Monte Carlo methods for valuation of ratchet equity indexed annuities

Equity Indexed Annuities (EIAs) are popular insurance contracts. EIAs provide the insured with a guaranteed accumulation rate on their premium at maturity. In addition, the insured may receive extra benefit if the return of the linked index is high enough. There are a few variations of EIAs. We consider two types of EIAs: compound ratchet and simple ratchet. Under the geometric Brownian motion assumption for the equity index, plain compound ratchet options is known to have closed form solutions, but plain simple ratchet option is not. In this paper, we derive a closed form solution for plain simple ratchet option. For more exotic options, Monte Carlo methods are usually used for their valuation. To improve their efficiency, we propose two control variates based on the analytical solutions for the price of plain ratchet options. The effectiveness of the proposed control variates is examined via numerical examples of a typical contract.