Not-so-complex logarithms in the Heston model

By Christian Kahl, Peter J̈ackel. 2006

155 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/19333ecd9e09a963ccb1466d8cd206a1230f1c1e

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Citations in the corpus

An Analytical Formula for VIX Futures and its Applications (2012, background): “There have been examples reported in the literature (e.g., Kahl & Jackel 2005) showing some wrong results when the Fourier inversion is performed numerically.”
A tree-based method to price American options in the Heston model (2009, background): “This closed form actually requires the numerical approximation of a certain integral, and some care has to be taken when dealing with the complex logarithm in this integral (see the excellent recent papers by Lord, Kahl and Jäckel [16, 12] and Albracher et al [1] on this issue).”
Multilevel Monte Carlo Path Simulation (2008, methodology): “Note that √ V is replaced by √ V + ≡√max V 0 , but as h→ 0, the probability of the discrete approximation to the volatility becoming negative approaches zero for the chosen values of , / , 2 (Kahl and Jäckel 2006). Because the volatility does not satisfy a global Lipschitz condition, there is no exi”
A CLOSED‐FORM EXACT SOLUTION FOR PRICING VARIANCE SWAPS WITH STOCHASTIC VOLATILITY (2010, background): “There have been examples reported in the literature (e.g., Kahl and Jackel 2005) for the wrong numerical integration that those complex-valued integrand may result in.”
The characteristic function of rough Heston models (2016, methodology): “From this formula, efficient numerical methods have been developed, allowing for instantaneous model calibration and pricing of derivatives, see [1, 8, 31, 32].”