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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Veraart, A.E.D., Veraart, L.A.M. Stochastic volatility and stochastic leverage. Ann Finance 8, 205–233 (2012). https://doi.org/10.1007/s10436-010-0157-3
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DOI: https://doi.org/10.1007/s10436-010-0157-3
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