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

Natsumi Ochiai, Masamitsu Ohnishi

Graduate School of Economics, Osaka University, Osaka, Japan.

DOI: 10.4236/jmf.2015.54035                

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.

Keywords

Generalized Ho-Lee Model, Callable Bond, Putable Bond, Stochastic Game, Key Rate Duration

Conflicts of Interest

The authors declare no conflicts of interest.

References

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