The year 2010 is an exceptional time for currencies in terms of cash prices, futures and options. From Dec. 9, 2009, to May 18, 2010, the U.S. dollar index has risen from approximately 74 to 86, while the euro plunged from more than $1.50 to less than $1.25.
Debt and economic problems in euro-based countries such as Greece and Portugal undermined confidence in the European financial structure and caused those in charge of future payments and current investments to seek a safe haven in U.S. dollar assets. The resulting financial and economic shifts are advantageous for European exporters and U.S. citizens traveling abroad this summer. Meanwhile, U.S. products look more expensive — a possible cause for concern in terms of exports and trade deficits.
With currency prices having moved so decisively — up for the U.S. dollar and down for the euro — this is a good time to look at the consensus of the options market as it views currencies over the period May 2010 to March 2011. "September 2010 euro calls" (below) shows options prices predicted by the log-log parabola (LLP) option pricing regression model for 15 strike prices on May 14, 2010.
The futures price on that date is $1.2395 per September euro, and it is noted that the predicted prices are generally accurate to one hundredths of one cent. Close correlation between market prices and prices predicted by the regression model reflects the fact that options on futures are valued to a large extent by Black-Scholes or similar theoretical price models. This is a tightly controlled market in terms of pricing and underlying variables such as volatility measures and short-term interest rates.
Breakeven prices at each strike price show the price range forecast by the options market. These prices will produce an ending profit or loss of zero for a delta-neutral trade involving September euro calls and the underlying futures contract. Prices at expiration between the upper and lower breakeven prices will result in a profit for the delta-neutral trade, while prices beyond breakeven in either direction will result in a loss.
At a strike price near the futures price on "September 2010 euro calls," the delta-neutral breakeven prices produce a price range at expiration from $1.33 to $1.17. Price ranges estimated by probability models are key inputs for determining put and call option values. As shown on "Breakeven prices" (below), the slope of the option price curve at each strike price results in a diagonal line that intersects the horizontal axis (the upper breakeven price) and also intersects the intrinsic value line directly above the lower breakeven price.
Volatility matters
The volatility of the underlying futures contract — in this case September euro — determines the distance between the breakeven prices because these are the prices that traders depend on to generate profits on delta-neutral trades. The more volatile the underlying, the wider the breakeven spread and the higher the option price curve. A succession of similarly sloped lines connecting the horizontal axis and intrinsic value line produce a smooth option price curve whose slope extends from zero for higher strike prices to 1.00 for the lowest strikes, where changes in the call option’s price equal those of the underlying futures.
Call options on six currencies are compared on "Currency options" (below). The currencies are the euro, Japanese yen, British pound, Swiss franc, Australian dollar, and Canadian dollar — respectively, the euro, JPY, GBP, CHF, AUD and CAD. The higher curves indicate more valuable options because they have higher slopes and thus more positive price movements as the underlying price increases, and the market consensus has applied wider breakeven spreads for greater volatility.
In this sample of six call options, the most valuable underlying from the viewpoint of volatility and height of option price curve is the Swiss franc, while the least volatile and thus the least valuable set of call strike prices is the Canadian dollar. The other four — including the euro September call options — form curves between those for the Canadian dollar and Swiss franc.
The height of an option price curve, as measured by the ratio of the call price-to-strike price at the point where the strike price equals the underlying futures price, is a measure of comparative volatility — an important asset because options are only as valuable as the volatility of the underlying will permit. However, it is also true that the height of the curve does not imply the direction of future price movements. Curve height, related to the upper and lower breakeven prices as shown above, is implicitly a negotiated variable agreed upon by many hedgers and speculators in the options market and includes those who are bullish on the underlying as well as those who are bearish.
"Forecast of price ranges" (below) emphasizes the concept of price neutrality indicated by an option’s delta-neutral breakeven price spread. For each of the six initial call options and for calls on the September 2010 U.S. dollar index, spreads are computed to show the distance between the futures price and upper breakeven as a percentage of the current futures price. In each column the positive and negative percents are equal — the breakeven spread is purely about volatility estimates and not about direction of future price changes.
Corresponding to the finding on the "Currency options" chart, Swiss franc calls are significantly higher than options on the other five currencies. Moderate volatilities and percentage spreads range from approximately 7% to 8% up and down from the current futures price. The lowest volatility shown on "Forecast of price ranges" is computed for September 2010 calls on U.S. dollar index futures. This is understandable because the dollar index is based on six different currencies, including five of the six currencies used above, dropping out the Canadian dollar and substituting Swedish krona. Variations in the U.S. dollar’s relative value are averaged, resulting in a lower level of volatility.
More interesting is the lack of volatility for the euro in the light of recent publicity regarding financial problems in Greece, specifically, and Europe in general. On the "Forecast of price ranges" and "Currency options" charts, the euro is in the center — with slightly higher volatility than the yen and Canadian dollar, and slightly lower volatility than the Australian dollar and British pound. The higher volatility of the Swiss franc may be explained by the recent decline from $0.95 to $0.87 in the one-month period April 15 to May 18, following a relatively stable February and March.
Although the euro call price curve is currently just average with respect to the other five currencies in the present sample, it is significantly higher than the price curve of the U.S. dollar index. The comparison is shown on "U.S. dollar index and euro" (below). The heights of the two curves at the point where the futures price equals the strike price are 3.12% for the euro and 2.18% for the dollar index.
Profits in time
Time value for put and call options may be measured by the relative heights of the option price curves. Over the near-term, the Swiss franc may fall back in line with the other currencies as their call options gradually lose value toward September expirations.
As shown by the comparative option price curves, call options on the individual currencies have a valuation advantage over the dollar index. Depending on whether the underlying is below or above the call strike price at expiration, the final option value will equal either zero or the intrinsic value. In the race to the finish, it appears that none of the currencies studied here has the lead, but a bet against the dollar index appears to be a sure choice.
The pattern of price curves shown on "Currency options" suggests that speculative trades and hedging between the six currencies are keeping their valuations closely connected. Currently bound by the low option value of the Canadian dollar and the higher value of Swiss franc calls, September options are progressing as a group toward their expiration prices.
"Calls on euro futures" (above) shows call price curves for successive euro futures expirations in September and December 2010 and March 2011. On May 14, 2010, the options are described by the following figures:
In summary, current data show that euro options are not too volatile despite the publicity surrounding European financial problems. All six of the currency options studied are closely grouped in terms of option valuation based on comparative volatilities, and options on the U.S. dollar index are predictably low-valued in respect to expected volatility. In the near future, other economic and financial changes may cause significant shifts in the options described above, but for the present the charts speak
for themselves.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.
More articles by Paul Cretien:
Using options on eurodollar futures to predict Fed policy
Eurodollar futures: Rate, yield and price structures
Softs futures: Know your options
