Black Scholes Calculator Mystockoptions.com

Black-Scholes Formula:

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

Current Stock Price (S₀):

Strike Price (X):

Time to Maturity (T):

years

Risk-Free Rate (r):

decimal

Volatility (σ):

decimal

Option Type:

Option Price:

Unit Converter ▲

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1. What is the Black-Scholes Model?

The Black-Scholes model is a mathematical model for pricing options contracts. Developed by Fischer Black, Myron Scholes, and Robert Merton in 1973, it provides a theoretical estimate of the price of European-style options.

2. How Does the Calculator Work?

The calculator uses the Black-Scholes formula:

\[ C = S_0N(d_1) - Xe^{-rT}N(d_2) \] \[ P = Xe^{-rT}N(-d_2) - S_0N(-d_1) \]

Where:

\( C \) — Call option price
\( P \) — Put option price
\( S_0 \) — Current stock price
\( X \) — Strike price
\( T \) — Time to maturity
\( r \) — Risk-free interest rate
\( N() \) — Cumulative normal distribution function
\( d_1 \) and \( d_2 \) — Intermediate calculations

Explanation: The model calculates the theoretical value of options based on the stock price, strike price, time to expiration, volatility, and risk-free rate.

3. Importance of Option Pricing

Details: Accurate option pricing is crucial for traders, investors, and financial institutions to determine fair value, hedge positions, and assess risk.

4. Using the Calculator

Tips: Enter all required parameters in the correct units (dollars for prices, years for time, decimals for rates). The calculator supports both call and put options.

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 continuous trading.

Q2: What's the difference between European and American options?
A: European options can only be exercised at expiration, while American options can be exercised anytime before expiration.

Q3: How accurate is the Black-Scholes model?
A: While widely used, the model has limitations, especially for deep in/out-of-the-money options and long-dated options.

Q4: What is implied volatility?
A: The volatility value that makes the model price equal to the market price, often used as a measure of market expectations.

Q5: Can this model price dividend-paying stocks?
A: The basic model doesn't account for dividends, but there are modified versions that do.