Option premium

An option premium refers to the price paid by the buyer of an option contract to the seller (or writer) for acquiring the right, but not the obligation, to buy or sell an underlying asset at a specified price within a predetermined period. The premium represents the market value of the option and compensates the writer for the risks associated with granting this right. It is a crucial element of options trading in financial markets, influencing investment decisions and hedging strategies across equities, commodities, currencies, and derivatives markets.

Meaning and Components

The option premium is the cost incurred by the buyer to secure the right conferred by the option contract. The premium amount depends on several measurable and market-driven components:

• Intrinsic Value: The difference between the current market price of the underlying asset and the strike price of the option. It reflects the immediate exercisable value of the option.
• Time Value: The portion of the premium that reflects the potential for the option to gain intrinsic value before expiration. It depends on the time remaining until expiry, volatility, and interest rates.
• Volatility: Greater volatility in the underlying asset increases the likelihood of profitable price movements, thereby raising the premium.
• Interest Rates and Dividends: Higher interest rates tend to increase call option premiums and decrease put option premiums, while expected dividends can affect option values inversely for calls and directly for puts.

The formula representing the relationship between premium and its components can be expressed as:
Option Premium = Intrinsic Value + Time Value

Determinants of Option Premium

A wide range of factors influence the valuation of an option premium in real-world financial markets:

1. Price of the Underlying Asset: The premium generally moves in the same direction as the price of the underlying security. For call options, an increase in the asset price raises the premium, while for put options, it lowers the premium.
2. Strike Price: The difference between the strike price and the market price of the underlying asset determines whether an option is in the money (ITM), at the money (ATM), or out of the money (OTM). Options that are ITM command higher premiums.
3. Time to Expiry: Longer time periods increase the time value of an option because there is a greater chance for favourable price movements before expiry. As expiry approaches, the time value declines — a phenomenon known as time decay.
4. Market Volatility: Volatility plays a central role in determining option prices. Higher volatility increases the probability of an option finishing in the money, which raises the premium.
5. Interest Rates: Rising interest rates generally lead to higher call option premiums and lower put option premiums, as holding the underlying asset becomes more expensive compared to holding the option.
6. Dividends and Expected Payouts: Dividends reduce call option premiums because they lower the price of the underlying stock on the ex-dividend date, whereas put premiums often increase correspondingly.

Calculation and Valuation Models

In financial markets, option premiums are calculated using sophisticated mathematical models. The most widely recognised is the Black-Scholes Model, developed by Fischer Black, Myron Scholes, and Robert Merton in the early 1970s. The model estimates theoretical prices for European-style options based on factors such as the underlying asset price, strike price, time to expiration, risk-free interest rate, and volatility.
Other notable models include:

• Binomial Option Pricing Model (BOPM): Useful for valuing American options that can be exercised at any time before expiry.
• Monte Carlo Simulation: Employs random sampling techniques to simulate possible price paths for the underlying asset.
• Finite Difference Models: Used for complex derivative structures and exotic options.

Types of Option Premiums

Option premiums can be categorised according to their intrinsic and time value components:

• Pure Intrinsic Premium: Applies when an option is deep in the money and most of its value is derived from its intrinsic worth.
• Pure Time Premium: Seen when an option is out of the money and has no intrinsic value, relying entirely on its time value.

Behaviour and Decay of Premium

The time decay of an option premium, often represented by the Greek term Theta (Θ), illustrates the rate at which an option loses value as it approaches expiration. This decay is non-linear; it accelerates sharply in the final weeks before expiry. Option sellers, therefore, benefit from the passage of time as the premium declines, whereas buyers face erosion in value.
The volatility sensitivity, represented by Vega, measures how much the option premium changes for each percentage point change in volatility. The combined effects of the Greeks — Delta, Gamma, Theta, Vega, and Rho — help traders manage the risk profile of their option positions.

Practical Implications in Trading and Hedging

Option premiums are central to several market strategies:

• Hedging: Investors use options to protect portfolios against adverse price movements. Paying a premium for a put option acts as an insurance policy against falling stock prices.
• Speculation: Traders buy or sell options to profit from anticipated changes in price or volatility.
• Income Generation: Writing options allows investors to earn premium income, especially in low-volatility markets. Covered call writing is a common income strategy.

For example, if a trader purchases a call option on Company X with a strike price of £100 and a premium of £5, and the stock rises to £110, the trader can exercise the option to make a profit, offset by the cost of the premium paid.