Actuarial Finance

7Engineering advanced derivatives

In Chapter 6, we engineered basic derivatives, including an investment guarantee, binary options and gap options. European call and put options, in addition to the abovementioned derivatives, fall into the category of simple options because their payoffs depend only on the underlying asset price S_T at the maturity of the derivative.

However, on financial markets, institutional investors such as banks, insurance companies and pension plans design and trade more sophisticated contracts tailored for their specific needs. Those derivatives/options are said to be exotic or path-dependent, while others are called event-triggered derivatives.

A derivative is said to be exotic or path-dependent if its payoff depends on the underlying asset price at more than one date during the life of the derivative. Event-triggered derivatives are contracts whose payoff depends on the occurrence and/or severity of events such as natural catastrophes. Just like forwards, futures and simple options, exotic options and event-triggered derivatives are used by investors for speculation or hedging purposes.

The main objective of this chapter is to familiarize the reader with exotic/path-dependent options and event-triggered derivatives. The specific objectives are to:

• understand and compute the payoffs of barrier, Asian, lookback and exchange options;
• understand and compute the payoffs of weather, catastrophe and longevity derivatives;
• understand why complex derivatives ...