TITLE:
Valuation of Game Option Bonds under the Generalized Ho-Lee Model: A Stochastic Game Approach
AUTHORS:
Natsumi Ochiai, Masamitsu Ohnishi
KEYWORDS:
Generalized Ho-Lee Model, Callable Bond, Putable Bond, Stochastic Game, Key Rate Duration
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.5 No.4,
November
25,
2015
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.