The natural-gas and oil price run-up since hurricanes Katrina and Rita has subsided somewhat following a warmer than usual winter, record natural-gas storage levels, and successful conservation...

## The Art of Gas Storage Valuation

Benefits and drawbacks of the most popular estimation methods or modeling techniques.

a 10-year deal, the user has to make up the numbers while ensuring that the matrix remains positive semi-definite. In such a scenario, mean reversion becomes paramount. Otherwise the value of the option becomes very large. The user then has to tweak the correlation coefficient so that the spread is a reasonable value. At this point, the problem has moved out of the control of the user. Despite these limitations, the spread option method is widely used for a number of reasons. It can be built relatively quickly, the inputs can be seen, and the process is transparent. Users develop a certain degree of comfort with these models and continue to use them.

#### Monte Carlo Simulation Method

In a Monte Carlo simulation, one attempts to generate prices according to a distribution. We have the forward price and volatility curves. This translates into a distribution for a price vector that has a mean (forward price curve), a standard deviation (forward volatility curve), and a correlation matrix. Using a random number generator, one can generate a large number of sample vectors according to the distribution. For each of these price vectors, we have to value the storage deal. Taking the average over all these sample values provides us with the value of storage.

A large number of simulations are required to reduce sample error. As the number of simulation runs increases, the size of the sample error decreases by the square root of the number of runs. As a result, it takes a long time to reduce the size of the error. Techniques used in Monte Carlo simulation ( *e.g.*, Control Variate method) can be used to reduce the sample error, but it is hard to apply the control variate method to the case of natural-gas storage. Furthermore, calculating the moments requires special care. When one uses the Monte Carlo simulation to calculate the price deltas (or first moments), one needs to take special care.

To calculate the delta, the value of the deal usually is calculated, then the price is “tweaked” by a small amount and the new value is calculated. The difference yields the price delta. The problem that arises is that each of the calculations has a sample error. How much of the price difference is due to the change in prices and how much is due to the sample error?

Monte Carlo methods are inappropriate for valuing American options. A fundamental problem arises with the use of Monte Carlo simulation for valuing American options. The problem arises from the way the prices are generated in a Monte Carlo simulation. In a Monte Carlo simulation, the prices are generated ex post—in other words, the model assumes that the deal has been completed, it then looks at the settlement prices for each of the time periods, and it uses this price vector to determine the optimal injection and withdrawal schedule. In an American option—where an option can be exercised early for each given possible sample price path—the holder cannot “peek” along the path into the future to determine what the settlement