Options on constant proportion portfolio insurance with guaranteed minimum equity exposure

Abstract

In the present paper we study a new exotic option offering participation in a dynamic asset allocation strategy, which is an extension of the well‐known Constant Proportion Portfolio Insurance (CPPI) strategy. Our novel approach consists in assuming that the percentage of wealth invested in stocks cannot go under a fixed level, called guaranteed minimum equity exposure (GMEE). In particular, our proposal ensures to overcome the so‐called cash‐in risk, typically related to a standard CPPI technique, simultaneously guaranteeing the equity market participation. We look deeper into the valuation of call and put options linked to this new CPPI‐GMEE strategy. A particular attention is devoted to the analysis of key parameters' value as to gain a better understanding of the sensitivities of the option prices, when changing, for example, the embedded guarantee level. To show the effectiveness of our proposal we provide a detailed computational analysis within the Heston‐Vasicek framework, numerically comparing the evaluation of the price of European plain vanilla options when the underlying is either a purely risky asset, a standard CPPI portfolio and a CPPI with GMEE.

Time‐invariant portfolio strategies in structured products with guaranteed minimum equity exposure

“…Remark It is worth noting that the introduction of the GMEE is not exclusive to time‐invariant strategies, as we have shown above. The construction of such an allocation mechanism has recently been introduced in the literature in the case of CPPI strategies, see, for example, Reference 20. Here we do not provide the details of the CPPI strategy with GMEE (which will be denoted as G‐CPPI, for the sake of notation uniformity), but we deem it appropriate to take it into account, as it might be used as an additional benchmark for derivative pricing, as we will see in detail in Section 3.3.…”

“…Consequently, we first propose to modify the standard TIPP strategy by adding an investment threshold in the risky asset allocation, the so‐called guaranteed minimum equity exposure (GMEE). The GMEE has been introduced in Reference 20 within the CPPI framework to buffer the so‐called cash‐lock risk. Also for the TIPP allocation mechanisms, a guaranteed minimum equity exposure could overcome the risk of low market participation in a V‐shapes market environment.…”