Share This Article:

Valuation of Game Option Bonds under the Generalized Ho-Lee Model: A Stochastic Game Approach

Abstract Full-Text HTML XML Download Download as PDF (Size:869KB) PP. 412-422
DOI: 10.4236/jmf.2015.54035    3,707 Downloads   4,291 Views   Citations

ABSTRACT

We propose a valuation for the bond in which an issuer and a holder are simultaneously granted the right to exercise a call and put options. As the term structure model of interest rate, we use the Generalized Ho-Lee model that is an arbitrage-free binomial lattice interest rate model. The issuer and the holder play a series of stage games in each exercisable node on the lattice whose payoff structure is dependent on the nodes. We formulate the valuation problem as a stochastic game or a Markov game. Our stochastic games possess saddle points in pure strategies for each stage game. We derive the optimality equation to solve backwardly the bond values and the exercise strategies from the maturity to the initial time. Our numerical results are useful to intuitively understand the risk to a change of interest rates for options embedded in bond.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Ochiai, N. and Ohnishi, M. (2015) Valuation of Game Option Bonds under the Generalized Ho-Lee Model: A Stochastic Game Approach. Journal of Mathematical Finance, 5, 412-422. doi: 10.4236/jmf.2015.54035.

References

[1] Ho, T.S.Y. and 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.
http://dx.doi.org/10.3905/jfi.2007.700217
[2] Ho, T.S.Y. and Lee, S.B. (1986) Term Structure Movements and Pricing Interest Rate Contingent Claims. The Journal of Finance, 41, 1011-1029.
http://dx.doi.org/10.1111/j.1540-6261.1986.tb02528.x
[3] Shapley, L.S. (1953) Stochastic Games. Proceedings of the National Academy of Sciences, 39, 1095-1100.
http://dx.doi.org/10.1073/pnas.39.10.1095
[4] Ben-Ameur, H., Breton, M., Karoui, L. and L’Ecuyer, P. (2007) A Dynamic Programming Approach for Pricing Options Embedded in Bonds. Journal of Economic Dynamics & Control, 31, 2212-2233.
http://dx.doi.org/10.1016/j.jedc.2006.06.007
[5] Sato, K. and Sawaki, K. (2012) The Valuation of Callable Financial Options with Regime Switches: A Discrete-Time Model. Kyoto University, RIMS Kokyuroku, 1818, Financial Modeling and Analysis, 33-46.
[6] Ochiai, N. and Ohnishi, M. (2012) Pricing of the Bermudan Swaption under the Generalized Ho-Lee Model. Kyoto University, RIMS Kokyuroku, 1802, Mathematical Decision Making under Uncertainty and Ambiguity, and Related Topics, 256-262.
[7] Ho, T.S.Y. (1992) Key Rate Durations Measures of Interest Rate Risks. The Journal of Fixed Income, 2, 29-44.
http://dx.doi.org/10.3905/jfi.1992.408049
[8] Ho, T.S.Y. and Lee, S.B. (2004) The Oxford Guide to Financial Modeling, Applications for Capital Markets, Corporate Finance, Risk Management, and Financial Institutions. Oxford University Press, New York.
[9] Ho, T.S.Y. and Lee, S.B. (2009) A Unified Credit and Interest Rate Arbitrage-Free Contingent Claim Model. The Journal of Fixed Income, 18, 5-17.
http://dx.doi.org/10.3905/JFI.2009.18.3.005

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.