In the derivatives market, options are flexible financial contracts. An option allows the holder to buy or sell the underlying asset without any obligation to do so. The option premium is the price at which the option is bought or sold. The option holder pays the option premium for buying or selling the instrument. However, there is no obligation on the buyer to exercise the right. The seller, on the other side of the contract, receives the premium on selling the underlying asset if the buyer chooses to exercise the right. The option premium determines both buyer and seller profits. Any investor who wants to profit from a derivative market must learn about premiums in options trading. Let's explore the calculation of this crucial component in options contracts.
The option premium is the price of the financial contract of the underlying asset for the strike price. The buyer pays the premium to purchase the options contract. The seller’s profit is determined by the premium at which the contract is sold. Due to the dynamic pricing in the derivatives market, the option premium changes with every transaction. Determining the right option premium for the call and put order is crucial to generating profit with an options contract. The generic option premium formula is,
Option Premium = Intrinsic value + Time value + Volatility value
Apart from the supply and demand of the options contract, numerous factors affect the price of an option. Crucial factors that influence option premium calculation are:
The intrinsic value is the difference between the option's strike price and the underlying asset's current price. For calculations, the difference between the spot price and the strike price is the intrinsic value. The intrinsic value can be positive or zero. Generally, all in-the-money call and put options have positive intrinsic value.
The excess of the option's price over its intrinsic value is the time value. It is also called extrinsic value. It is the intangible portion of the option value. Depending on the expiration date of the options contract, time is available for the option's price to move in favour of the buyer. Option holders have more chances of making a profit with extended time till expiry as the price can align favourably.
Depending on the market conditions, there may be significant price movements. This volatility of the underlying assets also influences the option premium. The higher volatility results in a premium increase, thus making the option more valuable.
The relationship of the option to the underlying asset also influences the premium. In-the-money options generally have higher premiums due to the higher demand in the market. Out-of-the-money options have lower premiums.
The duration until the expiration date of the option also affects the premium. Options with more extended expiration periods carry higher premiums. This is because of the availability of time for the options to move favourably.
The prevailing interest rates also impact the option premium due to the opportunity cost of the tying up of capital. Higher rates result in an increase in the put option premium and a decrease in the call option premium. Similarly, lower interest rates have the opposite effect.
Computing the option premium is not simple. The Black Scholes pricing model is the most common mathematical model for calculating option premiums. The critical data points used in this type of calculation are:
According to Black Scholes formula,
Options price for a call, C = SN(d1) – Xe-rtN(d2) Options price for a put, P = Xe-rtN(-d2) – SN(-d1)\ S is the market price of the underlying asset X is the strike price of the underlying asset r is the expiration rate t is the interest rate N(d1) and N(d2) are the standard distributive functions (cumulative) |
For option pricing equations, the above-mentioned components are expressed in Greek. They are necessary to calculate the intangible components used for extrinsic value determination. These measure the sensitivity of the option price relative to the change in the underlying security's price, time to expiration, rate of interest, and volatility. The Greek letters used are:
The following table shows what these Greek letters represent:
Greek |
Meaning |
Delta |
Measures rate of change of option premium for a 1-point change in the price of the underlying security |
Gamma |
Measures the rate of change of Delta for a 1-point change in the price of the underlying security |
Vega |
Measures the change in option premium for a 1% change in implied volatility |
Theta |
Measures decay in time value for a 1-day change in time till expiry |
Rho |
Measures change in option premium for a 1% change in interest rate |
The Black Scholes model enables investors to calculate the fair market value of options considering multiple volatile factors. The systematic approach revolutionised option pricing to estimate the value of financial derivatives. It is an important tool in financial markets.
The option premium is a dynamic pricing influenced by multiple volatile factors. It is a representation of the cost of entering an option contract. Knowing this, investors can understand the potential profit or loss in the derivatives market. You can compare the premiums for different options to make informed decisions.