# Pricing of Options

8th September 2022

In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: Mathematical finance Derivatives pricing: the Q world for discussion of the mathematics; Financial engineering for the implementation; as well as Financial modeling Quantitative finance generally.

Intrinsic value

The intrinsic value is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder. For a call option, the option is in-the-money if the underlying spot price is higher than the strike price; then the intrinsic value is the underlying price minus the strike price. For a put option, the option is in-the-money if the strike price is higher than the underlying spot price; then the intrinsic value is the strike price minus the underlying spot price. Otherwise the intrinsic value is zero.

For example, when a DJI call (bullish/long) option is 18,000 and the underlying DJI Index is priced at \$18,050 then there is a \$50 advantage even if the option were to expire today. This \$50 is the intrinsic value of the option.

In summary, intrinsic value:

= Current stock price − strike price (call option)

= Strike price − current stock price (put option)

Time value

The option premium is always greater than the intrinsic value. This extra money is for the risk which the option writer/seller is undertaking. This is called the time value.

Time value is the amount the option trader is paying for a contract above its intrinsic value, with the belief that prior to expiration the contract value will increase because of a favourable change in the price of the underlying asset. The longer the length of time until the expiry of the contract, the greater the time value. So,

Time value = option premium − intrinsic value