When an option payoff depends only on the spot rate at the maturity of the contract (e.g., European vanilla options) the price of the option can be calculated using the terminal spot distribution and the option payoff.
First, future spot levels must be generated using a log-normal distribution. The inputs to the function are:
Within log-normal world:
For a given return of X standard deviations:
This framework can be set up in an Excel sheet:
Under a normal distribution, a range from –5 to +5 standard deviations covers almost all possible theoretical returns. Starting with 0.1 steps, go from –5 to +5 standard deviations and calculate the return level and corresponding spot level for each standard deviation value: ...