臺灣博碩士論文加值系統

An equity indexed annuity （EIA） with a minimum rate of return guarantee (EIAMG) has become one of the most popular instruments in the life insurance industry. In this research, we deal with the EIAs embedded exotic options. However, as the stochastic volatility features inherent in the linked financial asset prices are extensively witnessed, few academic works pay attention to the pricing and hedging of stochastic volatility EIAMG. This paper extends the study of Hull and White (1987) and integrates the Taylor series expansion for deriving analytic solution of EIAMG with stochastic volatility. Numerical experiments show that our analytic solution performs very well and is computationally efficient as benchmarked with large sample Monte Carlo simulations. Our analytic formula can also be treated as a practical tool for pricing and hedging stochastic volatility EIAMG, since it is easy to implement and is more desirable as the computing speed is an important consideration. Besides, considering stochastic volatility can lower the value of EIAMG and the hedging cost.

1.Introduction………………………………………………………………….1
2.Literature Review…………………………………………………………….1
3.Analytic Approximately Formulae for Valuation of EIAMG…………………5
3.1.Financial Model Settings……………………………………………………5
3.2.The EIA with an Extended Point-to-point Design…………………………..5
3.3.Derivation of Valuation Formula……………………………………………6
3.3.1.The Stochastic Volatility Problem…………………………………………7
3.3.2.Incorporating Stochastic Volatility………………………………………..9
4.Hedge Ratios…………………………………………………………………..11
5.Numerical Analysis……………………………………………………………14
6.Conclusions……………………………………………………………………18
Reference………………………………………………………………………..19
Appendix A --- The Analytic Formula of an EIA with Constant Volatility………21
Appendix B --- The Analytic Formula of an EIA with Stochastic Volatility……..22
Appendix C --- The Hedge Ratios of an EIA with Constant Volatility…………..24
Appendix D --- The Hedge Ratios of an EIA with Stochastic Volatility…………25

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