A new approach for option pricing under stochastic volatility

By Peter P. Carr, Jian Sun. 2007

147 citations recorded by the source corpus.

Subfields: Finance

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THE 4/2 STOCHASTIC VOLATILITY MODEL: A UNIFIED APPROACH FOR THE HESTON AND THE 3/2 MODEL (2017, methodology): “In conclusion, the 4/2 provides a nice application of the powerful theory of Lie symmetries that could also work for other stochastic volatility models in the spirit of Craddock and Platen (2004), Goard and Mazur (2013) and mostly of Goard (2000), Goard (2011), and Carr and Sun (2007).”
Options on realized variance by transform methods: a non-affine stochastic volatility model (2009, methodology): “2 (Carr and Sun 2007): In the 3/2 model with time-dependent mean-reversion level, the joint conditional Fourier–Laplace transform of XT and the de-annualized realized variance R T t vs ds is given by E e iuXT R T”
Pricing swaps and options on quadratic variation under stochastic time change models—discrete observations case (2010, methodology): “As shown in [25] the conditional Laplace Transform EQ[e−λ R T 0 vtdt|Fθ T ] depends on the particular θ path only through the sufficient statistic I0 defined in (72).”
The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments (2010, background): “…as a traded asset with the most direct (and linear) exposure to variance risk, several researchers propose to directly model the dynamics of the variance swap rate (Duanmu (2004), Carr and Sun (2007)) or the forward variance swap rate (Dupire (1993), Bergomi (2005), (2008), and Buehler (2006)).”