How to Calculate Option Premium with Formula & Example

What is Option Premium?

Imagine you’re interested in buying a house. You find a property you like and negotiate a price of ₹50 lakhs with the seller. However, you’re not ready to buy it immediately. So, you ask the seller if you can lock in that price for the next six months by paying a small fee. This small fee is similar to an option premium.

Strike Price

The ₹50 lakhs you’ve agreed upon is the strike price. It’s the price at which you have the option to buy the house within the next six months.

• If the house value increases to ₹60 lakhs within those six months, you can exercise your option to buy the house at the agreed-upon price of ₹50 lakhs, making a profit.
• If the house value drops to ₹45 lakhs, you might choose not to exercise the option, as you can buy the house cheaper on the open market.

Expiry Date

That six-month period is the expiry date of your option. After six months, your option to buy the house at ₹50 lakhs expires. If you still want the house, you’ll have to negotiate a new price with the seller based on the current market value.

Components of an Option Premium

In options trading, the fee you pay for the option to buy the house (the option premium) consists of two parts:

1. Intrinsic Value:

The house’s current market value is similar to the intrinsic value of an option. If the house is worth more than the price you agreed to pay, the option has intrinsic value.

In fancy terms, the intrinsic value is the inherent worth of the option if it were exercised immediately. It reflects the difference between the current price of the underlying asset and the strike price of the option.

2. Extrinsic Value

The potential for the house’s value to increase is similar to the extrinsic value of the option. If you believe the house’s value will increase significantly in the future, you might be willing to pay a higher premium for the option.

In fancy terms, the extrinsic value, often referred to as time value, represents the additional amount that traders are willing to pay for the potential of the option to gain value before expiration.

How Option Premium is Affected by Extrinsic Value

1. Time until expiration

• The longer you can wait: If you have more time to decide whether to buy the house, the option is more valuable. There’s a better chance the house price will go up, making your option worth more. Hence you may see a higher option premium.
• Tick Tock: As the deadline to buy the house gets closer, the option becomes less valuable. This is because their is less time for the house price to increase. Hence you may see a lower option premium.This is also known as time decay.

2. Implied Volatility: How much could the house price jump?

• Increase/decrease in house prices: If you think the house price could go up or down a lot, the option to buy it at a fixed price becomes more valuable. There’s a high chance of making a profit.
• Steady house prices: If you think the house price will stay about the same, the option is less valuable. There’s less chance of making a profit.

In a nutshell:

• More time to decide = higher option premium.
• More uncertainty about the house price = higher option premium.

Just like buying a house, these two things also affect the price of options in the stock market. The more time you have and the more uncertain the stock price is, the more expensive the option will be.

Option Premium = Intrinsic Value + Extrinsic Value

Calculation of option premium

The method to calculate the option premium is a bit complex. One of the most popular pricing methods used to calculate option premiums is the Black-Scholes pricing model.

The Black-Scholes model is a mathematical formula used to calculate the theoretical price of options. It is one of the most widely used models in finance.

Key Inputs:

• Underlying asset price (S): The current market price of the underlying asset.
• Strike price (K): The price at which the option can be exercised.
• Time to expiration (T): The remaining time until the option expires.
• Risk-free interest rate (r): The interest rate on a risk-free investment.
• Volatility (v): The expected standard deviation of the underlying asset’s returns.

The Black-Scholes formula is complex, but it essentially combines these factors to calculate the theoretical value of the option.

C = S * N(d1) – K * e^(-rT) * N(d2)

N(d1) and N(d2): Cumulative normal distribution functions of d1 and d2

d1 and d2: Complex functions involving S, K, r, T, and volatility

d1= [In(S/K)+(r+v2/2)T*]/(v**√T) d2 = d1 – v*√T

Why are option premiums important?

The option premium is the cost of buying an option, and it’s important for several reasons:

• Profit and Loss: The premium shows how much you can lose or gain. A lower premium means less risk but also smaller potential profits. A higher premium means more risk but potentially bigger gains.
• Breakeven point: It helps you figure out the price at which you start making money. For call options, add the premium to the strike price; for put options, subtract it from the strike price.
• Volatility: The premium reflects how much the market thinks the price of the asset will move. Higher premiums usually mean more expected price swings.

Bottom Line

In summary, the option premium is a critical aspect of options trading, comprising intrinsic and extrinsic values, influenced by various market factors. Understanding these components helps investors make informed decisions in their trading strategies.