Call Put Option Calculator

Black-Scholes Option Pricing Formula:

\[ C = S \cdot N(d_1) - K \cdot e^{-rt} \cdot N(d_2) \] \[ P = K \cdot e^{-rt} \cdot N(-d_2) - S \cdot N(-d_1) \] \[ d_1 = \frac{\ln(S/K) + (r + \sigma^2/2)t}{\sigma\sqrt{t}} \] \[ d_2 = d_1 - \sigma\sqrt{t} \]

Stock Price (S):

Strike Price (K):

Interest Rate (r):

Time to Expiration (t):

years

Volatility (σ):

Option Type:

Option Price:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Black-Scholes Model?

The Black-Scholes model is a mathematical model for pricing options contracts. It calculates the theoretical price of European-style options using current stock price, strike price, time to expiration, risk-free interest rate, and volatility.

2. How Does the Calculator Work?

The calculator uses the Black-Scholes formula:

Where:

$ C $ — Call option price
$ P $ — Put option price
$ S $ — Current stock price ($)
$ K $ — Strike price ($)
$ r $ — Risk-free interest rate
$ t $ — Time to expiration (years)
$ \sigma $ — Volatility
$ N() $ — Cumulative normal distribution function

Explanation: The model assumes stock prices follow a lognormal distribution and provides a theoretical value for options pricing.

3. Importance of Option Pricing

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

4. Using the Calculator

Tips: Enter stock price and strike price in dollars, interest rate and volatility as percentages, time in years. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of the Black-Scholes model?
A: The model assumes constant volatility, no dividends, European-style options, and efficient markets, which may not reflect real-world conditions.

Q2: Can this calculator price American options?
A: No, the Black-Scholes model is specifically for European options. American options require different pricing models.

Q3: How does volatility affect option prices?
A: Higher volatility generally increases option prices for both calls and puts due to greater potential price movement.

Q4: What is the risk-free rate typically based on?
A: The risk-free rate is usually based on government bond yields, such as US Treasury bills, with similar maturity to the option.

Q5: How accurate is the Black-Scholes model in real markets?
A: While widely used, the model has known limitations and may not perfectly match market prices, especially for deep in/out-of-the-money options.