7
Other Exotic Options

7.1 INTRODUCTION

In this chapter we examine a varied range of exotic contracts. They are less frequently traded in the market, yet deserve a detailed treatment for pricing and risk management. Some of them can simply be derived by a static replication argument by means of standard plain vanilla options (e.g., volatility swaps and barrier options monitored at expiry, denominated at-end or at-expiry barriers) or by some other tricks allowing for the use of already derived formulae for other contracts (e.g., first-in-then-out barriers). For some others, specific pricing formulae have to be devised (e.g., forward start options and compound options).
We start with barrier options monitored at expiry, ideally carrying on and completing the analysis of the previous chapter.

7.2 AT-EXPIRY BARRIER OPTIONS

Barrier options monitored only at expiry can be either knock-in or knock-out, but they can only be of the reverse kind. Actually, it is easy to see that if the barrier is set at a level where the option is out-of-the-money at expiry, and whose effect operates only at the end of the contract, then the exotic option is exactly equal to an otherwise identical plain vanilla option. The pricing of at-expiry barrier options can be performed by means of plain vanilla options and digitals. They have been analysed at length in Chapter 5, so we effortlessly derive pricing formulae.
 
Definition 7.2.1. At-expiry barrier FX option contract. An XXXYYY at-expiry barrier ...

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