An Optimization Approach for Pricing of Sherpa Target Redemption Notes

Abstract

Based on the one-factor CIR interest rate model, the pricing of Sherpa Target Redemption Notes (STARN) with early-excise features is investigated in this paper. Firstly, the characteristics of Sherpa target redemption notes were described and the partial differential equation was proposed. Secondly, both non-arbitrage jump conditions on the coupon date and early-excise policy on the redemption date were provided; furthermore, the boundary conditions of partial differential equations were also discussed. Thirdly, a numerical method for solving the partial differential equation was obtained based on the control volume in the theory of finite volume by making use of the upwind weighting scheme to avoid the numerical oscillation phenomenon. Finally, the sensitivity of the model parameters was analyzed. The results show that the STARN value decreases rapidly with the increase in short-term interest rates, furthermore, when short-term interest rates reached a turning point the rate of decline slowed. As volatility increases, the value of the Notes is increased; increasingly as the proportion redeemed is large, STARN value increases.

Keywords

• one-factor CIR interest rate model
• sherpa target redemption notes