1. What is the Simple Black-Scholes Approximation?

The simple Black-Scholes approximation provides a quick estimate of a European call option's value when volatility is very low or time to maturity is very short. It's derived from the full Black-Scholes model by eliminating the volatility component.

2. How Does the Calculator Work?

The calculator uses the simplified Black-Scholes formula:

Where:

• \( S \) — Current stock price (USD)
• \( K \) — Strike price (USD)
• \( r \) — Risk-free interest rate (decimal)
• \( T \) — Time to maturity (years)
• \( e \) — Base of natural logarithm (~2.71828)

Explanation: This approximation works best when the option is deep in-the-money and volatility is negligible.

3. Importance of Option Valuation

Details: Even this simplified valuation helps traders understand the time value component of options and the impact of interest rates on option pricing.

4. Using the Calculator

Tips: Enter all values as positive numbers. Stock price and strike price in USD, risk-free rate as decimal (e.g., 0.05 for 5%), and time in years.

5. Frequently Asked Questions (FAQ)

Q1: When is this approximation valid?
A: When volatility is very low or time to expiration is very short (near expiration).

Q2: What are the limitations of this approximation?
A: It ignores volatility completely and doesn't account for dividends. Not suitable for out-of-the-money options.

Q3: How does interest rate affect the option value?
A: Higher rates increase the present value discounting of the strike price, increasing the option value.

Q4: Can this be used for put options?
A: No, this specific approximation is only for call options. Put options require different valuation.

Q5: What's the difference between this and full Black-Scholes?
A: The full model includes volatility (σ) and uses the standard normal CDF, making it more accurate but more complex.