1. What is Delta?

Delta (Δ) measures the rate of change of the option price with respect to changes in the underlying asset's price. For call options, delta ranges from 0 to 1. For put options, delta ranges from -1 to 0.

2. How Does the Calculator Work?

The calculator uses the Black-Scholes formula to compute delta:

Where:

• \( N(d1) \) — Cumulative standard normal distribution of d1
• \( d1 = \frac{\ln(S/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}} \)
• \( S \) — Stock price
• \( K \) — Strike price
• \( T \) — Time to expiration
• \( \sigma \) — Volatility
• \( r \) — Risk-free interest rate

3. Importance of Delta Calculation

Details: Delta is crucial for understanding option price sensitivity, hedging strategies, and portfolio risk management. It indicates how much an option's price will change for a $1 change in the underlying asset.

4. Using the Calculator

Tips: Enter stock price in dollars, strike price in dollars, time to expiry in years, volatility as a percentage (e.g., 20 for 20%), and risk-free rate as a decimal (e.g., 0.05 for 5%).

5. Frequently Asked Questions (FAQ)

Q1: What does a delta of 0.5 mean?
A: For a call option, delta of 0.5 means the option price will increase by approximately $0.50 for every $1 increase in the underlying stock price.

Q2: How does delta change with moneyness?
A: Call deltas increase as options go deeper in-the-money (approaching 1) and decrease as they go out-of-the-money (approaching 0). Put deltas behave inversely.

Q3: What is delta hedging?
A: A strategy where traders offset delta risk by taking an opposite position in the underlying asset to become delta neutral.

Q4: Does delta remain constant?
A: No, delta changes with the stock price, volatility, and time to expiration (this change is measured by gamma).

Q5: What's the difference between delta and probability?
A: While delta is often used as a rough probability estimate, it's technically the hedge ratio, not exactly the probability of expiring ITM.