Input:
Option type: Select Call or Put option.
Spot: Current spot price of the underlying.
Time: Time until maturity of the option expressed in years.
Volatility: Annualised volatility of the underlying (implied volatility of the option).
Carry rate: continuously compounded, per annum carry rate of the underlying.
Interest rate: Typically the money market rate or risk free rate (continuously compounded rate).
Output:
Value: Theoretical Black-Scholes model value of the option.
Delta: ∂TV / ∂Spot. The change in the option's theoretical value for a change in the underlying spot price.
Gamma = ∂Delta / ∂Spot. The change in the option’s Delta for a change in the underlying spot price by 1 unit.
Vega: ∂TV / ∂Volatility. The change in the option's theoretical value for a change in the volatility by 1% point.
Theta: ∂TV / ∂Time. The change in the option's theoretical value for a change in the time to expiry. Note that the output is expressed as a change per year. Example: If TV = 6.00, and Theta = 5,20, then the value of the option decreases by 5.2/52 to 5.9, if 1 week goes by.
Forward price: The current forward price of the underlying with same expiry as the option.
Probability: Risk-neutral probability of the option ending In-The-Money:
