1. What is the Black-Scholes Formula?

The Black-Scholes formula is a mathematical model for pricing options contracts. The d1 component is a key part of this model that helps determine the probability that the option will be exercised.

2. How Does the Calculator Work?

The calculator uses the Black-Scholes d1 formula:

Where:

• \( S \) — Current stock price (USD)
• \( K \) — Strike price (USD)
• \( r \) — Risk-free interest rate (decimal)
• \( \sigma \) — Volatility of the stock (decimal)
• \( T \) — Time to maturity (years)

Explanation: The formula calculates how many standard deviations the stock price is from the strike price, adjusted for time and volatility.

3. Importance of d1 Calculation

Details: d1 is crucial in option pricing as it's used to calculate the probability that the option will finish in the money (N(d1) in the full Black-Scholes formula).

4. Using the Calculator

Tips: Enter all values as positive numbers. Volatility is typically between 0.2 and 0.6 (20%-60%). Time to maturity is in years (0.5 for 6 months).

5. Frequently Asked Questions (FAQ)

Q1: What does d1 represent?
A: d1 measures the expected return of the option relative to its volatility and time to expiration.

Q2: How is d1 used in option pricing?
A: In the full Black-Scholes formula, N(d1) represents the probability that the call option will be exercised.

Q3: What are typical values for volatility (σ)?
A: Most stocks have σ between 0.2 and 0.6 (20%-60%). High-growth stocks may have higher volatility.

Q4: What risk-free rate should I use?
A: Typically the yield on 3-month Treasury bills is used as the risk-free rate.

Q5: Are there limitations to the Black-Scholes model?
A: Yes, it assumes constant volatility and interest rates, no dividends, and log-normal distribution of stock prices.