A Didactic Note on Affine Stochastic Volatility Models

By Jan Kallsen. 2006

107 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/fc7917d1029b823851d431c5761e8d88e4a5d533

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Citations in the corpus

PRICING OPTIONS ON VARIANCE IN AFFINE STOCHASTIC VOLATILITY MODELS (2010, methodology): “Observe that we obtain the dynamics of the BNS model if L is chosen to be a Brownian motion with drift (cf. Kallsen 2006).”
Analysis of Fourier Transform Valuation Formulas and Applications (2008, background): “The class of affine processes contains as special cases – among others – many stochastic volatility models, such as the Heston (1993) model, the BNS model (cf. Barndorff-Nielsen and Shephard 2001, Nicolato and Venardos 2003), and time-changed Lévy models (cf. Carr et al. 2003, Kallsen 2006).”
MEAN–VARIANCE HEDGING AND OPTIMAL INVESTMENT IN HESTON'S MODEL WITH CORRELATION (2008, background): “…= L−1bL, cL(L) = L−2cL. Suppose E (η · MX) is a martingale and define a new measure, dP := E (η · MX)T dP.(2.7) Girsanov theorem (cf. Jacod and Shiryaev 2003, III.3.11 and Kallsen 2006, proposition 2.6) then yields characteristics bX and cX under P as follows: bX = bX + cXηᵀ,(2.8) cX = cX.(2.9) 3.”
A tree-based method to price American options in the Heston model (2009, background): “define a unique solution for the associated martingale problem (see for example [13]), we only need to check the conditions stated in the previous theorem.”
Exponentially affine martingales, affine measure changes and exponential moments of affine processes (2010, unknown): “[14] for the differential characteristics).”
UTILITY MAXIMIZATION IN AFFINE STOCHASTIC VOLATILITY MODELS (2010, background): “For the convenience of the reader we summarize a few basic properties which can be found in [17] or [21], respectively.”
Stochastic Volatility of Volatility and Variance Risk Premia (2013, unknown): “…out that asset price models where the logarithmic asset price is given by an Itô semimartingale and the squared stochastic volatility process is givenby a VMOU process generally do not belong to the class of affine models as introduced by Duffie et al. (2003), see also Kallsen (2006) for a survey.”