Valuation of Endowment-Insurance Equity-Linked Contracts for Stocks with Exotic Dynamics

Figure 2

Maturity component premium as a function of time to maturity in years corresponding to benefits Ψ_𝑇¹⁾=max{𝑋_𝑇,𝑥} and Ψ_𝑇¹⁾=max_{0≤𝑠≤𝑇}𝑋_𝑠. The thick dark line is the max-premium (26), whereas (12) is the thin, lower line. Parameters are taken as 𝑥=1, 𝑟=0.045, and 𝜎=20%.