Actuarial Finance

6Engineering basic options

The word engineering usually involves the application of mathematics to study the structure and design of machines, tools, etc. As a result, the term financial engineering became increasingly popular, with the growth of derivatives markets in the 1990s, to designate the study of the structure and design of financial derivatives.

In Chapter 5, we introduced basic (vanilla) options such as call and put options and determined how they can be used for various investment purposes. The focus of this chapter is more on the mathematical structure of payoffs with the goal of designing and replicating simple financial products, and also obtaining parity relationships. Engineering also applies to common life insurance policies (see Chapter 8) where death and maturity benefits are designed using the mechanics of options.

The main objective of this chapter is to understand the basic financial engineering tools, i.e. to understand how to build and relate simple payoffs and then use no-arbitrage arguments to derive parity relationships. The specific objectives are to:

• use simple mathematical functions to design simple payoffs and relate basic options;
• create synthetic versions of basic options;
• obtain parity relationships between stocks, bonds and simple derivatives;
• understand the payoff structures of binary options and gap options;
• derive relationships between the prices of binary options, gap options and vanilla options;
• understand when American options should ...