%0 Journal Article %A Alberto Bueno-Guerrero %T Black-Scholes and Heston Models with Stochastic Interest Rates and Term Structure of Volatilities %D 2019 %R 10.3905/jod.2019.1.078 %J The Journal of Derivatives %P jod.2019.1.078 %X We consider the Black-Scholes and Heston models and generalize them to stochastic interest rates and maturity-dependent volatilities. In the Black-Scholes case, we solve the extended model and provide a concrete form for the term structure of volatilities. In the Heston case, we prove that, under some conditions, the generalized model is equivalent to a hybrid model and we find semi-closed-form solutions in the Hull and White and CIR cases.TOPICS: Options, statistical methods, fixed income and structured finance %U https://jod.pm-research.com/content/iijderiv/early/2019/07/05/jod.2019.1.078.full.pdf