Stochastic Volatility Models
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.
KeywordsBrownian Motion Bilinear Form Option Price Stochastic Volatility American Option
- 13.D.S. Bates. Jumps stochastic volatility: the exchange rate process implicit in Deutsche Mark options. Rev. Finance, 9(1):69–107, 1996. Google Scholar
- 79.S.L. Heston. A closed-form solution for options with stochastic volatility, with applications to bond and currency options. Rev. Finance, 6:327–343, 1993. Google Scholar
- 81.N. Hilber, A.M. Matache, and Ch. Schwab. Sparse wavelet methods for option pricing under stochastic volatility. J. Comput. Finance, 8(4):1–42, 2005. Google Scholar
- 153.E.M. Stein and J.C. Stein. Stock price distributions with stochastic volatility: an analytic approach. Rev. Finance, 4(4):727–752, 1991. Google Scholar