Pricing Model Study On The Guaranteed Minimum Withdrawal Benefit In Variable Annuities

Nowadays in China, the number of older people keeps increasing; the Chinesepeople are suffering more and more pension pressure. All these bring the insurancemarket great potential for development. While the products in our pension insurancemarket is relatively onefold, the development of the industry is imbalanced, so the careneeds of the older are not met. China has launched a pilot project on Variable Annuitiesin Beijing、shanghai and other places since May2010, trying to enrich the product mixand establish a multi-level product structure to cater to the need of different levels ofconsumers.With guarantee benefits, the policyholder can get all the benefits of assetappreciation recklessly. These paper focuses on one of these minimum guaranteebenefits, the guaranteed minimum withdrawal benefit (GMWB). This guaranteedbenefit is vulnerable to systemic risk, making the insurance company suffering largelosses. How to make a reasonable price becomes the most important task of risk-averse.China Insurance Regulatory Commission hasn’t allowed the domestic insurancecompanies issue this type of Variable Annuities yet. As is the most popular guaranteeon foreign markets, GMWB does well in meeting the needs of retirement income. It isnecessary for our country to make up how to apply this type of guarantee in ourmarket.In this paper, we first introduces the development history and common features ofguaranteed minimum withdrawal benefit, then use numerical analysis to present theoperation of GMWB. Later we analysis the risk factors of GMWB, and introduceseveral foreign common approach to manage the risk. Finally, we give the pricingmodel of GMWB. The pricing model is based on Daniel Bauer, et al (2006), whichgives a general pricing model for all the guarantees. We innovate the model by add thestep-up features, roll-up features and the bonus features into it. State variables are usedto describe the policy each time during the operation process. Through this, we can getthe maturity returns, which are the function of the fee and is supposed to equal to theinitial premium. Since the GMWB is a path dependent options, the results of thepricing is too complex to get a closed solution, so I introduce the Monte-Carloalgorithm to simulate the solution of the pricing. Giving the option price ratio combinewith our data and pointing out the sensitivity of the price variable. This pricing methodis very close to reality and has a strong practicality.