At what daily temperature do customers turn on their furnaces? Or more realistically, given individual behavior, over what range of temperatures do they turn on their furnaces? To estimate the...

## The Art of Gas Storage Valuation

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

price will be in order to determine whether or not to exercise. The user has to look at the information available only at the time of exercise. Hence, the value obtained using the Monte Carlo method will always be higher because of the advantage that this method has over the reality. The modeler now has to adjust the parameters so that the values are consistent with those being seen in practice. It should also be pointed out that the Monte Carlo method can produce an inaccurate representation of how the value of storage is monetized.

In the Monte Carlo method, the assumption is that the information is available to the model after the fact. So the algorithm goes through the following steps:

- Generate a random price path;
- Determine the optimal injection withdrawal schedule for each path;
- Perform this step a number of times; and
- Take the average over all such paths to obtain the value.

The algorithm looks at a price path, determines the optimal schedule, and obtains the value. This is not the case in practice. The problem here is that in reality, all the decisions are not made simultaneously. On this sample path, one cannot implement the rolling intrinsic hedge strategy. If you were required to be delta neutral, this would require that any gas injected into the ground has a corresponding sale out in the future, but one could change the timing of the sale anytime before the gas was actually withdrawn from the ground. In conclusion, the Monte Carlo simulation fails to capture the true dynamics of storage valuation.

#### Probability Tree Method

The probability tree method is the most rigorous among all the methods, and also the most difficult to implement. The probability tree method uses the following inputs:

- Forward prices;
- Forward volatilities;
- Tree parameters.

The first step in this process is construction of a probability tree consistent with the forward price curve and the forward volatility curve. If one were using this tree to price a forward contract, one should get the same price as the forward price used as an input. If one used this tree to value a simple option— *i.e.*, call, put or straddle—one should get the same price as one would get pricing such an option using the implied volatility in the standard Black-Scholes formula.

At this point, the tree consists of a set of nodes (which represent prices) and arcs that represent the transition probabilities of moving from one node to another. The next step is to define at each node a set of inventory states that represent the level of inventory at that node, *i.e.*, price/time period, to create a forest. A transition from one inventory state to another represents an injection or withdrawal depending on the states. One can then use value the problem on the tree using the stochastic dynamic programming approach.

The underlying mathematics in most probability tree models (and most spread option and Monte Carlo methods as well) assumes that the prices of the asset being studied follows a geometric Brownian motion. The Brownian motion