A remark on Lin's and Chang's pager 'Consistent modelling of S&P500 and VIX derivatives'

摘要

Lin and Chang (2009, 2010) establish a VIX futures and option pricing theory when modelingS&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 pricingequation. More generally, we show that the characteristic function of their pricing equationcannot be exponentially ane, as proposed by them. Furthermore, their formula cannot serve asa reasonable approximation. Using the Heston (1993) model as a special case, we demonstratethat Lin and Chang formula misprices VIX futures and options in general and the error canbecome substantially large.