Black-Scholes calculator for European options
per % pt
- 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 risk-free rate.
- Option value: Theoretical option value calculated using the Black-Scholes 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).
- ITM-probability: Risk-neutral probability of the option ending In-The-Money.
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