Option pricing can be split into two components: intrinsic value and time value. The intrinsic value is the value that the option possesses if it were to be exercised today. This value is calculated as the difference between the exercise price and the spot price. The intrinsic value of the option is at least worth as much as this difference since riskless profits will always be arbitraged away by the market. Put simply, the intrinsic value represents the minimum value of an option.
The time value of the option accounts for the changes in value of the option between the time of the contract and the time at expiry. There are four main secondary factors that affect the time value of the option.
Time remaining until expiration
With a longer length of time, the time value of the option becomes greater. This is because there is more time for the stock price to translating into an increased probability that the option ends up to end up in the money
Volatility of the underlying asset
An increase in volatility increases the chance that the prices will wildly swing in the favour of the option holder. Since options protect the investor from the downside, the investor stands to benefit from sharp swings to the upside
Risk free interest rate
Interest rates affects call and put options differently, with rising interesting rates increasing the value of the former and decreasing the value of the latter. To understand the difference, a comparative analysis has to be performed between stock purchases and the corresponding option purchase. For call options, an investor can either purchase the stock directly or purchase a call option to own a stock in the future. Purchasing a call option requires less initial outlay and the difference that is invested elsewhere will benefit from increasing interest rates. On the other hand, buying a put option is mirrored by short selling a stock. Although both strategies benefit from price declines, the put option suffers from an interest disadvantage as it requires an initial outflow to purchase the outflow while the short selling strategy only requires the outflow to be made in the future to purchase the stock. The
Dividend rate of underlying asset
An increase in dividends paid out on the underlying stock will decrease call premiums and increase put premiums. Call premiums decrease since the owners of the stock at the ex-dividend date receive the cash dividend. This is assumed to be the seller of call options and hence the price of the call option is deducted by the dividend amount. Put premiums increase as a result of the stock price dropping by the dividend amount after the ex-dividend date.
The above factors interact with each other in complex ways to influence the price of an option. Academics have developed various models to account for the different factors with the most famous being the Black Scholes Equation pioneered by economists Fisher Black and Myron Scholes.
The Black Scholes Model calculates the theoretical price of an option by making key assumptions on the asset and the market.
The assumptions are as follows:
Assumptions for asset
- Risk free rate is constant
- Stock price follows a random walk
- Stock does not pay a dividend
Assumptions for market
- No arbitrage opportunity
- No restrictions on amount for borrowing and lending
- No restrictions on buying and selling amount
- No transaction fees or costs