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Pricing interest-rate-derivative securities. (English) Zbl 1386.91152
Summary: This article shows that the one-state-variable interest-rate models of O. Vasicek [J. Financ. Econ. 5, No. 2, 177–188 (1977; Zbl 1372.91113)] and J. C. Cox et al. [Econometrica 53, 385–407 (1985; Zbl 1274.91447)] can be extended so that they are consistent with both the current term structure of interest rates and either the current volatilities of all spot interest rates or the current volatilities of all forward interest rates. The extended Vasicek model is shown to be very tractable analytically. The article compares option prices obtained using the extended Vasicek model with those obtained using a number of other models.

91G30 Interest rates, asset pricing, etc. (stochastic models)
91G20 Derivative securities (option pricing, hedging, etc.)
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