Method for managing risk in markets related to commodities delivered over a network
View Patent ↗A system, method, software, and portfolios for managing risk in markets relating to a commodity delivered over a network are described, in which a market participant constructs portfolios of preferably liquid price risk instruments in proportions that eliminate the Spatial Price Risk for the market participant's underlying position. Techniques are also disclosed for constructing and evaluating new price risk instruments and other sets of positions, as well as identifying arbitrage opportunities in those markets. In particular, a “deltas vector” is calculated concerning a portfolio of future positions and derivative contracts, wherein the “deltas vector” is the partial derivative of the market participant's net market position taken with respect to the forward shadow prices λ of the network which depend upon congestion in the network. The “deltas vector” can then be used to simplify the valuation of a derivative contract, develop a hedging strategy, evaluate a hedging strategy with respect to congestion, identify a successful bidding strategy at auctions of derivative contracts, and determine an optimal position in a multi-settlement nodal market. Moreover, techniques are also described for evaluating the matrix of Power Transfer Distribution Factors and loss factors (comprising the A matrix) that are needed to estimate the “deltas vector”.
1. A method for calculating a fair market value, at time t 0 , of a locational derivative contract settled at time t T , in a market related to a commodity delivered over a network of one or more congestible lines, the market including at least one traded instrument and future shadow prices which depend on congestion in the one or more congestible lines, the method comprising the steps of:
identifying a fair market value equation for determining the fair market value of the locational derivative contract, wherein the fair market value is based, at least in part, on the future shadow prices, a payoff of the locational derivative contract at time t T and a portfolio, y, in the at least one traded instrument;
a computer system calculating a partial derivative of the fair market value equation with respect to the future shadow prices to obtain a calculated partial derivative;
a computer system solving the calculated partial derivative, for the portfolio y, to minimize any congestion risk associated with the locational derivative contract; and
a computer system generating an indication of the fair market value of the locational derivative contract according to (−y′)(F), where F represents the corresponding price of the at least one traded instrument,
wherein y′ denotes a transpose of y.
2. The method according to claim 1 , wherein the calculated partial derivative is a vector δ and the future shadow prices are a vector λ having the same cardinality as δ, such that each element of δ, δ i , corresponds to the partial derivative of the fair market value equation with respect to a respective element of λ, λ i .
3. The method of claim 2 , wherein the step of solving includes the step of:
setting the calculated partial derivative equal to zero and solving for y.
4. The method of claim 2 , wherein the step of solving includes the step of:
identifying that an attempted solution results in a set of overdetermined equations; and
setting a subset of the elements of λ equal to zero and solving for y.
5. The method of claim 2 , wherein the step of solving includes the step of:
identifying that an attempted solution results in a set of overdetermined equations; and
solving for y using a least-squares method.
6. The method according to claim 1 , further comprising the step of:
generating an indication of risk to congestion for the locational derivative contract based on the calculated partial derivative and the fair market value.
7. The method of claim 1 , wherein the locational derivative contract is one of a Transmission Congestion Contract, (“TCC”), TCC option with a zero strike price, TCC option with a non-zero strike price, portfolio of TCCs, portfolio of TCC options, seller's choice contracts, portfolios of seller's choice contracts, futures positions, options, portfolio of options, and portfolio of futures positions.
8. The method of claim 1 , wherein the locational derivative contract is a non-liner derivative contract.
9. The method of claim 8 , wherein the locational derivative contract is one of a seller's choice contract and an option.
10. The method of claim 1 , wherein the locational derivative contract is a Transmission Congestion Contract, (“TCC”) option with a non-zero strike price and y comprises a call option at a reference node of the network and a long position in a one-sided TCC portfolio.