Although total revenues were up by almost 5 percent for the third quarter of 2006 over Q3 2005, operating income and net income were up by 22.82 percent and 80 percent, respectively.

## Green Options On the Future

Call options can be used as a financing tool for fixed-cost renewable energy technologies.

financing arrangements.

The volatility of the asset—how much its price is likely to change in any given year—is a critical parameter in call-option valuation. Aggregate U.S. retail energy usage data shows total nominal electricity price volatility was 4.7 percent and 10.2 percent over the past 5 and 25 years, respectively. ^{1}

Unfortunately, aggregate U.S. energy data is not terribly useful for calculating volatility because averaging eliminates much of the volatility of interest within and across markets. Figure 1 shows average retail electricity price data by sector 1973-2005 and monthly 2003-2005. Electricity price (and, to a lesser extent, price volatility) depends in part on buyer size, as can be seen by comparing residential to industrial buyer pricing in Figure 1. Buyer location also affects price volatility. The best way to determine volatility is to look at actual electricity prices paid in the past. According to Figure 2, average city electricity prices have risen almost 22 percent (from 45 percent to 54.8 percent) during the last 6 years; data is for 500-kWh blocks of electricity sold in U.S. cities.

We present call-option pricing data for two scenarios. In the first, the volatility is assumed to be 10 percent, and in the second, 15 percent. Since different users pay different prices in different regions, using a ratio (future price cap/current price) actually is more helpful than creating multiple tables, each with different current and ceiling prices. The price cap/current ratio of 1.5 means the ceiling price is 50 percent above the current price (2.0 means the ceiling price is twice the current price).

Plugging the variables into a Black-Scholes calculator returns a call price expressed as a fraction of the current asset (electricity) cost. For simplicity, let’s assume the buyer currently pays 10 cents/kW-hour for electricity. To illustrate how to read the call-option price table, look at the first calculated number in Table 1 below: 0.17. This number means that this call option would cost 1.7 cents/kWh today. This call will cap the buyer’s electricity cost at 15 cents/kWh in 2016.

Tables 1 and 2 show that option value grows significantly over time, and selecting a higher future price cap will lower the call cost. Comparing call options with insurance, the price cap/current ratio works much like an insurance deductible: You can lower your insurance premium by selecting a higher deductible. In this case, the higher deducible exactly translates to a higher future energy price you are willing to pay. In most insurance products, you pay an annual or monthly premium for as long as you desire the insurance. In contrast, the call option is a single lump-sum payment for full protection for the given year. Of course, one can take this lump-sum payment and divide it up into smaller periodic payments by adding in the cost of financing.

One caveat in using a Black-Scholes valuation technique to value electricity call options is that Black-Scholes was developed primarily for valuing call options on stocks or other physical assets ( *i.e.*, an asset that can be purchased and held/stored indefinitely). Electricity differs from a stock