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Stochastic volatility and stochastic leverage

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  • Almut Veraart

    ()

  • Luitgard Veraart

Abstract

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new models. Furthermore, we give a detailed account on statistical properties of the new models.

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Bibliographic Info

Article provided by Springer in its journal Annals of Finance.

Volume (Year): 8 (2012)
Issue (Month): 2 (May)
Pages: 205-233

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Handle: RePEc:kap:annfin:v:8:y:2012:i:2:p:205-233

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Web page: http://www.springerlink.com/link.asp?id=112370

Related research

Keywords: Stochastic volatility; Volatility of volatility; Stochastic correlation; Leverage effect; Jacobi process; Ornstein–Uhlenbeck process; Square root diffusion; Lévy process; Heston model; Barndorff-Nielsen & Shephard model; C1; C5; G0; G1;

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Citations

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Cited by:
  1. Almut Veraart, 2011. "How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?," AStA Advances in Statistical Analysis, Springer, vol. 95(3), pages 253-291, September.
  2. René Aïd & Luciano Campi & Nicolas Langrené & Huyên Pham, 2012. "A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation," Working Papers hal-00747229, HAL.
  3. Ting, Sai Hung Marten & Ewald, Christian-Oliver & Wang, Wen-Kai, 2013. "On the investment–uncertainty relationship in a real option model with stochastic volatility," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 22-32.
  4. Carles Bret\'o, 2013. "On idiosyncratic stochasticity of financial leverage effects," Papers 1312.5496, arXiv.org.
  5. Ren\'e A\"id & Luciano Campi & Nicolas Langren\'e & Huy\^en Pham, 2012. "A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation," Papers 1210.8175, arXiv.org.
  6. Bretó, Carles, 2014. "On idiosyncratic stochasticity of financial leverage effects," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 20-26.
  7. Ole E. Barndorff-Nielsen & Almut E. D. Veraart, 2009. "Stochastic volatility of volatility in continuous time," CREATES Research Papers 2009-25, School of Economics and Management, University of Aarhus.
  8. Frederik Herzberg, 2013. "First steps towards an equilibrium theory for Lévy financial markets," Annals of Finance, Springer, vol. 9(3), pages 543-572, August.

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