Price a European style call and put with the Black Scholes model and see how each one reacts to the stock, time, volatility and rates.
Call value
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Put value
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Delta (call / put)
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Gamma
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Theta per day (call / put)
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Vega per 1% of volatility
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Rho per 1% of rates (call / put)
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Chance the call finishes in the money
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How it works
Black Scholes values an option from five things: the stock price, the strike, the time left, the volatility and the interest rate. Volatility matters most, which is why traders talk about options in terms of implied volatility.
The greeks show how the value moves. Delta is the change for a $1 move in the stock, gamma how fast delta changes, theta the daily time decay, vega the change for one point of volatility and rho the change for one point of interest rates.
A stock at $100, a $105 strike, 30 days left, 30% implied volatility and a 4.5% rate give a call worth about $1.67 and a put worth about $6.29. The call delta is about 0.32, so it gains roughly 32 cents for each $1 the stock rises.
Black Scholes and Greeks questions
Why does my broker show a different price?
Real prices come from supply and demand. Each strike has its own implied volatility, and US stock options can be exercised early, which this model ignores. Use the implied volatility from your option chain to get close.
What interest rate should I use?
Use a short term Treasury yield that roughly matches the time to expiration. For short dated options the rate barely changes the value.
What does theta per day mean?
It is how much value the option loses in one day if nothing else changes. It grows as expiration gets closer, especially for options near the money.
For informational and educational purposes only. Not investment advice, and not a recommendation to buy or sell any security. Results are estimates from the numbers you enter.