Option pricing under joint dynamics of interest rates, dividends, and stock prices

This paper proposes a unified framework for option pricing, which integrates the stochastic dynamics of interest rates, dividends, and stock prices under the transversality condition. Using the Vasicek model for the spot rate dynamics, I compare the framework with two existing option pricing models. The main implication is that the stochastic spot rate affects options not only directly but also via an endogenously determined dividend yield and return volatility; consequently, call prices can be decreasing with respect to interest rates.

► I propose a new option pricing model with stochastic interest rates.
► The model assumes that underlying dividends are discounted by the stochastic discount rate.
► The dividend yield becomes stochastic under my assumptions.
► The call price can be decreasing with respect to interest rates.