# Pricing Foreign Exchange Options: Incorporating Purchasing Power Parity (Second edition)

David W.K. Yeung
Michael Tow Cheung
Pages: 104
https://www.jstor.org/stable/j.ctt2jc1t8

1. Front Matter
(pp. [i]-[viii])
(pp. [ix]-[xii])
3. CHAPTER 1 PREAMBLE
(pp. 1-5)

This book is a revised and re-written version of part of a study, sponsored (from 1992 onward) by Cypress International Investment Advisors Ltd. Its purpose is to describe a new approach to the valuation of options on foreign exchange. Though the core of the original text remains, comments, especially from professional practitioners, have led the authors to re-orientate the exposition. In particular, the present edition has been recast with applications very much in mind.

The reason underlying this change in exposition would be clear if one remembers a bit of methodology. According to Friedman’s well known view (1953), in positive...

4. CHAPTER 2 DEFINITIONS AND TERMINOLOGY
(pp. 6-9)

Very briefly, let us summarise the definitions and terminology that will be used in the following chapters. There are two basic types of options: call options (or simply calls), and put options (or puts). A call option on an asset gives the owner the right to buy the asset on or before a certain date at a certain price. If the right is exercisable only on that date, the option is “European”: otherwise it is an “American” option. A put option gives the owner the right to sell an asset on or before a certain date. Puts can also be...

5. CHAPTER 3 TECHNICAL GLOSSARY
(pp. 10-18)

The technical terms and results which will be used in the exposition are summarised in this Chapter. For details and proofs, the reader is referred to any good text on stochastic processes, e.g., Karlin & Taylor (1975, 1981).

Let $(\Omega ,{\rm{ }}A,{\rm{ }}P)$ be a probability space, and $T$ an arbitrary set of numbers. Suppose we define the function:

${\rm{X(t,}}\omega {\rm{), t}} \in {\rm{T, w}} \in \Omega$ . (3.1)

A stochastic process is a family ${\rm{\{ X(t,}}\omega {\rm{)\} }}$ of such functions. For any given ${\rm{t}} \in {\rm{T, X(t,}} \cdot {\rm{)}}$ denotes a random variable (or a random vector) on the probability space $(\Omega ,{\rm{ }}A,{\rm{ }}P)$ . For any fixed $\omega \in \Omega ,X( \cdot ,\omega )$ is a real valued function (vector valued function) defined on $T$ ,...

6. CHAPTER 4 STOCHASTIC ASSUMPTIONS AND OPTION PRICING
(pp. 19-23)

In Chapter 1 we suggested that, since option pricing is applied economics, the choice of assumptions is a matter of primary importance. In particular, we referred to the view of Cox & Ross (1976), that if a different assumption is introduced regarding the stochastic behavior of an asset price, generally a different formula to price options on the asset would follow. The objective of present chapter is to convince the reader of the truth of this observation. We present an example, in which a call option on an equity is priced without any stochastic assumptions about the behavior of the...

7. CHAPTER 5 THE BLACK-SCHOLES OPTIONS THEORY
(pp. 24-42)

As we have seen in Chapter 4, the question is: what is the equilibrium price of an option, given its nature (whether it is American or European), exercise price, exercise date, the current price of the underlying asset, the discount rate, and given an assumption regarding the behavior of the asset price over time? A major breakthrough was achieved when Black & Scholes (1973) obtained a closed-form expression to price an European option on a stock which does not pay dividends, assuming that its price follows a Geometric Brownian Motion¹.

In their seminal work (1973), Black and Scholes adopted the...

8. CHAPTER 6 GEOMETRIC BROWNIAN MOTION, “ALMOST CERTAIN RUIN”, AND ASSET MARKETS EQUILIBRIUM IN OPTIONS PRICING
(pp. 43-56)

At the same time that he introduced geometric Brownian motion into finance, Samuelson (1965) pointed out that if asset prices are modelled in this way, a bias in the (Brownian) random walk must be taken into consideration. In this Chapter, we first explore some implications of Samuelson’s observations for the interpretation of asset markets equilibrium, in particular with respect to the assets which underlie options. Attention is drawn to the fact that given the assumption of geometric Brownian motion, the sample path behavior of a stock price (stochastic) process may differ from the behavior of its moments. Most importantly, a...

9. CHAPTER 7 NON RANDOM WALK EFFECTS AND A NEW STOCHASTIC SPECIFICATION
(pp. 57-70)

As we have seen in Chapter 5, a serious problem arises when geometric Brownian motion is used to model asset prices. In addition, recent research is beginning to “question the random walk dogma” associated with geometric Brownian motion (Samuelson 1991). One factor which may account for “runs” in the prices of assets like stocks is provided by standard economic theory, which tells us that in long period equilibrium, the value of the firm’s balance sheet is determined by exogenous variables like technology and tastes. If this value changes in response to changes in any one exogenous variable, the ‘intrinsic value’...

10. CHAPTER 8 PRICING FOREIGN EXCHANGE OPTIONS INCORPORATING PURCHASING POWER PARITY
(pp. 71-86)

One of the most useful and widely used applications of the theory of options is to price options on foreign exchange.² As we have seen in Chapter 4, according to a fundamental assumption in Black and Scholes’ theory, the stochastic process governing the (spot) price of the underlying foreign currency follows geometric Brownian motion.³ As a result, the exchange rate displays the characteristics of a random walk.⁴ On the other hand, a fundamental theorem in the international trade predicts that over time, the spot (relative) price of a currency would converge to its purchasing power parity.⁵ Fluctuations in the exchange...

11. CHAPTER 9 CONCLUSIONS
(pp. 87-89)

The appropriate choice of assumptions is a matter of primary importance in applied economics. In option pricing, it is generally assumed that the underlying asset has a price which fluctuates over time as a geometric Brownian motion. Since a number of problems then arise, the present volume proposes an approach to the valuation of foreign exchange options based on an alternative assumption. Definitions and terminology are introduced in Chapter 2. A technical glossary is given in Chapter 3. The remainder of the book is devoted to a new stochastic specification to model the spot price of the representative currency underlying...

12. Index
(pp. 90-92)