Call Option Calculator

Black-Scholes Formula:

\[ Call\_value = S \times N(d_1) - K \times e^{-rt} \times N(d_2) \]

Stock Price (S):

Strike Price (K):

Risk-Free Rate (r):

Time to Expiration (t):

years

Call Option Price:

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1. What is the Black-Scholes Formula?

The Black-Scholes formula is a mathematical model for pricing European-style options. It calculates the theoretical price of call and put options based on five input parameters: stock price, strike price, time to expiration, risk-free rate, and volatility.

2. How Does the Calculator Work?

The calculator uses the Black-Scholes formula for call options:

\[ Call\_value = S \times N(d_1) - K \times e^{-rt} \times N(d_2) \]

Where:

$ S $ — Current stock price ($)
$ K $ — Strike price ($)
$ r $ — Risk-free interest rate (%)
$ t $ — Time to expiration (years)
$ N $ — Cumulative normal distribution function
$ d_1 = \frac{\ln(S/K) + (r + \sigma^2/2)t}{\sigma\sqrt{t}} $
$ d_2 = d_1 - \sigma\sqrt{t} $

Explanation: The formula calculates the expected value of the option at expiration, discounted to present value.

3. Importance of Option Pricing

Details: Accurate option pricing is crucial for traders, investors, and financial institutions to make informed decisions about buying, selling, or hedging options positions.

4. Using the Calculator

Tips: Enter stock price and strike price in dollars, risk-free rate as a percentage, and time to expiration in years. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What assumptions does the Black-Scholes model make?
A: The model assumes constant volatility, no dividends, European exercise style, efficient markets, and log-normal distribution of stock prices.

Q2: Can this calculator price put options?
A: This calculator is specifically for call options. Put options require a different formula using put-call parity.

Q3: How accurate is the Black-Scholes model?
A: While widely used, the model has limitations and may not perfectly match market prices, especially for deep in/out-of-the-money options or during volatile markets.

Q4: What is implied volatility?
A: Implied volatility is the volatility parameter that makes the model price equal to the market price of an option.

Q5: Can I use this for American options?
A: No, the Black-Scholes model is specifically for European options. American options require more complex pricing models.