Black-Scholes Pricer

Live market data · Greeks · Options Chain · IV Solver · Sensitivity Analysis

Stock Finder
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Live Options Chain — click any row to load into calculator
Strike Last Bid Ask Volume Open Int. Mkt IV Model Price Difference Action

Data via Yahoo Finance (15-min delayed). Model price uses your current σ and r inputs. Difference = Market Last − Model Price. Click any row or use "Add to Strategy" to send a leg to the Strategy Builder.

Parameters
Stock Price (S) S
Strike Price (K) K
Time to Expiry (years) T
Risk-Free Rate (%) r
Volatility σ (%) σ
Dividend Yield (%) q
Results
Call Price
Put Price
Moneyness ?
Moneyness describes the relationship between spot (S) and strike (K).

ITM (In The Money): Call when S > K; Put when S < K — has intrinsic value.
ATM (At The Money): S ≈ K (within 1%). All value is time value.
OTM (Out of The Money): Call when S < K; Put when S > K — pure time value.
Intrinsic / Time Value
Break-Even (Call)
Break-Even (Put)
The Greeks — Call / Put  (hover for explanation)
Delta (Δ) — Rate of change of option price per $1 move in the stock.

Call Δ ranges 0→1. Put Δ ranges −1→0. ATM options ≈ ±0.50.

Example: Δ = 0.65 means the call gains ~$0.65 when the stock rises $1.
Δ
Delta
Gamma (Γ) — Rate of change of Delta per $1 stock move (Delta's delta).

High Γ = Delta changes rapidly. Peaks at ATM near expiry. Both calls and puts share the same Γ.

Long options have positive Γ (convexity works in your favor).
Γ
Gamma
Theta (Θ) — Daily time decay of the option's value (per calendar day).

Negative for long options — you lose money every day from time decay alone. At-the-money options near expiry have the fastest decay.

Theta is the "rent" you pay to hold an option.
Θ
Theta/day
Vega (ν) — Change in option price per 1% increase in implied volatility.

High Vega = option is very sensitive to volatility changes. Peaks near ATM with longer expiry.

Example: Vega = 0.25 means the option gains $0.25 if volatility rises 1%.
ν
Vega/1%
Rho (ρ) — Change in option price per 1% change in the risk-free interest rate.

Calls have positive Rho (higher rates → higher call value). Puts have negative Rho.

Rho matters most for long-dated options; it's small for short-term contracts.
ρ
Rho/1%
Implied Volatility Solver

Enter an observed market price to back-solve for the implied volatility using Newton-Raphson iteration. All other parameters are pulled from the inputs above.

Option Type
Observed Market Price ($)

Uses Newton-Raphson convergence (max 200 iterations, tolerance 1e-8).
A solution may not exist if the market price is outside arbitrage bounds.

Implied Volatility