CAN THE PRICE OF CURRENCY OPTIONS PROVIDE AN INDICATION OF MARKET PERCEPTIONS OF THE UNCERTAINTY ATTACHED TO THE KRONE EXCHANGE RATE?

• Author: Eitrheim, Oyvind

Prices in the currency options market can provide an indication of market perceptions of the uncertainty attached to future exchange rates. We have used these option prices to calculate the probability distribution for the krone exchange rate against the Deutsche mark since 1 January 1998. Until August 1998, the market expected relatively low volatility in the krone exchange rate, and the probability of an appreciation or a depreciation of the krone was considered to be virtually the same. The krone depreciated during the autumn of 1998 and uncertainty surrounding future movements of the krone exchange rate increased substantially. At the same time, the prevailing view among market participants seemed to be that a considerable depreciation of the krone was more probable than a corresponding appreciation. This volatility subsided during the spring of 1999 to about the level prior to the depreciation of the krone in the autumn of 1998. The estimated probability distribution for the krone exchange rate at end-May was approximately equal to the corresponding distribution in July of last year, ie the market assessment of krone exchange rate uncertainty seems to be about the same as it was prior to the currency unrest in the autumn of 1998.

Introduction

Financial variables are often employed as an indicator of market expectations. Provided there are no risk premia associated with currency investments, the forward exchange rate is an indicator of market expectations concerning future exchange rates.(2) However, forward rates provide no information about the uncertainty of exchange rate movements. One method of obtaining information concerning uncertainty in the foreign exchange market is to measure the volatility of the exchange rate over a given period. This can be done in several ways: through simple calculations of the standard deviation of changes in the exchange rate or by estimations using advanced models.(3) One disadvantage in using such methods to measure uncertainty in the exchange market is that the historical volatility measured by such means differs from market expectations of future volatility.

A more direct measure of market expectations of future volatility can be obtained by using currency option prices. As shown in this article, it is possible to use market expectations to estimate the implied probability distribution for the future exchange rate. A central bank can make use of this information in many ways: first, such information may be useful in interpreting the evolution of the interest rate differential. The interest rate differential reflects both a risk premium and depreciation expectations. The risk premium depends on the degree of uncertainty attached to the exchange rate, which means that currency options can provide information about the size of the risk premium. Second, the options market can be a source of valuable information on the effect of any exchange market interventions aimed at reducing volatility. Third, the very shape of the probability distribution may provide information on the market assessment of the probability of different outcomes. For example, "peso problems" can be more easily identified.(4)

This article begins by providing a brief review of the general theory of option prices, followed by a discussion of price determination for the most common type of currency options. Finally, we look at how currency options can be used to estimate the implied probability distribution for the exchange rate. The article is based on developments in the foreign exchange market from January 1998 to May 1999.

What determines the price of an option?

A call option is a contract that confers on one party the right, albeit not the obligation, to purchase an (underlying) asset at a fixed price -- the strike price -- at or before a designated future date. As payment for this right, a premium must be paid to the option writer. The option writer is under the obligation to sell the underlying asset if the buyer wishes to exercise his right to buy. A put option is a contract whereby the buyer of the option has the right, albeit not the obligation, to sell the underlying asset at a fixed price. The majority of options trading involves equities and bonds, but the market for options with foreign currency as the underlying asset is growing. In this article, we examine currency options.

It may be useful to examine a stylised example of a currency option: Suppose an investor purchases an option at a price of NOK 1.0, which gives the buyer the right to buy 10 euros at a price of NOK 8.30 per euro (the strike price) one month forward. Whether the option will be exercised or not depends on the relationship between the exchange rate at maturity and the strike price on the agreed date. If the krone exchange rate is NOK 8.50 after one month, the option will result in a profit for the buyer. The buyer of the option may then purchase 10 euros at the price of NOK 8.30 per euro and sell them for NOK 8.50 per euro. The profit is 10 x (8.50-8.30) -- 1.0 (the option price) = NOK 1.0. On the other hand, if the krone exchange rate against the euro is NOK 8.10, it would not be profitable to exercise the option and it would be worthless at maturity. The loss is limited to the option purchase premium, ie NOK 1.0.

Many different models for valuing currency options have been developed.(5) A variant of the Black-Scholes model is the one most commonly employed. This model's exchange rate assumptions imply that the return on investments in a given currency has a log-normal distribution with a constant variance. In this model, which is described in Annex A, European-style currency options are determined by five factors:(6)

* The current spot rate

* The difference between domestic and foreign interest rates

* The maturity of the option

* The strike price of the option

* The volatility (standard deviation) of the underlying exchange rate

A higher volatility will -- ceteris paribus -- increase the value of the option. The reason for this is that higher volatility increases the probability that the option will be exercised -- ie that it will be "in-the-money" - when the option expires.(7) This is shown in Chart 1 where it is assumed that one option is based on an underlying asset x which is less uncertain than underlying asset y. In both cases, the probability of the option resulting in a profit or of becoming worthless is 50 per cent. The potential loss for the buyer is equal to the option price, whereas there is no upper limit for gains. As shown in the chart, the probability that an option which is based on an asset with wide price variability (option y) will result in a considerable profit is greater than for the option for which the price of the underlying instrument is more certain (option x). The price of option y will be higher, reflecting the higher profit potential.

[Chart 1 OMITTED]

It is assumed that the two options are based on an underlying asset with the same price and same strike price. The options are assumed to be at-the-money.

Of the variables listed above, only volatility is not directly observable. With an estimate for volatility, the price of the option follows directly from the formula. Similarly, volatility can be calculated if the market price for the option is known. This calculated volatility, known as "implied volatility", is a key element of our discussion of the information content in option prices.(8)

The currency options market

Currency options, and derivatives in general, are traded both on stock exchanges and OTC (over-the-counter) markets. Derivatives traded on the stock exchange are standardised in respect of quality, quantity and terms of delivery, and are settled via a cleating house. Contracts traded in the OTC market are less standardised, and the terms of delivery are set according to the preferences of the contracting parties. Most international currency option trading occurs in the OTC market. Prices are quoted in terms of implied volatility. At the time of settlement, the estimated implied volatility is entered into the Black-Scholes formula to determine the option price. This does not necessarily imply that market participants agree with the assumptions of the Black-Scholes model. As will be shown in this article, there are many indications that the Black-Scholes model's assumption of log-normally distributed relative changes in the exchange rate is...