Pricing CPPI Capital Guarantees: A Lagrangian Framework

Computational Finance;CPPI;Constant Proportion Portfolio Insurance;Capital Guarantees;Numerical methods;Partial integro-differential equations;Valuation;Borrowing limit;Exotic options;Jump diffusion;Applied Mathematics

Morley, Christopher Stephen Band

University of Waterloo

关键词: Computational Finance;    CPPI;    Constant Proportion Portfolio Insurance;    Capital Guarantees;    Numerical methods;    Partial integro-differential equations;    Valuation;    Borrowing limit;    Exotic options;    Jump diffusion;    Applied Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/6277/1/Morley_Chris.PDF

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

A robust computational framework is presented for the risk-neutral valuation of capitalguarantees written on discretely-reallocated portfolios following the Constant ProportionPortfolio Insurance (CPPI) strategy. Aiming to address the (arguably more realistic)cases where analytical results are unavailable, this framework accommodates risky-assetjumps, volatility surfaces, borrowing restrictions, nonuniform reallocation schedules andautonomous CPPI floor trajectories. The two-asset state space representation developedherein facilitates visualising the CPPI strategy, which in turn provides insight into griddesign and interpolation. It is demonstrated that given a deterministic process for therisk-free rate, the pricing problem can be cast as solving cascading systems of 1D partialintegro-differential equations (PIDEs). This formulation’s stability and monotonicity arestudied. In addition to making more sense financially, the limited borrowing variant ofthe CPPI strategy is found to be better suited than the classical (unlimited borrowing)counterpart for bounded-domain calculations. Consequently, it is demonstrated how theunlimited borrowing problem can be approximated by imposing an artificial borrowing limit.For implementation validation, analytical solutions to special cases are derived. Numericaltests are presented to demonstrate the versatility of this framework.