**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.