45 research outputs found
On the spot-futures no-arbitrage relations in commodity markets
In commodity markets the convergence of futures towards spot prices, at the
expiration of the contract, is usually justified by no-arbitrage arguments. In
this article, we propose an alternative approach that relies on the expected
profit maximization problem of an agent, producing and storing a commodity
while trading in the associated futures contracts. In this framework, the
relation between the spot and the futures prices holds through the
well-posedness of the maximization problem. We show that the futures price can
still be seen as the risk-neutral expectation of the spot price at maturity and
we propose an explicit formula for the forward volatility. Moreover, we provide
an heuristic analysis of the optimal solution for the
production/storage/trading problem, in a Markovian setting. This approach is
particularly interesting in the case of energy commodities, like electricity:
this framework indeed remains suitable for commodities characterized by
storability constraints, when standard no-arbitrage arguments cannot be safely
applied
An optimal trading problem in intraday electricity markets
We consider the problem of optimal trading for a power producer in the
context of intraday electricity markets. The aim is to minimize the imbalance
cost induced by the random residual demand in electricity, i.e. the consumption
from the clients minus the production from renewable energy. For a simple
linear price impact model and a quadratic criterion, we explicitly obtain
approximate optimal strategies in the intraday market and thermal power
generation, and exhibit some remarkable properties of the trading rate.
Furthermore, we study the case when there are jumps on the demand forecast and
on the intraday price, typically due to error in the prediction of wind power
generation. Finally, we solve the problem when taking into account delay
constraints in thermal power production.Comment: 39 pages, 11 figure
A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation
In this paper, we present a probabilistic numerical algorithm combining
dynamic programming, Monte Carlo simulations and local basis regressions to
solve non-stationary optimal multiple switching problems in infinite horizon.
We provide the rate of convergence of the method in terms of the time step used
to discretize the problem, of the size of the local hypercubes involved in the
regressions, and of the truncating time horizon. To make the method viable for
problems in high dimension and long time horizon, we extend a memory reduction
method to the general Euler scheme, so that, when performing the numerical
resolution, the storage of the Monte Carlo simulation paths is not needed.
Then, we apply this algorithm to a model of optimal investment in power plants.
This model takes into account electricity demand, cointegrated fuel prices,
carbon price and random outages of power plants. It computes the optimal level
of investment in each generation technology, considered as a whole, w.r.t. the
electricity spot price. This electricity price is itself built according to a
new extended structural model. In particular, it is a function of several
factors, among which the installed capacities. The evolution of the optimal
generation mix is illustrated on a realistic numerical problem in dimension
eight, i.e. with two different technologies and six random factors
A McKean-Vlasov approach to distributed electricity generation development
This paper analyses the interaction between centralised carbon emissive
technologies and distributed intermittent non-emissive technologies. In our
model, there is a representative consumer who can satisfy her electricity
demand by investing in distributed generation (solar panels) and by buying
power from a centralised firm at a price the firm sets. Distributed generation
is intermittent and induces an externality cost to the consumer. The firm
provides non-random electricity generation subject to a carbon tax and to
transmission costs. The objective of the consumer is to satisfy her demand
while mini\-mising investment costs, payments to the firm and intermittency
costs. The objective of the firm is to satisfy the consumer's residual demand
while minimising investment costs, demand deviation costs, and maximising the
payments from the consumer. We formulate the investment decisions as
McKean-Vlasov control problems with stochastic coefficients. We provide
explicit, price model-free solutions to the optimal decision problems faced by
each player, the solution of the Pareto optimum, and the Stackelberg
equilibrium where the firm is the leader. We find that, from the social
planner's point of view, the carbon tax or transmission costs are necessary to
justify a positive share of distributed capacity in the long-term, whatever the
respective investment costs of both technologies are. The Stackelberg
equilibrium is far from the Pareto equilibrium and leads to an over-investment
in distributed energy and to a much higher price for centralised energy
Numerical investigations on global error estimation for ordinary differential equations
AbstractFour techniques of global error estimation, which are Richardson extrapolation (RS), Zadunaisky's technique (ZD), Solving for the Correction (SC) and Integration of Principal Error Equation (IPEE) have been compared in different integration codes (DOPRI5, DVODE, DSTEP). Theoretical aspects concerning their implementations and their orders are first given. Second, a comparison of them based on a large number of tests is presented. In terms of cost and precision, SC is a method of choice for one-step methods. It is much more precise and less costly than RS, and leads to the same precision as ZD for half its cost. IPEE can provide the order of the error for a cheap cost in codes based on one-step methods. In multistep codes, only RS and IPEE have been implemented since they are the only ones whose theoretical justification has been extended to this case. There, RS still provides a more reliable estimation than IPEE. However, as these techniques are based on variations of the global error, irrespective of the numerical method used, they fail to provide any more usefull information once the numerical method has reached its limit of accuracy due to the finite arithmetic
Forward Hedging and Vertical Integration in Electricity Markets.
This paper analyzes the interactions between vertical integration and (wholesale) spot, forward and retail markets in risk management. We develop an equilibrium model that fits electricity markets well. We point out that vertical integration and forward hedging are two separate levers for demand and spot price risk diversification. We show that they are imperfect substitutes as to their impact on retail prices and agents’ utility because the asymmetry between upstream and downstream segments. While agents always use the forward market, vertical integration may not arise. In addition, in presence of highly risk averse downstream agents, vertical integration may be a better way to diversify risk than spot, forward and retail mar kets. We illustrate our analysis with data from the French electricity market.producers; hedging; forward; spot; vertical integration; retailers; electricity markets;
A probabilistic numerical method for optimal multiple switching problems in high dimension
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the regression basis used to approximate conditional expectations, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants in dimension eight, i.e. with two different technologies and six random factors