### Mathematical models

Together with long term bilateral contrac=
ts, other - possibly additional - ways of managing =
various risks can be considered by a producer. Indeed he can also buy or se=
ll financial instruments, such as derivatives. The simplest form of derivat=
ives are the call and the put which may be specialized for the electricity commodity. They tipically gi=
ve the right (but not the obligation) to sell or buy a certain amount of en=
ergy at a given price. The price of this option is the strike price. =
Other, more sophisticated, options do exist, for instance a combination of =
both usually named a collar or other such as s=
wing options. In choosing this options, two fundamental problems arise:

- from the selling side, the pricing, i.e. how much is the value of=
the instrument.
From the buying side, the portfolio optimization, i.e. given a=
set of proposed derivatives, decide which one to buy and if/when to exerci=
se them.

### Modeling and alg=
orithmic considerations

The pricing problem can be solved in a closed form with the well-known <=
a href=3D"https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model" class=
=3D"external-link" rel=3D"nofollow">Black and Sholes (B&S) approach=
that has been criticized by various authors. However in the c=
ontext of the electricity market more advanced pricing models may be useful=
. A recent and interesting approach is based on robust optimization models.=
Indeed, as the classical B&S approach, the option pricing problem is t=
o replicate an option with a portfolio of underlying (available) securities=
in each possible scenario, and therefore the robust valuation scheme propo=
sed by some author is natural and conceptually sound. Therefore one ca=
n use manageable robust optimisation linear programming problems, based on =
a dynamic hedging strategy with a portfolio of electricity futures contract=
s and cash (risk-free asset). The model can be used to find a risk-free bid=
(buyer's) price of the swing option.

**Contributor**

Dr Fabrizio Lacalandra, QuanTek

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