Ebook Derivatives markets (2nd edition): Part 2

(BQ) Part 2 book Derivatives markets has contents: Exotic options; financial engineering and security design; corporate corporate; real options; monte carlo valuation; the lognormal distribution; the black scholes equation; interest rate models; value at risk,...and other contents.

www.downloadslide.com Exotic Options: I T : u, fruc we have di,cu"ed """dan! option,, futu=, ond 'wap, By altering the tenru of standard contracts like these, you obtain a "nonstandard" or "exotic" option Exotic options can provide precise tailoring of risk exposures, and they permit investment strategies difficult or costly to realize with standard options and securities In this chapter we discuss some basic kinds of exotic options, including Asian, barrier, compound, gap, and exchange options In Chapter 22 we will consider other exotic options 14.1 INTRODU CTION Imagine that you are discussing currency hedging with Sally Smith, the risk manager of XYZ Corp., a dollar-based multinational corporation with sizable European operations XYZ has a large annual inflow of euros that are eventually converted to dollars XYZ is considering the purchase of -year put options as insurance against a fall in the euro but is also interested in exploring alternatives You have already discussed with Smith the hedging variants from Chapters and 3, including different strike prices, a collar, and a paylater strategy Suppose that Smith offhandedly mentions that XYZ receives large euro payments on a monthly basis, amounting to hundreds of millions of dollars per quarter In thinking about how to hedge this position, you might reason as follows: "A standard -year put option would hedge the firm against the level of the euro on the one day the option expires This hedge would have significant basis risk since the price at expiration could be quite different from the average price over the year Buying a strip of put options in which one option expires every month would have little basis risk but might be expensive Over the course of the year what really matters is the average exchange nite over this period; the ups and downs around the average rate cancel out by definition I wonder if there is any way to base an option on the average of the euro/dollar exchange rate?" This train of thought leads you to construct a new kind of option-based on the average price, rather than the price at a point in time-that addresses a particular business concern: It provides a more precise hedge against the risk that matters, namely the average exchange rate This example demonstrates that exotic options can solve a particular business problem in a way that standard options not Generally, an exotic option (or nonstandard option) is simply an option with some contractual difference from standard options Although we will focus on hedging examples, these products can also be used to speculate 443 444 � EXOTI C O PT I O N S : I www.downloadslide.com It is not hard to invent new kinds of options The challenge is to invent new options that are potentially attractive to buyers (which we did in the preceding example) and that can be priced and hedged without too much difficulty In Chapters and , we saw how a market-maker can delta-hedge an option position That analysis led us to see how the price of an option is equivalent to the cost of synthetically manufacturing the option In particular, an option is fairly priced when there is a certain relationship among the Greeks of the option Options with exotic features can generally be priced and delta-hedged in the same way as ordinary options As a consequence, exotic derivative products are quite com­ mon in practice and the technology for pricing and hedging them is well understood In fact, since many such options are in common use, the term "exotic" is an anachronism We will continue to use it, however The goal in this chapter is not to master the mathematical details of particular products, but rather to gain an intuitive understanding of the trade-offs in design and pric;ing Consequently, most of the formulas appear in the chapter appendix Since exotic options are often constructed by tweaking ordinary options in minor ways, ordinary options are useful as benchmarks for exotics To understand exotic options you should ask questions like these: • How does the payoff of the exotic compare to that of a standard option? • Can the exotic option be approximated by some portfolio of other options? • • • Is the exotic option cheap or exp�nsive relative to standard options? Understanding the economics of the option is a critical step in understanding its pricing and use What is the rationale for the use of the exotic option? How easily can the exotic option be hedged? An option may be desirable to a customer, but it will not be sold unless the risk arising from market-making can be controlled 14.2 ASIAN OPTIONS An Asian option has a payoff that is based on the average price over some period of time An Asian option is an example of a path-dependent option, which means that the value of the option at expiration depends upon the path by which the stock arrived at its final price Such an option has the potential to solve XYZ's hedging problem However, as we will see in Chapter 22, there are options that are quite difficult to hedge even though they are easy to price You can think of path dependence in the context of a binomial pricing modeL In the binomial model of Chapter 0, udu and duu are a series of up and down stock price moves-paths-