Stock Price:


Strike:


Volatility (%):


Risk-free Interest Rate (%):


Dividend Yield (%):


Days until Expiration:





Price ⓘ Delta ⓘ Gamma ⓘ Theta ⓘ Vega ⓘ Rho ⓘ
Call - - - - - -
Put - - - - - -





Theortical Option Price

The theoretical option price is the price that an option should have according to the Black Scholes pricing model.

There can be (and oftentimes is) a great difference between the theoretical price and the true price for which an option is traded in the market.

This is because the market is driven by perceptions of its participants. Therefore there is a constant reevaluation of the underlying stock and of its options. This reevaluation is driven mostly by news about the stock, the respective industry, and the market and the world in general.

For each current option price in the market there is a so called implied volatility. This is the volatility that if you enter it into the Black Scholes formula while leaving all other variables unchanged will yield the price payed in the market. It is the volatility the market assumes at a given point in time.

Option Delta

The delta of an option is the amount by how much the price of the option would change if the price of the underlying stock changes by one dollar and all other parameters stay unchanged.

If the price of the stock decreases by one dollar and all else stays equal the price of the option will decrease by the delta.

Example:

Let's say we have a call option on IBM stock with a price of $1.5:

Stock Price: $150
Strike: $152
Delta: 0.5

⚡IBM rises to $151
👉The new price of the option is $2

Option Gamma

The gamma of an option is the amount by how much the delta changes if the price of the underlying stock changes by one dollar (and all else stays equal).

Example:

Let's say we have a call option on IBM stock with a price of $2:

Stock Price: $150
Delta: 0.5
Gamma: 0.018

⚡IBM rises to $151
👉The new delta of the option is 0.518

Option Theta

The theta of an option is the change in the value of an option if it gets one day closer to expiration.

Example:

Let's say we have a call option on IBM stock with 30 days till expiration and a price of $2.5:

Stock Price: $150
Strike: $152
Theta: -0.05

⚡One day passes
👉The new price of the option is $2.45

Option Vega

The vega of an option is the change in option price for every one percent increase in volatility of the underlying stock.

Example:

Let's say we have a call option on IBM stock with a price of $2.5:

Stock Price: $150
Strike: $152
Vega: 0.17

⚡The volatility of IBM stock increases by 1%
👉The new price of the option is $2.67

Option Rho

The rho of an option is the cange in option price for one percent change in the risk-free interest rate.

Example:

Let's say we have a call option on IBM stock with a price of $2.5:

Stock Price: $150
Strike: $152
Rho: 0.1

⚡The risk-free interest rate increases by 1%
👉The new price of the option is $2.6