# Options Calculator

Supporting Black-Scholes and Binomial Tree Models
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The below calculator will calculate the fair market price, the Greeks, and the probability of closing in-the-money (ITM) for an option contract using your choice of either the Black-Scholes or Binomial Tree pricing model.

The binomial model is most appropriate to use if the buyer can exercise the option contract before expiration, i.e., American style options. In contrast, traders should use the Black-Scholes model for contracts that they can exercise only at option expiration, i.e., European style.

The current price of an option under the binomial model is equal to the present value of the probability-weighted future payoffs. See binomial option pricing model. For details about the Black-Scholes see what is the Black-Scholes-Merton model.

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## The Greeks

This Wikipedia article explains Greeks in detail. What follows below is a summary.

Delta measures the rate of change of the theoretical option value to changes in the underlying asset's price. Delta is on a scale from 1.00 to -1.00. Deep-in-the-money options eventually move dollar for dollar with the underlying stock. Note, calls, and puts have opposite delta signs.

Gamma is the measurement of the rate of change of the Delta.

Theta measures the rate of decline in the price of an option due to time passing. Theta is also known as "time decay."

Vega measures an option's sensitivity when there are changes in the volatility of the underlying asset. In finance, we express Vega as the amount of money per underlying share that the option's value will gain or lose as volatility rises or falls by one percentage point. All options (both calls and puts) will gain value with increasing volatility.

Rho measures the sensitivity of a stock option price to a change in interest rates.

Omega (Elasticity) is the percentage change in option value per percentage change in the underlying price. Omega is a measure of leverage. The higher the Omega, the greater the leverage (or the greater the risk).

Probability, while not a Greek, probability measures how likely an option contract will close ITM (in-the-money). You should note that just because a contract is ITM does not mean the option trade will be profitable. Profitability depends on the premium paid.

## 7 Comments on “Options Calculator”

Join the conversation. Tell me what you think.
• ##### Jim Nancesays:

Hi Karl,
I’m looking to automate, as fully as possible, the pricing & manipulation of american stock options such as Google, Apple, IBM, etc. (I don’t trade indexes, futures, european, etc.)
I’m having the devil of a time getting a risk-free interest rate I feel confident to use – from every source I’ve read nobody can agree between using the S&P, or T-Bill rates, or LIBOR swap curve.
Do you have a binomial option pricing calculator that will calculate the historical volatility & implied volatility, populate the risk free interest rate, chart multiple legs & show the affects of time erosion for strategy analysis and forecast price probability?