Black-Scholes Option Pricing & Greeks Calculator
Compute theoretical European Call and Put option premiums along with essential option Greeks using the Nobel Prize-winning Black-Scholes-Merton mathematical model.
Sensitivity Analysis
Evaluate how variations in key operational drivers impact Call Option Premium.
| Sensitivity Case | Assumption Shift | Driver Value | Call Option Premium | Impact vs Base |
|---|
Formula & Methodology
Call = S*N(d1) - K*e^(-r*T)*N(d2); Put = K*e^(-r*T)*N(-d2) - S*N(-d1)SCurrent market spot price of asset.
KOption exercise strike price.
TDays to expiry ÷ 365.
rAnnualized sovereign risk-free treasury rate.
σExpected annualized standard deviation of asset returns.
Practical Worked Example
Price a 30-day Call and Put option on a stock trading at Rs 2,500 with a strike of Rs 2,550, 22% implied volatility, and 6.8% risk-free rate.
Interpretation & Industry Benchmarks
Black-Scholes is the industry standard benchmark for European option pricing and hedging.
Maximum time value premium.
Behaves almost identical to underlying stock.
Industry Nuance: Black-Scholes assumes constant volatility and no early exercise (European style); American options with early exercise are priced using Binomial trees.
Analytical Limitations
- Does not account for volatility smile/skew or sudden earnings jump risks.
Frequently Asked Questions
What is Delta in options?
Delta measures the expected change in option price per $1 move in the underlying stock price.