价格跳跃风险下CPPI策略多期收益保证价值的测算

价格向下跳跃是引致CPPI策略收益保证缺口风险的主要因素之一，对CPPI策略收益保证价值贴近实际的测算必须考虑价格跳跃因素的影响. 本文对风险资产价格服从对数正态跳跃扩散过程情形下CPPI策略多期收益保证的价值进行测算. 文章给出了固定混合策略下多期收益保证价值封闭形式的测算公式. 数值分析的结果表明：1）当风险资产价格服从几何布朗运动时，CPPI策略多期收益保证的价值为0，且模型参数的变动对该结论无影响；2）当风险资产价格服从对数正态跳跃扩散过程时，CPPI策略多期收益保证的价值与CPPI策略的乘数、 收益保证水平以及风险资产价格的波动率正相关.

Valuation of CPPI-managed multiperiod rate of return guarantee with price jumps

Since downward jumps in asset prices play an important role in triggering gap risk of CPPI-managed rate of return guarantee, it is of crucial importance to incorporate the impact of downward jumps in valuation of the return guarantee products. This paper investigates the valuation of CPPI-managed multi-period return guarantee under the condition that the active asset price follows a log-normal jump diffusion process. Due to the piecewise property of the CPPI-managed portfolio, analytic results can not be obtained and we resort to numerical methods. For illustrative purposes, valuation formulae in closed form are obtained for the constant-mix strategy. Our numerical results indicate that, under the geometric Brownian motion setting, there is no gap risk in the CPPI-managed portfolio and thus the price of CPPI-managed multi-period return guarantee is zero, and that changes in parameters do not affect the price. When the price process of active asset is characterised by a log-normal jump process, however, the value of CPPI-managed multi-period return guarantee is positive and is positively correlated with the CPPI multiple, the guarantee level and the volatility of the active asset price.