Modeling Tools for Financial Options

What do we mean by option? An option is the right (but not the obligation) to buy or sell a risky asset at a prespecified fixed price within a specified period. An option is a financial instrument that allows —amongst other things— to make a bet on rising or falling values of an underlying asset. The

underlying

asset typically is a stock, or a parcel of shares of a company. Other examples of underlyings include stock indices (as the Dow Jones Industrial Average), currencies, or commodities. Since the value of an option depends on the value of the underlying asset, options and other related financial instruments are called

derivatives

(→ Appendix A2). An option is a contract between two parties about trading the asset at a certain future time. One party is the

writer

, often a bank, who fixes the terms of the option contract and sells the option. The other party ist the

holder

, who purchases the option, paying the market price, which is called

premium

. How to calculate a fair value of the premium is a central theme of this book. The holder of the option must decide what to do with the rights the option contract grants. The decision will depend on the market situation, and on the type of option. There are numerous different types of options, which are not all of interest to this book. In Chapter 1 we concentrate on standard options, also known as

vanilla options

. This Section 1.1 introduces important terms.