Portfolio Insurance Strategies in an Extended Black- Scholes Framework Including Jumps in Asset Prices

Abstract

The Constant Proportion Portfolio Insurance (CPPI) and Option Based Portfolio Insurance(OBPI) strategies are examined and evaluated in an extended Black-Scholes framework including jumps in asset prices, stochastic volatility, and stochastic interestrate and bond prices. The Kou model (an exponential Levy model) was used to mode the dynamics of the risky assets. Interest rate was modelled according to the Vasicek model (an Ornstein-Uhlenbeck model). The method of empirical characteristic exponent was applied in order to calibrate the Kou model towards real-world financial data.By means of the Monte Carlo method, the portfolio strategies were analysed through simulation.If was found that in calmer market conditions, the OBPI strategy slightly outperforms the CPPI. As the CPPI has negligible risk of default in those market conditions, it can be used as a replacement for the OBPI in the absence of a liquid options market. In highly volatile markets, on the other hand, the CPPI clearly outperforms the OBPI,especially when the time to maturity is relatively short. However, as the intensity and sizes of jumps in asset prices increase, the CPPI can reach important levels of risk of default.The risk of default as a function of the multiplier in the CPPI strategy is examined in detail, using model parameters estimated from MSFT, BMW and AZN stocks as well as SNP500, SX5E and NIKKEI225 indices.