A scenario-based description of optimal American capital guaran- teed strategies

The aim of the paper is to describe portfolio strategies with partial
guarantee of the initial capital. We consider the option-based (OBPI)
and the constant proportion portfolio insurance (CPPI) strategies with
both European and American features. First, we provide explicit for-
mulae for all strategies and contribute to the literature by providing the
value of the American CPPI. Second, relying on both historical data
and path simulations, we show that strategies perform differently in a
bear market. We focus on liquidation values when the market recovers
after a sharp drop. We find that the American CPPI strategy usually
outperforms the American OBPI one due to the Asian component of
the former and despite the lookback feature of the latter. To complete
our analysis, we investigate both deltas and gammas of our strategies.