Recall that the OBPI payoff corresponds to m=1 ("linear"case).
When the financial market is bearish, the portfolio value reaches quickly the floor but remains above the OBPI payoff.
We have compared this strategy with the standard OBPI method and illustrated more precisely the influence of risk aversion on the insured portfolio.
The second effect has a bigger impact on the return of the OBPI than the first one.
For both the CPPI and the OBPI, we set the same initial value of the portfolio.
For moderate values of the risky asset above the strike, the OBPI payoff is above the CPPI payoff.
The payoff at maturity associated to the OBPI method is still a function of S(T), defined by:
If we compare the first two moments (mean-variance analysis), note that for m high, the expectation and variance of the CPPI portfolio are greater than those of the OBPI one and so there is no-dominance with respect to the mean-variance criterion.
For that value of m, CPPI strategy is dominated, in a mean-variance sense, by OBPI strategy.
We evaluate the probability that the CPPI portfolio value is greater than that of the OBPI.
For K=90 (in the money call), the probability that the CPPI portfolio value is higher than the OBPI one is approximatively 0.
We have shown that on one hand stochastic volatility increases the return of OBPI while reducing slightly the return of the CPPI.