372 research outputs found
Utility indifference pricing and hedging for structured contracts in energy markets
In this paper we study the pricing and hedging of structured products in
energy markets, such as swing and virtual gas storage, using the exponential
utility indifference pricing approach in a general incomplete multivariate
market model driven by finitely many stochastic factors. The buyer of such
contracts is allowed to trade in the forward market in order to hedge the risk
of his position. We fully characterize the buyer's utility indifference price
of a given product in terms of continuous viscosity solutions of suitable
nonlinear PDEs. This gives a way to identify reasonable candidates for the
optimal exercise strategy for the structured product as well as for the
corresponding hedging strategy. Moreover, in a model with two correlated
assets, one traded and one nontraded, we obtain a representation of the price
as the value function of an auxiliary simpler optimization problem under a risk
neutral probability, that can be viewed as a perturbation of the minimal
entropy martingale measure. Finally, numerical results are provided.Comment: 32 pages, 5 figure
Optimal installation of renewable electricity sources: the case of Italy
Starting from the model in Koch-Vargiolu (2019), we test the real impact of
current renewable installed power in the electricity price in Italy, and assess
how much the renewable installation strategy which was put in place in Italy
deviated from the optimal one obtained from the model in the period 2012--2018.
To do so, we consider the Ornstein-Uhlenbeck (O-U) process, including an
exogenous increasing process influencing the mean reverting term, which is
interpreted as the current renewable installed power. Using real data of
electricity price, photovoltaic and wind energy production from the six main
Italian price zones, we estimate the parameters of the model and obtain
quantitative results, such as the production of photovoltaic energy impacts the
North zone, while wind is significant for Sardinia and the Central North zone
does not present electricity price impact. Then we implement the solution of
the singular optimal control problem of installing renewable power production
devices, in order to maximize the profit of selling the produced energy in the
market net of installation costs. We extend the results of \cite{KV} to the
case when no impact on power price is presented, and to the case when
players can produce electricity by installing renewable power plants. We are
thus able to describe the optimal strategy and compare it with the real
installation strategy that was put in place in Italy
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