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Stochastic volatility and stochastic leverage

  • Almut Veraart


  • Luitgard Veraart

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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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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