When given the risk discount rate/risk free rate of return/risk free force of interest and asked to calculate the value of an option, how do you know whether to write exp(-rt) or (1+i)^-t? I.e. How do you know which of the following two equations to write: 1) Value at time zero = exp(-r) {qCu + (1-q)Cd} 2) Value at time zero = (1+i)^-1 {qCu + (1-q)Cd}
The way the interest rate is expressed in the question will direct you to which one to use. If the interest rate is compounded continuously, then it's \(e^{-rt}\), if it's the effective rate of interest you're given then use \((1+i)^{-t}\).
