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Option pricing in interest rate derivatives

Küçüksaraç, Doruk
The valuation of interest rate derivatives and embedded options in fixed-income securities is crucial for market practitioners. Although there have been many models to price interest rate derivatives, the inconsistency across the assumptions of the models creates difficulty in aggregating interest rate exposures. Besides, the models tend to be applicable to specific cases. In this regard, adaptation of a general methodology to price all interest rate derivatives without making additional assumptions has critical importance. This study is expected to contribute to the literature by providing a general approach that can be applied to any fixed-income security with regular or irregular cash flows using the Vasicek model. The methodology involves four main steps: (i) deriving the closed-form solution for the interest rate derivatives traded in the market, (ii) estimating the Vasicek model parameters, (iii) deriving the exhibit solution for the interest rate derivatives and (iv) plugging the estimated Vasicek model parameters to price the security. This methodology provides a general solution that is applicable to all interest rate derivatives with regular or irregular cash flows. Additionally, it allows aggregation of exposures to different interest rate derivatives and allows the derivation of sensitivities of the option values to the changes in model parameters. Although the study provides empirical evidence for European type of options, it also can be applied to price American or Bermudan type of options as well. Besides, the methodology can be implemented using other interest rate models with desirable properties.