臺大管理論叢 NTU Management Review VOL.29 NO.2

49 NTU Management Review Vol. 29 No. 2 Aug. 2019 The notations used in this paper are as shown in Table 1. Table 1 Notations of Variables Variables Description r Real n Nominal α constant floor value β constant cap value A fixed amount S(t j ,x 0 ) a survival probability in which a person aged x 0 at time t 0 is still alive at time t, I t inflation index at time t P n (t, T) time price of nominal zero-coupon bonds maturing at time T in dollar P r (t, T) time price of real zero-coupon bonds maturing at time T in dollar f n (t, T) time nominal forward rates for date T f r (t, T) time real forward rates for date T α n (t, T) drift term of nominal forward rates σ n (t, T) volatility of nominal forward rates α r (t, T) drift term of real forward rates σ r (t, T) volatility of real forward rates α I (t) drift term of inflation index at time t σ I (t) volatility of inflation index at time t r n,t nominal risk free rates at time t r r,t real risk free rates at time t ρ nI correlation coefficient between nominal forward rates and inflation index ρ rI correlation coefficient between real forward rates and inflation index ρ nr correlation coefficient between nominal forward rates and real forward rates Figure 1 Payments of Inflation-Linked Annuities A×Y t1 ×S(t 1 , x 0 ) t 0 t 1 t 2 t m ...... A×Y t2 ×S(t 2 , x 0 ) A×Y tm ×S(t m , x 0 )