体制转换模型下具备最低身故利益保证的变额年金的定价(英文)

An FFT Approach to Price Guaranteed Minimum Death Benefit in Variable Annuities under a Regime-Switching Model

本文研究具备最低身故利益保证的变额年金的定价问题.该模型中,假设无风险利率,投资基金的波动率是被连续时间有限状态马尔科夫链所调制的.运用体制转换Esscher变换方法得到唯一的等价鞅测度.在风险中性测度下,通过逆傅里叶变换得到最低身故利益保证的变额年金中嵌入期权的定价公式,然后通过快速傅里叶变换进行求解,并对数值例子进行了分析比较.

This paper considers the valuation of guaranteed minimum death benefit in variable annuities under a regime-switching model. More specifically, the risk-free interest rate, the appreciation rate and the volatility of the reference investment fund are modulated by a continuous-time, finite-state, observable Markov chain. A regime-switching Esscher transform is adopted to select an equiva- lent martingale measure in the incomplete financial market. Inverse Fourier transform is used to derive an analytical pricing formula for the embedded option in variable annuity with guaranteed minimum death benefit. To calculate the fair guarantee charge, fast Fourier transform approach is applied. Numerical exafnples are provided to illustrate the practical implementation and the relationship between the fair guarantee charges and other parameters.