PT  - JOURNAL ARTICLE
AU  - Alberto Bueno-Guerrero
TI  - Black-Scholes and Heston Models with Stochastic Interest Rates and Term Structure of Volatilities
AID  - 10.3905/jod.2019.1.078
DP  - 2019 Jul 05
TA  - The Journal of Derivatives
PG  - jod.2019.1.078
4099  - https://pm-research.com/content/early/2019/07/05/jod.2019.1.078.short
4100  - https://pm-research.com/content/early/2019/07/05/jod.2019.1.078.full
AB  - 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