The Mathematics of Financial Models: Solving Real-World Problems with Quantitative Methods

CHAPTER 5 Valuing Exotic Options

In Chapter 3, I presented examples on how vanilla options are priced and how these pricing models are used to analyze various simple risk-management strategies. I also introduced the terminology exotic options¹ (i.e., options with in-the-money payoffs that are different from those of the vanilla options). Although examples of exotic options appeared in the late 1980s, the use of exotic options became more prevalent in the early 1990s when practitioners started to better appreciate the power of exotic options to better manage risks or take market view across multiple underlyings and asset classes.

Unlike vanilla European-style options, where one had access to the accurate analytical pricing formulae (examples of which were illustrated and discussed in Chapter 3), due to the complexity of the option payoffs, it is usually difficult to obtain similar analytical expressions for pricing European-style exotic options. As a consequence of this, in the absence of cheap, high-powered computers before the early 1990s, practitioners had to resort to using simplifying assumptions, clever mathematical tricks, and specific numerical algorithms to arrive at reasonable analytical approximations to value these complex, customized options. As mentioned in Chapter 4, it is also precisely this reason why Boyle's 1977 seminal paper on the use of Monte Carlo simulations to value vanilla European-style exotic options did not get the attention it deserved.

When computer ...