Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

11

Options on specific underlyings and exotic options

The option pricing methodology has been developed in the previous chapter, exemplified with the most used – and simplest – underlying, namely stocks and stock indexes. In this chapter, particular features are considered, on other types of underlyings as well as in the case of more complex option pay offs, relative to second-generation or exotic options. To avoid cramming this chapter, there will be no references to the content of the previous one. Also, to remain within the limits of this book, as stated in the Introduction, since several of the topics developed hereafter are more complex, they are only outlined; that is the reason why the references in footnotes and the further reading are more abundant than in previous chapters.

11.1 CURRENCY OPTIONS

Currency options do not present particular features, and the pricing methods proposed in the previous chapter hold. We have to simply take into account the peculiar nature of the currency, as an underlying that is priced in a relative way: see Chapter 3, Section 3.4. Buying a reference currency against selling the counter-value currency results in the fact that a currency option is not simply a call or a put, but a call and a put: for example with EUR/USD, we have to consider either a call EUR/put USD (i.e., the right to buy EUR against selling USD) or a put EUR/call USD. Once this is viewed clearly, there is nothing to add to the previous chapter, Section 10.2.2. Besides regular ...