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The CO OBPIs are consistent with and complement both the Balance Scorecard and Command Business Performance Indicators (BPIs).
There exist various portfolio insurance models, among them the Option Based Portfolio Insurance (OBPI) and the Constant Proportion Portfolio Insurance (CPPI).
The OBPI, introduced by Leland and Rubinstein (1976), consists in a portfolio invested in a risky asset S (usually a financial index such as the S&P) covered by a listed put written on it.
In a first section, a generalized OBPI method is introduced, based on utility risk aversion.
Recall that for the standard OBPI method, the payoff is given by:
Then, the parameters d, m, d' and m' are such that the initial values of both the CPPI payoff and the payoff [h.sup.**] have the same price [V.sub.0] as the OBPI payoff.
Figure 9 provides examples of trajectories when using Power Call options and standard OBPI method.
One of the more popular strategies of portfolio insurance is the Option Based Portfolio Insurance (OBPI), introduced in Leland and Rubinstein (1976).
For the OBPI method, introduce the portfolio value [V.sup.OBPI] which is defined at the terminal date T by:
Thus, the OBPI has just one parameter, the strike K of the put.
Using the preceding values, we can compare the first four moments of the OBPI return at maturity for BS and SV models.
The OBPI SV exhibits higher expected return and skewness but also higher standard deviation and kurtosis.
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