Portfolio insurance under rough volatility and Volterra processes

Affine Volterra processes have gained more and more interest in recent years. In particular, this class of processes generalizes the classical Heston model for which widely-used calibration techniques have long been known, as well as the rough Heston model which has garnered lots of attention from academicians and practitioners since 2014. The aim of this work is therefore to revisit and generalize the constant propotion portfolio insurance (CPPI) under the class of affine Volterra processes. Indeed, existing simulation-based methods for CPPI do not apply easily to affine Volterra processes, in particular when the variance process of the underlying risky asset is non-Markovian in the current variance state (as in the rough Heston model). We instead propose an approach based on the characteristic function of the log-cushion which appears to be more consistent, stable and particularly efficient in the case of affine Volterra processes compared with classical simulation techniques. Using such approach, we describe in this paper several properties of CPPI (moments, density and risk measures), which naturally result from the form of the log-cushion’s characteristic function under affine Volterra processes. This allows to consider different behaviors and more complex dynamics for the underlying risky asset in the context of CPPI and hence build portfolio strategies that are extremely tractable and consistent with financial data.