We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main processes. By an appropriate change of measure the dimension of the corresponding pricing PDE can be gre...

In this paper, we study pricing of American put options on a nondividend-paying stock in the Black and Scholes market with stochastic interest rate finite-time maturity. We prove that option value is C1 function initial time, rate, price. By means Itô calculus, rigorously derive value's early exercise premium formula associated hedging portfolio. existence an optimal boundary splitting state sp...