Simultaneous option prices and an implied risk-free rate of interest: A test of the Black-Scholes models

Two parameters in the Black-Scholes model, the risk-free rate of interest and standard deviation of stock returns, cannot be directly observed. Nevertheless, it is possible to simultaneously solve for the two parameters by using the prices of two different options written on the same security. If the Black-Scholes model is valid, then the implied interest rate from one repair of options should equal the implied interest rate from another pair of options for a given trading day. The analysis reexamines simultaneous option price data from a previous study using the implied interest rate test, and the results support the validity of the Black-Scholes model if we consider the bid/ask spread of option prices and that options are traded over discrete intervals.