Best Black Scholes Calculator

Black-Scholes Formula:

\[ C = S_0N(d_1) - Ke^{-rT}N(d_2) \] \[ d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}} \] \[ d_2 = d_1 - \sigma\sqrt{T} \]

Current Stock Price (S₀):

Strike Price (K):

Time to Maturity (T):

years

Risk-free Rate (r):

decimal

Volatility (σ):

decimal

Call Option Price:

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1. What is the Black-Scholes Model?

The Black-Scholes model is a mathematical model for pricing options contracts. Developed in 1973, it provides a theoretical estimate of the price of European-style options and is widely used in options trading.

2. How Does the Calculator Work?

The calculator uses the Black-Scholes formula:

\[ C = S_0N(d_1) - Ke^{-rT}N(d_2) \] \[ d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}} \] \[ d_2 = d_1 - \sigma\sqrt{T} \]

Where:

\( C \) — Call option price
\( S_0 \) — Current stock price
\( K \) — Strike price
\( T \) — Time to maturity (in years)
\( r \) — Risk-free interest rate
\( \sigma \) — Volatility of the stock
\( N \) — Standard normal cumulative distribution function

3. Importance of Black-Scholes

Details: The Black-Scholes model revolutionized options trading by providing a standardized way to price options. It's fundamental to modern financial theory and is used by traders worldwide.

4. Using the Calculator

Tips: Enter all values as decimals. Volatility should be entered as a decimal (e.g., 0.20 for 20%). Time to maturity should be in years (e.g., 0.5 for 6 months).

5. Frequently Asked Questions (FAQ)

Q1: What are the model's assumptions?
A: The model assumes log-normal distribution of stock prices, no dividends, no transaction costs, constant volatility, and risk-free rate.

Q2: Can this price American options?
A: No, this calculator prices European options only. American options require different models.

Q3: How accurate is the model?
A: Very accurate for European options, but less so for American options or when assumptions don't hold.

Q4: What is implied volatility?
A: The volatility value that makes the model price match the market price of an option.

Q5: Why does volatility matter?
A: Higher volatility increases option prices because of greater potential for price movement.