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. [ABSTRACT FROM AUTHOR]