How Is The Premium Of An Options Contract Calculated

# How Is The Premium Of An Options Contract Calculated ## Introduction

The premium plays an important role in options contracts, as it determines the gains of the writer of the options contract. Various pricing models are used in this calculation process. However, options premium is not calculated by any stock exchange.

## What is the Options Premium?

• The term 'options premium' refers to the price at which the holder of the option gets the right to buy or sell the underlying asset at a predetermined price on a specific date.
• The holder needs to pay the premium if he wants to buy or sell the underlying asset, but it's not an obligation to do so.
• On the other hand, the writer of the option is under an obligation to sell or buy the underlying asset if the options contract is exercised by the holder. In return, the writer receives the fees in the form of an option's premium.
• The price of the options premium keeps changing with each transaction.

## What is the Method of Calculating Options Contract Premium?

The options premium is made up of two main components: intrinsic value and extrinsic value.

Options Premium = Intrinsic Value + Extrinsic Value (or Time Value)

### Intrinsic Value:

• The intrinsic value is the difference between the spot price and the strike price of the options contract. In call options, the intrinsic value is determined by deducting the contract’s strike price from the underlying asset’s spot price. Whereas the opposite is the case with put options.
• To derive an intrinsic value for put options, you need to deduct the underlying asset’s spot price from the strike price of the contract. All in-the-money calls and put options reflect positive intrinsic value.
• The intrinsic value of options is uncertain and keeps varying according to the price of the underlying asset.

### Extrinsic Value:

• The extrinsic value is the intangible portion of the option value and is comparatively difficult to calculate. Various factors affect the extrinsic value, including time. An options contract’s extrinsic value is determined by the time remaining until its expiration. An option value calculator can be used to determine how an option's extrinsic value varies as the time until expiration gets closer.
• The intrinsic value is directly proportional to time; the more time left for a contract to expire, the higher the intrinsic value. This would increase the chances of earning higher profits.
• The extrinsic value of options reduces when it is near its expiration date. Since the options contract expires on a fixed date, there is a time limit for the options price to move in favour of the buyer.
• The method to calculate the options premium is a bit tough. One of the most popular pricing methods used to calculate options premiums is the Black-Scholes pricing model.

### The Black-Scholes Option Premium Calculation Model:

• The formula for calculating options premium for a call option is :
C = S × N (d1) – X × e – rt ×N (d2)
• The formula for calculating the options premium for a put option is :
P = X × e – rt × N (-d2) – S × N (-d1)
• All the variables used in the above formula are represented by the Greeks.

### When Does the Options Premium Change?

• The options premium changes quite often because it mainly depends on the price of an underlying asset and the time left for the contract's expiration.
• The closer the option contract is to in-the-money, the more the chances of a high premium. On the other hand, the premium goes down if the options contract is out of the money.
• The time left until expiration can also affect the premium. As the contract gets nearer to its expiration date, the premium also decreases.

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