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Valuation of Discrete Dynamic Fund Protection Under Lévy Processes

Abstract This paper investigates the valuation of discrete dynamic fund protection (DFP) under Levy processes. Specifically, the analytical solution of discrete DFP under Lévy processes is obtained in terms of Fourier transforms. The derivation uses Spitzer’s formula and leads to a recursion on computing the characteristic function of the maximum protection-to-fund ratio using the Fourier inversion. DFP can then be valued efficiently and accurately via the fast Fourier transform. The pricing behavior of the discrete DFP is numerically examined using several Levy processes, such as geometric Brownian motion, jump-diffusion models, and variance gamma process. Numerical experiments confirm that the proposed approach produces highly accurate discrete DFP values within 1 second.