Constant proportion portfolio insurance strategies in contagious markets

Constant Proportion Portfolio Insurance (CPPI) strategies are popular as they allow to gear up the upside potential of a stock index while limiting its downside risk. From the issuer’s perspective it is important to adequately assess the risks associated with the CPPI, both for correct ‘gap’ fee charging and for risk management. The literature on CPPI modelling typically assumes diffusive or Lévy-driven dynamics for the risky asset underlying the strategy. In either case the self-contagious nature of asset prices is not taken into account. In order to account for contagion while preserving analytical tractability, we introduce self-exciting jumps in the underlying dynamics via Hawkes processes. Within this framework we derive the loss probability when trading is performed continuously. Moreover, we estimate measures of the risk involved in the practical implementation of discrete-time rebalancing rules governing the CPPI product. When rebalancing is performed on a frequency less than weekly, failing to take contagion into account will significantly underestimate the risks of the CPPI. Finally, in order to mimic a situation with low liquidity, we impose a daily trading cap on the risky asset and find that the Hawkes process driven models give rise to the highest risk measures even under daily rebalancing.