We derive a model with qualitative implications for options pricing under counterparty credit risk and provide empirical evidence using the data from the Hong Kong derivatives market during 2005–2014. We find that the log-price difference between a derivative warrant with counterparty credit risk and an otherwise identical option without counterparty credit risk is significantly and negatively associated with the credit default swap spread on the warrant issuer. We also find that the prices of out-of-the-money put warrants are more sensitive to credit risk than those of other warrants. Our results show counterparty credit risk matters for derivative pricing.

Affine jump-diffusion models have been the mainstream in options pricing because of their analytical tractability. Popular affine jump-diffusion models, however, are still unsatisfactory in describing the options data and the problem is often attributed to the diffusion term of the unobserved state variables. Using prices of variance-swaps (i.e., squared VIX) implied from options prices, we provide fresh evidence regarding the misspecification of affine jump-diffusion models, as variance-swap prices are affine functions of the state variables in a broader class of models that do not restrict the diffusion term of the state variables. We apply the nonparametric methodology used by Aït-Sahalia (1996b), supplemented with bootstrap tests and other parametric tests, to the S&P 500 index options data from January 1996 to September 2008. We find that, while the affine diffusion term of the state variables may contribute to the misspecification as the literature has suggested, the affine drift of the state variables, jump intensities, and risk premiums are also sources of misspecification.