### 10.2.1 Financial Transmission Rights

Financial Transmission Rights (FTRs) are financial instruments that entitle the holder to the difference between LMPs at two defined locations. The parameters for an FTR are:

- A "source" node, which we will call node a
- A "sink" node, which we will call node b
- A quantity, in MW, which we will call M.

The holder of an M megawatt FTR from node a to node b is entitled to receive:

M*(LMP_{b} - LMP_{a})

For each hour during the duration of the FTR.

FTRs are typically auctioned off quarterly by the RTO and may have different durations (one-month FTRs versus quarterly FTRs, for example). Most FTRs are structured as obligations, which means that the holder of the FTR gets the difference between the LMPs at node a and node b, no matter whether that difference is positive or negative. If LMP_{b} > LMP_{a} then the holder of the FTR is paid money by the RTO. If LMP_{b} < LMP_{a} then the holder of the FTR must pay the RTO.

Some FTRs may be structured as options that renew every hour, in which case during a given hour the FTR holder would choose to exercise the option only if LMP_{b} > LMP_{a}, i.e. If the payoff would be positive. The payoff from an M-megawatt FTR option from node a to node b would thus be:

Max(0, LMP_{b} - LMP_{a})

FTRs also obey superposition, just like power flows. An M-megawatt FTR defined from a to b and an M-megawatt FTR from b to a will cancel each other out financially (as long as both FTRs are structured as obligations). An M-megawatt FTR from a to b and an M-2 megawatt FTR from b to a would have identical value as a 2 megawatt FTR from a to b.

As financial instruments, FTRs are very similar to swaps. A swap is an agreement to exchange the closing price of two different financial assets. In this case, the "swap" is between two nodes in the power network, not between two different financial assets.

Let's work through a few examples of valuing FTRs. We will use the three-node network in the figure below, where the LMP at node A is $14/MWh, the LMP at node B is $9/MWh and the LMP at node C is $14.50/MWh.

- Example #1: A 5 MW FTR from node A to node C would have a value of 5*($14.50 - $14) = $2.50.
- Example #2: A 5 MW FTR from node A to node B would have a value of 5*($9 - $14) = -$25.
- Example #3: A 5 MW FTR from node A to node C plus a 10 MW FTR from node A to node C would have a value of (5+10)*($14.50 - $14) = $7.50.

Now it is your turn. Show that a 5 MW FTR from node A to node C plus a 2 MW FTR from node C to node A would have a total combined value of $1.50.