Abstract
A game swaption, newly proposed in this paper, is a game version of usual interest-rate swaptions. It provides the both parties, fixed-rate payer and variable rate payer, with the right that they can choose an exercise time to enter a swap from a set of prespecified multiple exercise opportunities. We evaluate two types of game swaptions: game spot-start swaption and game forward-start swaption, under the generalized Ho-Lee model. The generalized Ho-Lee model is an arbitrage-free binomial-lattice interest-rate model. Using the generalized Ho-Lee model as a term structure model of interest rates, we propose an evaluation method of the arbitrage-free price for the game swaptions via a stochastic game formulation, and illustrate its effectiveness by some numerical results.
Highlights
A game swaption, newly proposed in this paper, is a kind of exotic interest-rate derivatives whose payoff depends on interest rates or bond prices
We evaluate two types of game swaptions: game spot-start swaption and game forward-start swaption, under the generalized Ho-Lee model
Using the generalized Ho-Lee model as a term structure model of interest rates, we propose an evaluation method of the arbitrage-free price for the game swaptions via a stochastic game formulation, and illustrate its effectiveness by some numerical results
Summary
A game swaption, newly proposed in this paper, is a kind of exotic interest-rate derivatives whose payoff depends on interest rates or bond prices. We propose an evaluation method of exotic interest-rate derivatives via a tree method based on the generalized Ho-Lee model [1], which is a discrete-time and arbitrage-free term-structure model of interest rates. Ben et al [4] discussed the pricing problem of an option-embedded bond with game characteristics, where they approximately calculated the value of that derivative based on a continuous-time interest-rate model by applying a dynamic programming approach. The theory on which we base in this paper is in the spirit of them [5] for valuating exotic interest-rate derivatives via a discrete-time and arbitrage-free term-structure model of interest rates.
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