CONSTANT PROPORTION PORTFOLIO INSURANCE IN THE PRESENCE OF JUMPS IN ASSET PRICES
研究了资产价格存在向下跳跃时恒定比例投资组合保险策略的风险，推导出触及保底概率、预期损失等解析表达式，并提出了根据风险厌恶调整乘数的标准，最后探讨了用期权对冲下行风险的问题。
Constant proportion portfolio insurance (CPPI) allows an investor to limit downside risk while retaining some upside potential by maintaining an exposure to risky assets equal to a constant multiple of the cushion , the difference between the current portfolio value and the guaranteed amount. Whereas in diffusion models with continuous trading, this strategy has no downside risk, in real markets this risk is nonnegligible and grows with the multiplier value. We study the behavior of CPPI strategies in models where the price of the underlying portfolio may experience downward jumps. Our framework leads to analytically tractable expressions for the probability of hitting the floor, the expected loss, and the distribution of losses. This allows to measure the gap risk but also leads to a criterion for adjusting the multiplier based on the investor's risk aversion. Finally, we study the problem of hedging the downside risk of a CPPI strategy using options. The results are applied to a jump‐diffusion model with parameters estimated from returns series of various assets and indices.