Soft bond game options valuation in discrete time using a fuzzy-stochastic approach

Abstract

Bond game options are complex financial instruments that include the aspects of the risk (stochastic uncertainty) of a term structure of interest rates, option (flexibility) and interactivity (game). Forecasting uncertainty also comprises the vagueness (fuzzy uncertainty), often neglected. The fuzzy-stochastic models encompass both features. The paper objective is to develop and apply the fuzzy-stochastic soft bond game option model in discrete time. This model is based on normal fuzzy sets of the T-number type, the decomposition principle and epsilon-cuts. The forward induction arbitrage-free method for the Ho- Lee calibration of interest rates, the binomial model and the two-person zero-sum games are used. An application example of the fuzzy-stochastic soft bond game option model from the buyer perspective based on the power triangle numbers for three variants of fuzziness is developed and computed. Inclusion of vagueness allows reflecting better valuation conditions and getting a more complex valuation picture. The developed model can adequately reflect valuation conditions and considers all aspects of the complex valuation problem of the bond game options, besides risk, flexibility, interactivity and vagueness.