1. What is the Black-Scholes Model?

The Black-Scholes model is a mathematical model for pricing options contracts. The d2 parameter is a key component in calculating the probability that an option will be exercised.

2. How Does the d2 Calculation Work?

The calculator uses the Black-Scholes formula:

Where:

• \( d1 \) — Intermediate calculation from Black-Scholes formula
• \( \sigma \) — Volatility of the underlying asset
• \( T \) — Time to expiration (in years)

Explanation: d2 represents the standardized distance to the strike price adjusted for volatility and time.

3. Importance of d2 in Option Pricing

Details: d2 is used in calculating the probability that a call option will expire in the money (N(d2) in the Black-Scholes formula).

4. Using the Calculator

Tips: Enter d1 (from Black-Scholes calculations), σ (volatility as decimal), and T (time to expiration in years). All values must be valid (σ > 0, T ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between d1 and d2?
A: d2 is derived from d1 by subtracting the term σ√T. Both are used in different parts of the Black-Scholes formula.

Q2: What are typical values for d2?
A: d2 can range from negative to positive values. More negative values indicate lower probability of option exercise.

Q3: How does volatility affect d2?
A: Higher volatility (σ) decreases d2, all else being equal, as it increases the uncertainty in the option's outcome.

Q4: What are limitations of the Black-Scholes model?
A: Assumes constant volatility, no dividends, continuous trading, and log-normal distribution of returns.

Q5: How is d2 used in practice?
A: d2 is used to calculate N(d2), which represents the risk-neutral probability that a call option will be exercised.