Effectiveness of CPPI strategies under discrete-time trading

The paper analyzes the effectiveness of the constant proportion portfolio insurance (CPPI) method under trading restrictions. If the CPPI method is applied in continuous time, the CPPI strategies provide a value above a floor level unless the price dynamics of the risky asset permit jumps. The risk of violating the floor protection is called gap risk. In practice, it is caused by liquidity constraints and price jumps. Both can be modelled in a setup where the price dynamics of the risky asset are described by a continuous-time stochastic process but trading is restricted to discrete time. We propose a discrete-time version of the continuous-time CPPI strategies which satisfies three conditions. The resulting strategies are self-financing, the asset exposure is non-negative and the value process converges. We determine risk measures such as the shortfall probability and the expected shortfall and discuss criteria which ensure that the gap risk does not increase to a level which contradicts the original intention of portfolio insurance. In addition, we introduce proportional transaction costs and analyze their effects on the risk profile.