1 Introduction
Options are a type of financial derivative. This means that their price is not based directly on an asset’s price. Instead, the value of an option is based on the likelihood of change in an underlying asset’s price. More specifically, an option is a contract between a buyer and a seller. This contract gives the holder the right but not the obligation to buy or sell an underlying asset for a specific price (strike price) within a specific amount of time. The date at which the option expires is called the date of expiration.
Options fit into the classification of call options or put options. Call options give the holder of the option the right to buy the specific underlying asset, whereas put options give the holder the right to sell the specific underlying asset.
Further, within the categories of call and put options, there are both American options and European options. American options give the holder of the option the right to exercise the option at any time before the date of expiration. In contrast, European options give the holder of the option the right to exercise the option only on the date of expiration. This research focuses specifically on estimating the premium of European call options.
In general, when a party seeks to buy an option, that party can easily research the history of the asset’s price. Furthermore, both the date of expiration and strike price are contracted within a given option. With this, it becomes the responsibility of that party to take into consideration those known factors and objectively evaluate the value of a given option. This value is represented monetarily through the option’s price, or premium.
As the market for financial derivatives continues to grow, the success of option pricing models at estimating the value of option premiums is under examination. If a participant in the options market can predict the value of an option before the value is set, that participant will have an advantage. Today, the Black-Scholes model is widely used in the asset pricing industry. Praised for its computational simplicity and relative accuracy, it treats the volatility of an underlying asset as a constant. Stochastic volatility models, on the other hand, allow for variation in both the asset’s price and its price volatility, or standard deviation. This research focuses specifically on one stochastic volatility model: the Heston model [3].