A remark on Lin and Chang’s paper ‘Consistent modeling of S&P 500 and VIX derivatives

Jun Cheng, Meriton Ibraimi, Markus Leippold () and Jin E. Zhang
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Jun Cheng: Shanghai Stock Exchange and Nanjing University
Meriton Ibraimi: University of Zurich
Jin E. Zhang: University of Hong Kong and University of Otago

No 11-54, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: Lin and Chang (2009, 2010) establish a VIX futures and option pricing theory when modeling S&P 500 index by using a stochastic volatility process with asset return and volatility jumps. In this note, we prove that Lin and Chang’s formula is not an exact solution of their pricing equation. More generally, we show that the characteristic function of their pricing equation cannot be exponentially affine, as proposed by them. Furthermore, their formula cannot serve as a reasonable approximation. Using the Heston (1993) model as a special case, we demonstrate that Lin and Chang formula misprices VIX futures and options in general and the error can become substantially large.

Keywords: VIX option pricing; Affine Jump Diffusion; Characteristic Function. (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2011-10
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Related works:
Journal Article: A remark on Lin and Chang's paper ‘Consistent modeling of S&P 500 and VIX derivatives’ (2012)
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