For learning only. Markets use bid-ask spreads, early exercise (American), dividends, and volatility skew not fully captured here.
Inputs
Sliders (live)
Slider uses hundredths of a year (100 = 1.00 yr).
Option values
Call
—
Put
—
Greeks (per share, European)
Θ = per calendar day; ν = per 1% σ; ρ = per 1% r.
| Greek | Call | Put |
|---|
Volatility scenarios (call price)
| σ | Call | Put |
|---|
Implied volatility (from call price)
P/L at expiry (long option, premium = model price)
Strategy premiums (same inputs)
Payoff at expiry (vs ST)
Uses selected strategy; long positions; premium from BS above.
What is the Black-Scholes model?
It prices European options under geometric Brownian motion with constant volatility and a known risk-free rate. The famous formula links spot, strike, time, rate, and volatility to a fair value before considering supply and demand.
What are option Greeks?
Delta is price sensitivity to the underlying. Gamma is how Delta changes. Theta is time decay. Vega is sensitivity to volatility. Rho is sensitivity to the interest rate.
Limitations
- Constant σ and r; real markets have skew and term structure.
- No cash dividends (use adjusted spot or other models if needed).
- American options can exceed European value before expiry.
Embed
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FAQ
- How is Black-Scholes calculated?
- Compute d1 and d2 from S, K, T, r, σ, then use the standard normal CDF to get call and put values.
- What is implied volatility?
- The volatility that makes the model price equal an observed market price, found by numerical root finding.
- What are option Greeks?
- Risk sensitivities: Delta, Gamma, Theta, Vega, and Rho as commonly reported by brokers.
- Is Black-Scholes accurate?
- It is a benchmark; real trading adds adjustments for dividends, borrow, liquidity, and model risk.