#### Gamma

Gamma is one of the market risk Greeks

It measures the sensitivity of the Delta to an underlier or market value

It is of use when the value of the Delta itself varies with the value of the underlier - the Delta being the ratio of the value of the trade or portfolio to the value of an underlier or market value

Detail

A Physical Forward has a delta of approximately one with respect to the physical underlier, that is the value of a trade increases by 1% for every 1% increase in the underlier

By contrast an Option may have a delta of anywhere between -1 and +1, and the delta is not constant

At an underlier price of $20/tonne an Option might have a delta of 0.1, but at$40/tonne the delta might be 0.5

Trades with deltas that are constant are called linear (if we were to plot a graph of value against underlier it would be a straight line, the slope is the delta)

Trades with deltas that change with the value of an underlier are called non-linear (if we were to plot a graph of value against underlier it would be not be straight - the gamma is the measure of curvature of the plot at a particular point on the graph)

As an analogy think of delta as speed, it is the ratio of distance to time. Gamma is acceleration, just knowing the speed of an object doesn't tell us whether it is braking hard, accelerating, or at uniform speed - for that we need the acceleration

Because gamma is the change in delta per unit change of price per unit volume of commodity and delta is dimensionless then Gamma has units of 1 / (Price/Volume) = Volume/Price, e.g. Therms/\$

Some ETRMs use the term Gamma for the change in Exposure per unit change of price per unit volume of commodity and get Volume / (Price/Volume) = Volume2/Price e.g. MWh2/€