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Global Financial Markets - Update |
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PART 2: FOREIGN-EXCHANGE PREDICTION AND HEDGING TOOLS
Main Contents Page • Part 1 • Part 3 • Part 4 • Part 5 • About the book
New: self-test problems on the foreign-exchange and Eurocurrency markets.
This document contains updates to my book, Global Financial Markets (Houghton Mifflin, 1994). It also contains information on developments and research in the international financial markets that might be of interest to students and professionals.
Contents
Chapter 6: Currency Prediction Versus Market Efficiency
Forward rate bias and expected inflation; New research results
Chapter 7: Currency Forwards and the Futures Market
Futures in Speculation; Forwards in Speculation; A problem's problem
Chapter 8: Foreign-Exchange Options
Quanto options--applications; Hedging options positions; New research results
Main Contents Page Back to the top of this section
Chapter 6: Currency Prediction Versus Market Efficiency
Forward rate bias and expected inflation
See Chapter 5.
Main Contents Page Back to the top of this section
Chapter 7: Currency Forwards and the Futures Market
Futures in Speculation
See Chapter 15, "Does Futures Speculation Stabilize Spot Prices? Evidence from Metals Markets" by A. Enis Kocagil.
Forwards in Speculation
It is often difficult, especially in the context of a corporation's complex international transactions, to separate hedging from speculative transactions in the foreign exchange markets. In Example 7.4, Kodak is undertaking "selective hedging" of its current and anticipated receivables. The action is speculative--it is precipitated by an individual's forecast of the yen's direction, not purely by the company's natural business. In short, the company, like most, is using its foreign-currency receivables as an excuse to take a view on a currency in the hope of profiting.
This is, of course, a fictional example. The next one is real.
On February 20, 1993, Showa Shell Sekiyu, a Japanese oil refiner and distributor that was 50% owned by Royal Dutch/Shell, reported that it had lost Y125 billion ($1.05 billion) in 1992. The firm's losses, equal to 82% of its shareholders' equity, stemmed from $6.4 billion worth of speculative foreign exchange contracts. These were accumulated by the firm's treasury department, apparently without authorization. The contracts, taken out in 1989 and subsequently rolled over, bought the dollar forward at an average exchange rate of Y145, to which level the yen had briefly weakened that year. At the end of 1992, the yen was trading at Y125 per dollar.
In Showa Shell's case, because the losses were "unrealized," i.e. not closed out, they did not have to be reported in company accounts. Banks in Japan routinely allowed their counterparties to defer settlement of lossmaking contracts by rolling them over until they were advised by the ministry of finance to desist.
A problem's problem
On page 200, in Problem 9., replace "in Figure 7.7" with "in Figure 7.13".
New research results
Fractals and Intrinsic Time - A Challenge to
Econometricians by ULRICH A. MULLER, MICHEL M. DACOROGNA,
RAKHAL D. DAVE, OLIVIER V. PICTET, RICHARD B. OLSEN and J.
ROBERT WARD.
Contact: Olsen, E-mail: info@olsen.ch, Olsen & Associates AG
Research Institute for Applied Economics, Seefeldstrasse
233, CH-8008 Zurich, Switzerland Tel 41 (1) 386 48 48 Fax 41
(1) 422 22 82.
A fractal approach is used to analyze financial time series, applying different degrees of time resolution, and the results are interrelated. Some fractal properties of foreign exchange (FX) data are found. In particular, the mean size of absolute values of price changes follows a "fractal" scaling law (a power law) as a function of the analysis time interval ranging from a few minutes up to a year. In an autocorrelation study of intraday data, the absolute values of price changes are seen to behave like the fractional noise of Mandelbrot and Van Ness rather than those of a GARCH process. Intraday FX data exhibit strong seasonal and autoregressive heteroskedasticity. This can be modeled with the help of new time scales, one of which is termed intrinsic time. These time scales are successfully applied to a forecasting model with a fractal structure for both the FX and interbank interest rates, which present similar market structures as the Foreign Exchange. The goal of this paper is to demonstrate how the analysis of high-frequency data and the finding of fractal properties lead to the hypothesis of a heterogeneous market, where different market participants analyze past events and news with different time horizons. This hypothesis is further supported by the success of trading models with different dealing frequencies and risk profiles. Intrinsic time is proposed for modeling the frame of reference of each component of a heterogeneous market.
Main Contents Page Back to the top of this section
Chapter 8: Foreign-Exchange Options
Customized exchange-traded contracts
In mid-1994 the Philadelphia Stock Exchange, the self-styled "world's largest organized market for currency options," announced that it would henceforth offer market participants tailor-made trading and hedging tools, but with all the safeguards of a regulated exchange.
In its first phase, the market offered customizable strike prices, a choice of matching any existing currency pairs, and inverse (European-quoted) contracts.
This is an example of how futures and options exchanges are attempting to market themselves more effectively as regulators cast a negative light on the over-the-counter derivatives market.
Quanto options--applications
Quanto options, mentioned on page 234 in Chapter 8, sound exotic. They give the right to buy or sell an unknown quantity of foreign currency, where the quantity depends upon some market variable such as equity prices or interest rates. In fact, they have some very down-to-earth applications. Three examples follow.
1. Quanto options can be useful to international equity portfolio managers who wish to take a view on share prices in a foreign market, but not on the exchange rate. Such a portfolio manager might invest in a foreign market, purchasing shares valued at X units of the foreign currency. One way to hedge this is by selling forward X units of the currency. However if, after one quarter, the shares' value has changed by Y%, some of the foreign investment will be exposed. To solve this, he can buy a quanto option whose payoff depends on both the exchange rate and Y. Specifically, the appropriate quanto to purchase will be one that will lock in the exchange rate at which not just X, but X(1 + Y) units of foreign currency can be sold.
2. A quanto option could be useful to a corporation that plans to buy a fixed amount of a commodity in a foreign market at a certain date in the future. For example, a Japanese utility may anticipate purchasing 20 million barrels of oil for the winter months. Instead of hedging by buying a fixed dollar amount forward, the utility could employ a quanto option where the number of dollars purchased at a fixed exchange rate depends on the price of oil.
3. Quanto options are needed to hedge the risks entailed in writing a differential swap. Banks that write diff swaps guarantee to exchange the interest rate in one currency for that in another, but the exchange is all done in one currency. For example, NatWest may agree to pay (or receive), in dollars, the difference between US dollar and sterling Libor every six months for two years. Hedging this requires NatWest to engage in separate interest rate swaps in the dollar and sterling markets, and to use a quanto option to hedge the dollar-sterling exchange rate risk. The quanto would assure NatWest of the dollar-sterling rate at which sterling Libor could be exchanged, whatever the level of sterling Libor.
Hedging options positions
Some readers have pointed out that the section on page 229 entitled "Hedging Options with Futures Versus Hedging Options with Options" is a little hard to follow. (Even the title is a mouthful.) I thought I'd amplify the ideas with an example and three diagrams.
Suppose we are FX options traders at a bank. In response to a customer's request, we sell 100 at-the-money call options on sterling. (The market price of sterling is currently $1.50.) We must now hedge the position.
From the slope of the options price line (see Fig. 8.8 on p. 226), the hedge ratio is 50%. Hence to hedge the 100-option position with futures contracts, we buy 50 sterling futures. We are now delta-hedged.
As the diagram below shows, hedging options with futures entails hedging with a number of futures determined by the slope of, or tangent to, the options price line. But this slope changes whenever the underlying currency's value changes. In our example, when the price of sterling moves up, the options writer is underhedged (the slope has increased), so we lose more on our short option position than we gain on our futures position. When sterling falls, the options writer is overhedged, so we gain less on our options position than we lose on the futures.
The reason for our problem is simple. We are using an instrument whose price line is linear to hedge one whose price line is curved. The degree of curvature is measured by the option's gamma, which is the second derivative of the price with respect to the price of the underlying instrument.
The solution is to use options to hedge options: hedge a curve with a curve. The proportion of one option we use to hedge another option is determined by the relation between the deltas, the hedge ratios. The option we're selling has a delta of 50%. If the one using to hedge our position has delta of 40%, then we would need more of it--100*50/40, i.e. 125.
As the next diagram shows, the hedging-gap is less even for a fairly big move in sterling.
Even so, the hedging-gap cannot be zero unless the curvature or gamma of the options we've bought, and those that we've sold, are identical. Being delta-neutral is not enough. Normally the gamma of the one we've bought is greater than the ones we've sold (we are "long gamma"), or vice-versa ("short gamma"). Gamma is a desirable property for options one owns, and undesirable for options one has written. For options one owns, the more the curvature the more losses are cushioned and gains accelerated. As the diagram below shows, being short gamma (but delta neutral) gives losses for large upside and downside moves. It's a little like selling a straddle.
New research results
"The Valuation of Black-Scholes Options Subject to Intertemporal Default Risk" (OFOR Working Paper Number 93-03)
BY: DON R RICH
CONTACT: DON RICH
E-MAIL: drich@lynx.neu.edu
POSTAL: Finance Group - CBA, 413 Hayden Hall,
Northeastern University, Boston, MA 02115, USA
PHONE: (617) 373-3155
FAX: (617) 373-8798
REF: WPS94-289
The valuation of many types of financial contracts and contingent claim agreements is complicated by the possibility that one party will default on their contractual obligations. This paper develops a general model that prices Black-Scholes options subject to intertemporal default risk.
The explicit closed-form solution is obtained by generalizing the reflection principle to k-space to determine the appropriate transition density function. The European analytical valuation formula has a straightforward economic interpretation and preserves much of the intuitive appeal of the traditional Black-Scholes model. The hedging properties of this model are compared and contrasted with the default-free model. The model is extended to include partial recoveries. In one situation, the option holder is assumed to recover alpha (a constant) percent of the value of the writer's assets at the time of default. This version of the partial recovery option leads to an analytical valuation formula for a first passage option - an option with a random payoff at a random time.
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