Abstract
In Sect. 4.5, we considered local volatility models as an extension of the Black–Scholes model. These models replace the constant volatility by a deterministic volatility function, i.e. the volatility is a deterministic function of s and t. In stochastic volatility (SV) models, the volatility is modeled as a function of at least one additional stochastic process. Such models can explain some of the empirical properties of asset returns, such as volatility clustering and the leverage effect. These models can also account for long term smiles and skews.
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Hilber, N., Reichmann, O., Schwab, C., Winter, C. (2013). Stochastic Volatility Models. In: Computational Methods for Quantitative Finance. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35401-4_9
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