One-Dimensional Pricing of CPPI

Details One-Dimensional Pricing of CPPI One-Dimensional Pricing of CPPI

2009-05-18

arxiv.org/abs/0905.2926v2

Economy

Quantitative Finance

Pricing of Securities

19 pages; v2: improved algorithm, error analysis

Scientific paper

Constant Proportion Portfolio Insurance (CPPI) is an investment strategy designed to give participation in the performance of a risky asset while protecting the invested capital. This protection is however not perfect and the gap risk must be quantified. CPPI strategies are path-dependent and may have American exercise which makes their valuation complex. A naive description of the state of the portfolio would involve three or even four variables. In this paper we prove that the system can be described as a discrete-time Markov process in one single variable if the underlying asset follows a homogeneous process. This yields an efficient pricing scheme using transition probabilities. Our framework is flexible enough to handle most features of traded CPPIs including profit lock-in and other kinds of strategies with discrete-time reallocation.

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