Theoretical value of a callIn 1973, Merton produced a model with a non-constant interest rate. He assumed that interest rates follow a special type of random process.
By taking into consideration the dynamic process of interest rate determination, and the correlation between the underlying price and the options price, this model provides an improvement over the Black-Scholes model. This model is generally used to value European options written on stocks.
Notation
Theoretical value of a call
Theoretical value of a put
Underlying price
Strike price
Time to expiration in years
Cumulative normal density
function
Volatility
Volatility of an interest rate contract
Interest rate
Correlation between the underlying and interest rate contracts
The theoretical values for European calls and puts are:
Where:
