section, 2023.
  9. On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility. Finance and stochastics, 11(4):571–589, 2007.
  10. Pricing under rough volatility. Quantitative Finance, 16(6):887–904, 2016.
  11. A regularity structure for rough volatility. Mathematical Finance, 30(3):782–832, 2020.
  12. L Bergomi. Smile dynamics II. Risk Magazine, 2005.
  13. Lorenzo Bergomi. Stochastic volatility modeling. CRC press, 2015.
  14. Stochastic volatility’s orderly smiles. Risk, 25(5):60, 2012.
  15. Rough volatility, path-dependent pdes and weak rates of convergence. arXiv preprint arXiv:2304.03042, 2023.
  16. Towards a theory of volatility trading. Option Pricing, Interest Rates and Risk Management, Handbooks in Mathematical Finance, 22(7):458–476, 2001.
  17. What type of process underlies options? a simple robust test. The Journal of Finance, 58(6):2581–2610, 2003.
  18. Long memory in continuous-time stochastic volatility models. Mathematical finance, 8(4):291–323, 1998.
  19. Rough volatility: fact or artefact? arXiv preprint arXiv:2203.13820, 2022.
  20. Multifractional stochastic volatility models. Mathematical Finance, 24(2):364–402, 2014.
  21. Generalized feller processes and markovian lifts of stochastic volterra processes: the affine case. Journal of evolution equations, 20(4):1301–1348, 2020.
  22. Yet another analysis of the sp500 at-the-money skew: Crossover of different power-law behaviours. Available at SSRN 4428407, 2023.
  23. A long memory property of stock market returns and a new model. Journal of empirical finance, 1(1):83–106, 1993.
  24. Bruno Dupire. Arbitrage pricing with stochastic volatility. Société Générale, 1992.
  25. The rough bergomi model as h→ 0–skew flattening/blow up and non-gaussian rough volatility. preprint, 2020.
  26. Derivatives in financial markets with stochastic volatility. Cambridge University Press, 2000.
  27. Multiscale stochastic volatility asymptotics. Multiscale Modeling & Simulation, 2(1):22–42, 2003.
  28. Maturity cycles in implied volatility. Finance and Stochastics, 8:451–477, 2004.
  29. Forests, cumulants, martingales. The Annals of Probability, 50(4):1418–1445, 2022.
  30. Masaaki Fukasawa. Asymptotic analysis for stochastic volatility: martingale expansion. Finance and Stochastics, 15:635–654, 2011.
  31. Masaaki Fukasawa. Volatility has to be rough. Quantitative Finance, 21(1):1–8, 2021.
  32. Jim Gatheral. Consistent modeling of spx and vix options. In Bachelier congress, volume 37, pages 39–51, 2008.
  33. Volatility is rough. Quantitative finance, 18(6):933–949, 2018.
  34. Archil Gulisashvili. Large deviation principle for volterra type fractional stochastic volatility models. SIAM Journal on Financial Mathematics, 9(3):1102–1136, 2018.
  35. Julien Guyon. The smile of stochastic volatility: Revisiting the bergomi-guyon expansion. Available at SSRN 3956786, 2021.
  36. Julien Guyon. Dispersion-constrained martingale schrödinger bridges: Joint entropic calibration of stochastic volatility models to s&p 500 and vix smiles. Available at SSRN 4165057, 2022a.
  37. Julien Guyon. The vix future in bergomi models: Fast approximation formulas and joint calibration with s&p 500 skew. SIAM Journal on Financial Mathematics, 13(4):1418–1485, 2022b.
  38. Does the term-structure of equity at-the-money skew really follow a power law? Available at SSRN 4174538, 2022.
  39. Volatility is (mostly) path-dependent. Volatility Is (Mostly) Path-Dependent (July 27, 2022), 2022.
  40. Affine representations of fractional processes with applications in mathematical finance. Stochastic Processes and their Applications, 129(4):1185–1228, 2019.
  41. Functional central limit theorems for rough volatility. arXiv preprint arXiv:1711.03078, 2017.
  42. Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models. Quantitative Finance, 21(1):11–27, 2021.
  43. Large and moderate deviations for stochastic volterra systems. Stochastic Processes and their Applications, 149:142–187, 2022.
  44. Rough fractional diffusions as scaling limits of nearly unstable heavy tailed hawkes processes. The Annals of Applied Probability, 26(5):2860–2882, 2016. ISSN 10505164.
  45. Correlations in economic time series. Physica A: Statistical Mechanics and its Applications, 245(3-4):437–440, 1997.
  46. Serguei Mechkov. Fast-reversion limit of the Heston model. Available at SSRN 2418631, 2015.
  47. Modelling fluctuations of financial time series: from cascade process to stochastic volatility model. The European Physical Journal B-Condensed Matter and Complex Systems, 17:537–548, 2000.
  48. Multiple time scales in volatility and leverage correlations: a stochastic volatility model. Applied Mathematical Finance, 11(1):27–50, 2004.
  49. L Rogers. Things we think we know, 2019.
  50. Sigurd Emil Rømer. Empirical analysis of rough and classical stochastic volatility models to the spx and vix markets. Quantitative Finance, 22(10):1805–1838, 2022.
  51. A martingale approach for fractional brownian motions and related path dependent pdes. The Annals of Applied Probability, 29(6):3489–3540, 2019.
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Authors (3)

  1. Eduardo Abi Jaber
  2. Shaun
  3. Li
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