BlackScholes calculator for European options
Inputs
Outputs
Option value  
Delta  
Gamma  
Vega 
per % pt

Theta 
per year

Forward price  
ITMprobability 
Descriptions
 Carry rate: Continuously compounded p.a. carry rate of the underlying. Example: Spot = 100, Forward =102, Time = 9 month, then the carry rate is ln(102/100)*4/3 = 2.64%.
 Interest rate: Continuously compounded p.a. interest rate. Typically the money market rate or riskfree rate.
 Option value: Theoretical option value calculated using the BlackScholes model.
 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. Example: If Spot = 85, Delta = 50% and Gamma = 3% then the Delta of the option increases to 53% if Spot moves from 85 to 86.
 Vega: ∂TV / ∂Volatility. The change in the option's theoretical value for a change in the volatility by 1% point. Example: If Volatility = 22%, Vega = 0.40, TV = 6.00, then the value of the option increases by 0.4 to 6.40 if the volatility increases from 22% to 23%.
 Theta: ∂TV / ∂Time. The change in the option's theoretical value for a change in the time to expiry. The output is expressed as a change per year. Example: If TV = 6.00, and Theta = 5.2, then the value of the option decreases by 5.2/52 to 5.9, if 1 week goes by.
 Forward: The forward price of the underlying (same expiry as the option).
 ITMprobability: Riskneutral probability of the option ending InTheMoney.
Who we are
NoscoPartners is a Swiss based company with international finance experience, servicing banks, asset managers and institutional investors. We combine financial expertise with business experience and applied training skills to deliver practical financial market education programs.
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