Abstract
This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.
Highlights
A variable annuity (VA) contract is issued by an insurance company, which offers upside opportunities in financial market and protects against downside risk by adding various types of benefit riders
A guaranteed minimum accumulation benefit (GMAB) guarantees a lump sum amount at a predetermined future date, a guaranteed minimum death benefit (GMDB) guarantees a minimum lump sum upon death, a guaranteed minimum living benefit (GMLB) provides income guarantees to protect the policyholder’s income from declining, and a guaranteed minimum maturity benefit (GMMB) is a guarantee that provides the policyholder with a minimum benefit on maturity of the VA contract
We focus on a VA contract embedded with a GMMB rider by incorporating regime-switching volatility. is problem can be viewed as an optimal stopping problem with regimeswitching
Summary
A variable annuity (VA) contract is issued by an insurance company, which offers upside opportunities in financial market and protects against downside risk by adding various types of benefit riders. Bernard et al [1] split the value of VA contract into a European part and an early exercise premium and derived a Volterra-type integral equation with respect to the optimal surrender boundary under the assumption that the underlying risky asset follows the geometric Brownian motion (GBM) model. Yang [15] studied the properties of free boundary arising from Russian option pricing problem with regime-switching volatility by the variational inequality approach. Compared with the sensitivity analysis in Shen et al [4], which was performed by numerical examples without proofs, we apply a rigorous variational inequality approach to explore the impacts of varying model parameters on the optimal surrender boundary.
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