Model risk and model choice in the case of barrier options and bonus certificates

In the pricing of exotic options, model risk arises when different models yield different prices, even though they are calibrated to the same observable prices of plain vanilla options. We analyze model risk in the case of barrier options and bonus certificates. This study uses an empirical data set of over 40,000 certificates to analyze the real market extent of model risk for traded barrier options. In particular, applying the local volatility model, the Heston model, and the Bates model, theoretical model risk amounts to about 8.5% (median) of the barrier option value. In contrast, the median empirical model risk, based on the range of market prices, is only 2.2%. We find evidence that the majority of issuers prefer stochastic volatility over local volatility models. Model risk is a factor priced into issuers’ margin policy—that is, they let retail customers pay for their model risk.