Options Premium

An option premium is the price you pay to buy an option. For the seller, it is the amount received for taking on the obligation under the contract. 

• An options premium is the amount a buyer pays to purchase an options contract.
• The option seller, also called the writer, receives the premium for accepting the contract obligation.
• An option’s premium has two parts: intrinsic value and time value.
• Intrinsic value is the immediate value available if an in-the-money option is exercised.
• Time value is the portion of the premium above the option’s intrinsic value.
• Higher implied volatility and more time until expiry generally increase the premium.
• The underlying price, strike price, interest rates and expected dividends can also affect the premium.
• The option premium changes with market conditions, while the strike price normally remains fixed.
• An option premium calculator can estimate the theoretical price, but the actual premium depends on market demand and supply.
   

An option premium is the price an option buyer pays to the option seller, also known as the writer. In return, the buyer receives the right to buy or sell an underlying asset at a fixed strike price within the contract period.
For example, suppose you buy a call option and pay a premium of ₹20 per unit. You pay ₹20 for the right to buy the underlying asset at the stated strike price.
The seller receives the premium but must meet the contract obligation if the buyer exercises the option according to its terms.
An options premium has two main parts:
Option premium = Intrinsic value + Time value
Implied volatility is not a separate amount added to this formula. Instead, it is one of the factors that affects time value.
 

The main factors that affect an option's premium are explained below.

1. Intrinsic value and time value

Intrinsic value is the immediate value of exercising an option. It depends on the difference between the current price of the underlying asset and the option’s strike price.
Time value is the portion of the premium above intrinsic value. It represents the possibility that the option may become more valuable before expiry.
For example, if an option has an intrinsic value of ₹10 and trades at a premium of ₹15, its time value is ₹5.

2. Implied volatility

Implied volatility shows how much the market expects the underlying asset’s price to move. It does not show whether the price will move up or down.
Higher implied volatility generally increases both call and put premiums. This is because larger expected price movements can increase the possibility of the option becoming profitable.
For example, an option on a stock with frequent and sharp price movements may have a higher premium than an option on a relatively stable stock.

3. In-the-money status

An option’s moneyness shows the relationship between its strike price and the underlying asset’s current price.
A call option is in the money when the underlying price is above the strike price. A put option is in the money when the underlying price is below the strike price.
In-the-money options have intrinsic value and generally carry higher premiums than similar out-of-the-money options. However, time to expiry and implied volatility also affect the final premium.

4. Time until expiration

Options with more time remaining until expiry generally have higher time value. More time gives the underlying asset a greater opportunity to move in a favourable direction.
Time value usually decreases as the option approaches expiry. This reduction is known as time decay.
For example, an option expiring after three months will generally have a higher premium than a similar option expiring after one week, assuming other factors remain unchanged.

5. Interest rates

Interest rates can influence options premiums because they affect the present value of the option’s strike price.
When other factors remain unchanged, higher interest rates generally increase call option premiums and reduce put option premiums. Lower interest rates generally have the opposite effect.
However, movements in the underlying price, time and volatility may have a larger effect on the premium.

6. Dividends

Expected dividends may affect option prices because a stock’s market price can fall when it trades without the right to receive the declared dividend.
When other factors remain unchanged, higher expected dividends generally reduce call premiums and increase put premiums. The effect depends on the dividend amount, payment timing and option expiry date.
 

An options premium consists of intrinsic value and time value.
Option premium = Intrinsic value + Time value

Intrinsic value

Intrinsic value is the amount by which an option is in the money. It cannot be negative.

For a call option:
Call intrinsic value = Current underlying price − Strike price
If the result is negative, the intrinsic value is treated as zero.
For example:
Strike price: ₹50
Current stock price: ₹60
Intrinsic value: ₹60 − ₹50 = ₹10

For a put option:
Put intrinsic value = Strike price − Current underlying price
If the result is negative, the intrinsic value is also treated as zero.

Time value

Time value is the amount by which the option premium exceeds its intrinsic value.
Time value = Option premium − Intrinsic value
For example:
Option premium: ₹17
Intrinsic value: ₹10
Time value: ₹17 − ₹10 = ₹7
The ₹7 reflects factors such as the time remaining until expiry, implied volatility, interest rates and expected dividends.

Volatility’s role in the premium

Volatility is not normally shown as a separate third component of the premium. Instead, implied volatility affects the option’s time value.
When traders expect larger price movements, they may be willing to pay a higher premium. This can increase the time value included in the option’s market price.
 

Consider a call option with the following details:

• Strike price: ₹50
• Current stock price: ₹60

• Market premium: ₹17

  
  

First, calculate its intrinsic value:

Intrinsic value = ₹60 − ₹50 = ₹10

Next, calculate its time value:

Time value = ₹17 − ₹10 = ₹7

Therefore:

Option premium = ₹10 intrinsic value + ₹7 time value = ₹17

The premium may change when the underlying price, volatility, time to expiry, interest rates or expected dividends change.

An options calculator can provide an estimated theoretical value. However, the actual traded premium is determined by buyers and sellers in the market.

The Black-Scholes model is a mathematical method used to estimate the theoretical value of certain options. Its basic form is commonly applied to European-style options, which can be exercised only on their expiry date.

1. Key factors

The model considers:

• Current price of the underlying asset
• Strike price
• Time remaining until expiry
• Risk-free interest rate

• Expected volatility

  
  

An adjusted version may also consider expected dividends.

2. Formula for a call option

The basic Black-Scholes formula for a European call option is:

C = S × N(d₁) − X × e⁻ʳᵗ × N(d₂)

3. Formula for a put option

The basic formula for a European put option is:

P = X × e⁻ʳᵗ × N(−d₂) − S × N(−d₁)

Here:

• C: Theoretical call option price
• P: Theoretical put option price
• S: Current underlying asset price
• X: Strike price
• t: Time remaining until expiry
• r: Risk-free interest rate
• N(d₁) and N(d₂): Values from the cumulative standard normal distribution

The model provides an estimate rather than a guaranteed market price. The actual premium may differ because of liquidity, demand, supply and changing market expectations.

4. Option Greeks

Option Greeks measure how sensitive an option’s premium is to different factors. They are not part of intrinsic value.

• Delta: Measures sensitivity to changes in the underlying price

  
  

• Gamma: Measures how quickly delta changes

  
  

• Theta: Measures the effect of time decay

  
  

• Vega: Measures sensitivity to changes in implied volatility

  
  
• Rho: Measures sensitivity to changes in interest rates

For example, an option with high vega may experience a noticeable premium change when implied volatility changes.

For example, suppose a call option has a strike price of ₹100 and a premium of ₹8. The strike price remains ₹100, but the premium may rise or fall during the trading session.

An options premium is the amount paid by an option buyer and received by the seller. It consists of intrinsic value and time value.
The premium changes with the underlying price, implied volatility, time to expiry, interest rates and expected dividends. In contrast, the strike price remains fixed and determines the price at which the underlying asset may be bought or sold.
Understanding both values can help you assess the cost and risk of an options contract. Options carry significant risk, and a buyer may lose the entire premium if the option expires without value.