Pricing Equity Derivatives under Stochastic Rates

Abstract

The well consolidated theory for pricing equity derivatives under the Black and Scholes (1973) model is based on the assumption of deterministic interest rates. Such an assumption is harmless in most situations since the interestrates variability is usually negligible if compared to the variability observed in equity markets. When pricing a long-maturity option, however, the stochastic feature of interest rates has a stronger impact on the option price. In such cases it is therefore advisable to relax the assumption of deterministic rates.

All possible definitions of probability fall short of the actual practice. William Feller, “An Introduction to Probability Theory and Its Applications”, Vol. 1, Wiley.