Valuing equity-linked annuities under high-water mark fee structure

Abstract

This paper studies the valuation of equity-linked investment products embedded with a high-water mark (HWM) fee structure. Under the HWM fee structure, the insurance company charges threshold fees at a constant rate from the policyholder's account whenever the account value is lower than a pre-specified level, and levies HMW fees at another constant rate whenever the account is hitting new record highs that are higher than another pre-specified level. The dynamics of the logarithmic value of the policyholder's account, before fees, is assumed to follow either a two-sided jump-diffusion process with double exponential jumps, or a down-ward jump-diffusion process with exponential jumps. For the two-sided jump-diffusion model with HWM fees, using the Wiener–Hopf factorisation theorem and the duality lemma, we derive an explicit expression for its potential measure. For the down-ward jump-diffusion model with both threshold fees and HWM fees, we are facilitated with the excursion theory to derive an explicit expression of the potential measure. Using the above newly derived potential measures, we are able to obtain formulas for valuing the equity-linked annuity under the HWM fee structure. Finally, we illustrate our results with some numerical examples.