Exotic options

Up to now, we discussed European and American options in Chapter 9, The Black-Scholes-Merton Option Model, which are also called vanilla options. One of the characters is path independent. On the other hand, exotic options are more complex since they might have several triggers relating to the determination of their payoffs. An exotic option could include nonstandard underlying instrument developed for particular investors, banks, or firms. Exotic options usually are traded over-the-counter (OTC). For exotic options, we don't have closed-form solutions, such as the Black-Scholes-Merton model. Thus, we have to depend on other means to price them. The Monte Carlo simulation is one of the ways to price many exotic options. In the next several subsections, we show how to price Asian options, digit options, and barrier options.

Using the Monte Carlo simulation to price average options

European and American options are path-independent options. This means that an option's payoff depends...