Question 1

What does implied volatility mean here?

Accepted Answer

Volatility (σ) is the one input Black-Scholes needs that isn't directly observable — it's the market's expectation of how much the stock will swing before expiration, expressed as an annualized percentage. Options exchanges publish implied volatility for actively traded options; for a rough estimate you can use a stock's historical volatility instead.

Question 2

Why doesn't this match the price I see on my broker's app?

Accepted Answer

Black-Scholes assumes European-style exercise (only at expiration), constant volatility, and no transaction costs — real markets have bid-ask spreads, American-style early exercise on most listed stock options, and volatility that isn't actually constant. It's a theoretical benchmark, not a live quote.

Question 3

What is delta?

Accepted Answer

Delta estimates how much the option's price moves for a $1 move in the stock — a call delta of 0.6 means the option's price moves roughly $0.60 for every $1 the stock moves. It's also commonly read as an approximate probability the option finishes in the money.

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