@article {Bueno-Guerrerojod.2019.1.078, author = {Alberto Bueno-Guerrero}, title = {Black-Scholes and Heston Models with Stochastic Interest Rates and Term Structure of Volatilities}, elocation-id = {jod.2019.1.078}, year = {2019}, doi = {10.3905/jod.2019.1.078}, publisher = {Institutional Investor Journals Umbrella}, abstract = {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}, issn = {1074-1240}, URL = {https://jod.pm-research.com/content/early/2019/07/05/jod.2019.1.078}, eprint = {https://jod.pm-research.com/content/early/2019/07/05/jod.2019.1.078.full.pdf}, journal = {The Journal of Derivatives} }