Nonparametric testing of ARCH for option pricing

This chapter nonparametrically examines the relevance of ARCH models in the specific context of option pricing, We argue that a stochastic interpretation of various option pricing formulae for econometric models of changing volatility implies the mean-sufficiency property of current volatility: No variable in the information set should have additional explanatory power given the volatility and other relevant variables. Based on this intuition, we apply the nonparametric specification tests of [Ait-Sahalia et al 1994], and [Fan and Li 1996] to European call option data where the volatility is estimated using various ARCH models. We find that ARCH models pass the nonparametric test of sufficiency. We then examine whether ARCH volatility has additional explanatory power given other relevant variables. Although the tests were somewhat sensitive to the bandwidth choice, we cautiously conclude that it may fail this test of necessity.