Options Valuation โ Black-Scholes Model
Price call and put options using the Black-Scholes formula. See intrinsic value, time value, and Greeks.
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Delta = $ move per $1 stock Theta = daily time decay High IV = expensive options Most options expire worthless
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For educational purposes only โ not financial advice. Consult a qualified advisor before making decisions.
๐ก Money Facts
Delta
โ Greeks
Theta
โ Decay
Implied vol
โ Price
๐ Key Takeaways
- โข Options are leveragedโsmall stock moves can mean big gains or losses.
- โข Time decay (theta) accelerates near expiration; most options expire worthless.
- โข High implied volatility makes options more expensive.
- โข Delta shows how much the option price moves per $1 move in the stock.
๐ก Did You Know?
The Black-Scholes model, developed in 1973, revolutionized options pricing. It assumes constant volatility and no dividendsโreal markets often differ, so actual prices may vary from the model.
๐ Understanding the Greeks
Delta: Price change per $1 move in stock. Call delta 0.5 = option moves ~$0.50 per $1 stock move. Theta: Time decay per day. Vega: Sensitivity to volatility. Gamma: Rate of delta change.
๐ฏ Expert Tips
- โข Sell premium (theta) when IV is high; buy when IV is low.
- โข ATM options have the most time value and decay fastest.
- โข Understand assignment risk before holding to expiration.
- โข Paper trade before using real capital.
โ๏ธ Option Moneyness
| Type | Call | Put |
|---|---|---|
| ITM | Stock > Strike | Stock < Strike |
| ATM | Stock = Strike | Stock = Strike |
| OTM | Stock < Strike | Stock > Strike |
โ Frequently Asked Questions
What is implied volatility?
The market's expectation of future stock volatility. Higher IV = more expensive options.
Why do most options expire worthless?
Sellers collect premium; many buyers hold OTM options that never reach the strike.
When should I use Black-Scholes?
For European-style options. American options (most US equities) can be exercised early, so actual prices may differ.
๐ By the Numbers
๐ Sources
- โข CBOE โ Options education
- โข Black & Scholes (1973) โ Original paper
- โข OCC โ Options clearing
โ ๏ธ Disclaimer: This calculator uses Black-Scholes. Actual market prices may differ. Options involve significant risk. Not financial advice.
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