Equity Autocalls and Vanna Negative Carries: Pricing and Hedging with a Simple Add-On

Abstract

Autocall products: a toxic best-seller. Over the past twenty years, the autocall pay-off has been the most traded exotic equity product. Outstandingly popular, it is mainly sold to final customers in Europe and Asia trough notes: its average yearly volumes reaches 100 billion euros. Nevertheless, it is responsible for major losses suffered by banks’ Exotic trading desks. Roughly, when the spot remains in a [80%,105%] area around the recall barrier, daily carry loss is worth 1 to 3 basis points (depending on the product complexity, as several variations exist). Indeed, it shows a strong model-dependency due to the cancellation feature: when the spot moves, books need dynamic rehedging via vanilla options, forward contracts, correlation products. As such, it requires the use of a pricing model which correctly combines market data dynamics (volatility, repo, equity correlations, quanto drifts…) and spot dynamic, in order to price properly the cost of daily rehedging. In practice, building a pricing model complex enough to calibrate the relevant covariances while remaining numerically stable and computationally reasonable has proved to be a very serious challenge. Not mentioning ultimately the need for comprehensive interpretations of outputs. Escaping this issue, we exhibit here, a convenient way to price and hedge autocalls toxic behaviors through an additional and corrective pay-off. There are approximations throughout the building of such an approach that have been tested numerically and justified qualitatively. Nonetheless, this is cheaper in terms of model complexity and development, and it provides a comprehensive and efficient pricing scheme combined with a hedging strategy which tackles the issue of negative carries generated by an autocall replication strategy.