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Option Calculator

Option Parameters

Call Option

Put Option

Underlying Price:

Exercise Price:

Days Until Expiration:

days

Interest Rates:

%

Volatility:

%

Rounding:

 

Theoretical Price:

Delta:

Gamma:

Vega:

Theta:

Rho:

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What is Black–Scholes?

The Black–Scholes model is a mathematical model of a financial market containing certain derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives the price of European-style options. lt is widely used by options market participants. Many empirical tests have shown the Black-Scholes price is “fairly close” to the observed prices.

The model was first articulated by Fischer Black and Myron Scholes in their 1973 paper, “The Pricing of Options and Corporate Liabilities.” They derived a partial differential equation, now called the Black–Scholes equation, which governs the price of the option over time. The key idea behind the derivation was to perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently “eliminate risk". This hedge is called delta hedging and is the basis of more complicated hedging strategies such as those engaged in by Wall Street investment banks. The hedge implies there is only one right price for the option and is given by the Black–Scholes formula.

Definition of Options Delta – options delta is a measure of how sensitive an option price is to a change in the price of underlying security or stock. The option delta tells you how much the option price will change if the price of a stock increases or decreases by $1 in price. An options delta is the single most important options Greeks one needs to understand in options trading.

Definition of Options Gamma - Options Gamma is defined as the rate of change of options delta with change of price of the underlying security.

Definition of Options Vega – Vega is the change in the price of an option from a 1% change in implied volatility of options. Vega is the single most important Greek that is ignored by many inexperienced options traders. Vega is very important and a slight change in implied volatility results in a very significant change in price of options. Out of the money options that contain only extrinsic value, the price is fully determined by Vega and Theta.

Definition of Options Theta – Options Theta is defined as measure of rate of change of time value with the passage of time. It also called time decay. If everything was held constant, then the option theta is the loss in price of option per day.

Definition of Rho – Rho measures the estimated change in the options price with a 1% change in Interest Rate. Rho is the only Greek that may not be very important in pricing of options because a 1% in interest change may only change the price of an option by about $0.01 which is not very significant.

 
 

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