Question 1

Why doesn't the model work perfectly in real markets?

Accepted Answer

Black-Scholes assumptions don't hold perfectly: volatility isn't constant, stocks don't follow perfect log-normal distributions, and markets aren't perfectly efficient. The model is a starting point - traders adjust for these factors. American options with early exercise, dividends, and jumps require modified models.

Question 2

What volatility should I use?

Accepted Answer

Two main choices: (1) Historical volatility - based on past price movements, or (2) Implied volatility - extracted from current option prices. For pricing, IV is more relevant as it reflects current market expectations. For strategy, comparing historical to implied helps identify expensive/cheap options.

Question 3

Can I use Black-Scholes for American options?

Accepted Answer

Black-Scholes is designed for European options (exercise only at expiration). American options can be exercised early, making them worth slightly more. For American calls on non-dividend stocks, Black-Scholes works well. For puts or dividend-paying stocks, use binomial models or approximations.

Question 4

What's the relationship between Delta and probability?

Accepted Answer

Delta roughly approximates the probability of the option expiring in-the-money. A 0.30 delta call has approximately 30% chance of being ITM at expiration. This isn't exact but is a useful rule of thumb for quick probability assessment.

Question 5

How does time decay (Theta) work?

Accepted Answer

Options lose time value as expiration approaches. Decay accelerates near expiration - an option might lose $0.01/day with 60 days left but $0.10/day with 5 days left. At-the-money options have the highest Theta because they have the most time value to lose.

Question 6

Why do out-of-the-money puts often seem expensive?

Accepted Answer

OTM puts often have higher implied volatility (volatility skew) because investors pay a premium for downside protection against market crashes. This reflects the market's assessment of tail risk, not a model error. It's why you might see a 'volatility smile' across strikes.

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