Abstract
The Singapore Savings Bonds (SSB) is a unique investment program offered by the Singapore government whereby retail investors can earn risk-free tax-free step-up interest closely matched to Treasury bond rates for up to 10 years and can redeem on any business day prior to maturity without any early redemption penalty. This study analyses the unique design of the SSB and provides a valuation of the Bermudan option for early redemption that is embedded in the SSB. The Black–Derman–Toy model is used to build the interest rate tree, and an iterative method is employed to avoid arbitrary specification of the pre-determined short rate volatility function. This bespoke Bermudan option can have changing strike prices over time. It also has a novel characteristic whereby the value of exercise to a buyer need not equal to the cost of being exercised to a seller. Better understanding of embedded options within government savings bonds leads to innovative designs that may encourage effective citizens’ savings.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
We use a generic par of S$100. For SSB, par of S$500 means that where we report coupon interest rate c%, the interest on a generic par is (c/100) × S$100, but the actual interest on SSB is (c/100) × S$500. For algebraic equations, we use par of 1 (representing 100) for parsimony.
Zero coupon bonds do not pay interim interest rates. The payments are accumulated and paid all at once at maturity. These types of bonds are typically sold at a deep discount and redeemed at a par of 1. They became highly popular for tax and other reasons when treasury bonds are stripped and the coupons are sold separately. The zero coupon bonds also augment the depth of the fixed income market and help to extend the maturity spectrum. These types of bonds are also available in the credit sector where corporate bonds with lower than AAA ratings are also stripped.
See https://www.mas.gov.sg/-/media/MAS/SGS/SGS-Announcements-pdf/SSB-PDF/FAQ/20190201-SSB-Technical-specifications_SRS.pdf for the Monetary Authority’s documentation.
The physical measure π is related to the Q-measure via the Girsanov theorem. Specifically, dW πt = dW Qt − λ(r,t) dt where λ(r,t) ≡ [½ σ(r,t)2Prr + μ(r,t)Pr + Bt)/P − r(t)] dt/[σ(r,t)Pr/P] and P is a zero coupon bond price at t.
References
Black, F., Derman, E., & Toy, W. (1990). A one-factor model of interest rates and its application to treasury bond options. Financial Analysts Journal, 46, 33–39.
Black, F., & Karasinski, P. (1991). Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47, 52–59.
Boyle, P., Tan, K. S., & Tian, W. (2001). Calibrating the Black–Derman–Toy model: Some theoretical results. Applied Mathematical Finance, 8, 27–48.
Brigo, D., & Mercurio, F. (2001). Interest rate models—Theory and practice with smile, inflation and credit. Berlin: Springer.
Chan, K. C., Andrew Karolyi, G., Longstaff, F. A., & Sanders, A. B. (1992). An empirical comparison of alternative models of the short-term interest rate. The Journal of Finance, 47(3), 1209–1227.
Ho, T. S. Y., & Lee, S. B. (1986). Term structure movements and pricing interest rate contingent claims. Journal of Finance, 41, 1011–1028.
Ho, T. S. Y., & Lee, S. B. (2004). A closed-from multi-factor binomial interest rate model. The Journal of Fixed Income, 14(1), 8–16.
Ho, T. S. Y., & Lee, S. B. (2007). Generalized Ho–Lee model: A multi-factor state-time dependent implied volatility function approach. The Journal of Fixed Income, 17(3), 18–37.
Iwaki, H., Kijima, M., & Yoshida, T. (1995). American put options with a finite set of exercisable time epochs. Mathematical and Computer Modelling, 22, 89–97.
Jamshidian, F. (1991). Forward induction and construction of yield curve diffusion models. Financial Strategies Group, Merryll Lynch Capital Markets Report, USA.
Joshi, M. S. (2007). A simple derivation of and improvements to Jamshidian’s and Rogers’ upper bound methods for bermudan options. Applied Mathematical Finance, 14(3), 197–205.
Schweizer, M. (2002). On Bermudan options. Advances in finance and stochastics (pp. 257–270). Berlin: Springer.
Singapore Accountant-General’s Department. (2016). Understanding Singapore Governm ent’s borrowing and its purposes: An overview. Published Report, August.
Xiao, T. (2011). An efficient lattice algorithm for the LIBOR market model. Journal of Derivatives, 19, 25–40.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The author is solely responsible for the view and the work done in this research paper. The idea was first mooted in 2015 when SS Bonds were introduced. All data are obtained from MAS publicly available website https://www.mas.gov.sg/bonds-and-bills. All errors are my sole responsibility.
Rights and permissions
About this article
Cite this article
Lim, K.G. Bermudan option in Singapore Savings Bonds. Rev Deriv Res 24, 31–54 (2021). https://doi.org/10.1007/s11147-020-09168-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11147-020-09168-y