The option premium is the price that is paid to buy an option. This price results from the demand and supply in the option market. In an arbitrage-free world, that is, in the absence of market frictions such as direct and indirect transaction costs, the option premium will represent the true value of the option. However, the real-world option premium may divert from the true value.
The divergence may be particularly high for over-the-counter (OTC) options and for real options, because market mechanisms can hardly be applied to these types of options. In order to determine the true value and to assess the deviation of the actual option premium from the true value, an option pricing model, also called option valuation model, is applied.
Despite some recent development of alternative option pricing models, the most widely used and discussed option pricing models are based on the application of a pricing tree, such as a binomial tree as proposed by Cox et al. (1979) or a trinomial tree, or they are based on the Black–Scholes model—sometimes referred to as the Black–Scholes–Merton model—as developed by Black and Scholes (1973) and Merton (1973).
The Black–Scholes model is typically used to determine the value of European options, whereas the pricing of American options and, in particular, of exotic options requires the application of other models such as pricing tree models.
The value of an option and, analogously, the option premium are typically inl uenced by six factors: the spot price of the underlying asset, the exercise price, the time to expiration, the volatility of the price of the underlying, the risk-free rate, and expected payments from the underlying before expiration.
An option becomes more valuable when its intrinsic value, that is, for call options the excess of spot over exercise price and for put options the excess of exercise over spot price, increases.
Consequently, the value of call/put options increases when the spot price increases/decreases, and call/put options with a lower/higher exercise price are more valuable than those with a higher/lower exercise price, respectively.
The influence of the time to expiration may differ between American options and European options. An American option with a longer time to expiration has an at-least-as-high value as a short-life American option, because it offers additional exercise opportunities compared to an otherwise equally endowed short-life option.
Since European options may not be exercised prior to expiration, a significant payment from the underlying before expiration that causes a spoftprice decline of the underlying may offset the possibly higher time value of a long-life European call option.
Due to its nonlinear payment structure, the value of an option increases when the volatility of the price of the underlying increases, because higher volatility implies higher probability of extreme spot price changes. The holder of a put or call option faces limited downside risk from the option position.
However, an extreme spot price movement that leads to a far-in-themoney option position strongly increases its intrinsic value. The inl uence of the risk-free rate cannot be unambiguously determined because it strongly depends on the price sensitivity of the underlying to interest rate changes.
As indicated above, a payment from the underlying, such as a dividend payment, tends to decrease the spot price of the underlying. Therefore, an expected payment typically decreases/increases the intrinsic value of a call/put option.