
\newcommand{\thistitle}{Lecture 5: Energy Trading}

\input{title.tex}


\section{Introduction to Energy Trading}



\begin{frame}
  \frametitle{What is energy trading?}

  \alert{Trading} is buying and selling, i.e. exchanging commodities.

  A \alert{commodity} is a homogeneous product – uniform and standardised.

  Examples of commodities: agricultural (wheat, coffee), metals (gold, steel) etc.

  Examples of energy commodities: electricity, natural gas, crude oil, LNG, coal.

  Related markets: freight, CO2 emission allowances.

  Distinguish between \alert{underlying} commodity and
  \alert{derivatives} (e.g. futures, forwards, options, swaps) that
  \alert{derive} their value from the underlying assets.

  Energy trading has parallels to financial markets (shares, bonds and
  other financial instruments) – even with its particularities due to
  the physical nature of electricity (gas/oil/coal etc.) as
  underlying.


\end{frame}

\begin{frame}
  \frametitle{Energy versus financial markets}

  Future prices cannot be predicted based on historical prices.

  The best prediction of tomorrow's price $p_{t+1}$ is today's price $p_t$.

  The unique reason for a change in price is arrival of ``news'' not correlated with information available at time $t$.

  Transparency (availability of information to all market participants) is a crucial prerequisite for efficient market functioning.

\end{frame}


\begin{frame}
  \frametitle{Trading forms: Exchange versus OTC}

  \begin{columns}[T]
    \begin{column}{7cm}
  \alert{Mediated trading}: pool or exchange

  \begin{itemize}
  \item   organised auction resulting in a uniform price
  \item  highly standardised products; no room for negotiation
    \item transparency
\item  regulated
\item  clearing and colateral costs
  \end{itemize}
    \end{column}
        \begin{column}{7cm}
  \alert{Bilateral trading}: over-the-counter (OTC)
  \begin{itemize}
  \item  intermediation cost (opportunity cost or broker fee)
    \item individual prices agreed between pairs of buyers and sellers
  \item ($\sim$ pay-as-bid principle)
  \item  standard framework agreements: EFET/GTMA; ISDA; DRV etc.
  \item unregulated
  \end{itemize}
        \end{column}
  \end{columns}

  \vspace{.5cm}

  Typically: Combination of exchange and OTC trading.
\end{frame}

\begin{frame}
  \frametitle{What is a trading product?}

  A \alert{trading product} is combination of transaction features:

    \ra{1.1}
  \begin{table}[!t]
    \begin{tabular}{ll}
      \toprule
      Feature & example \\
      \midrule
    \alert{Underlying asset} & electricity \\
    \alert{Delivery point} & TSO control area \\
    \alert{Delivery period} & start date / end date \\
    \alert{Delivery amount} & contract capacity [MW] / contract quantity [MWh] \\
      \bottomrule
    \end{tabular}
  \end{table}

  A \alert{bid} (offer to buy) or \alert{ask} (offer to sell) is characterised by: product, price, trading day and time.

\end{frame}



\begin{frame}
  \frametitle{Product types}

  \alert{Physical vs. Financial}
  \begin{itemize}
  \item   Physical product implies physical delivery of the underlying (i.e. electricity).
 \item Financial product implies exchange of cash without physical delivery (no set-up with TSO required) $\to$ Swap.
  \end{itemize}

  \alert{Fixed-price vs. floating price (index-based)}
  \begin{itemize}
  \item  Fixed price is stated as an amount of money per unit of underlying.
    \item Floating price is determined by reference to a price index publication at a time point after deal conclusion.
  \end{itemize}
  \alert{Fixed-amount vs. options}
\end{frame}

\section{Submarkets and trading forms}

\begin{frame}
  \frametitle{Energy sub-markets}

    \centering
  \includegraphics[height=7.5cm]{energy-sub_markets.png}



\end{frame}




\begin{frame}
  \frametitle{Energy sub-markets: detail for electricity}

    \centering
  \includegraphics[height=7.5cm]{energy-sub_markets-detail.png}


\end{frame}


\begin{frame}
  \frametitle{Electricity product types based on delivery period}

    \centering
  \includegraphics[height=7.5cm]{elec_products_delivery.png}

  \source{Energy Brainpool}
\end{frame}


\begin{frame}
  \frametitle{Sample power purchase portfolio}

  Standardised futures do not match with typical load schedules.

    \centering
  \includegraphics[height=6.8cm]{elec_non_matching.png}

\end{frame}


\begin{frame}
  \frametitle{Portfolio management of a power retailer}

      \centering
  \includegraphics[height=7.5cm]{elec_gaps.png}

\end{frame}

\begin{frame}
  \frametitle{Day-ahead contracts for single hours}

    \centering
  \includegraphics[height=7.5cm]{portfolio_matching.png}
\end{frame}

\begin{frame}
  \frametitle{Trading volumes for base are higher than peak; NB: effect of crisis}

    \centering
  \includegraphics[height=7.5cm]{handelsvolumen-base-peak.jpg}


\source{\hrefc{https://twitter.com/LionHirth/status/1585536456038178818}{Lion Hirth, 2022}}

\end{frame}

\begin{frame}
  \frametitle{EPEX Spot Day-ahead auction}

  A \alert{spot market} is so-called because delivery is ``on the spot'' i.e. now, as opposed to futures.

  The EPEX Spot day-ahead auction has the following features:

  \begin{itemize}
    \item Double-sided auction: bid and ask order book (order book trading)
    \item Uniform price auction: market clearing price for each product (hour or block)
    \item Hourly contracts and blocks (base, peak etc.)
    \item Occurs daily at 12h for delivery on the following day (0-24h) (i.e. \alert{day-ahead})
    \item Price publication time: asap from 12:42h
    \item Volume tick (min order amount/amount increment): 0.1 MWh
      \item Min price: -500 €/MWh; Max price: 4000 €/MWh

  \end{itemize}
\end{frame}

\begin{frame}[fragile]
  \frametitle{Supply-Demand Curve Real Example}

  At \hrefc{https://www.epexspot.com/en/market-data?market_area=AT&trading_date=2020-06-04&delivery_date=2020-06-05&underlying_year=&modality=Auction&sub_modality=DayAhead&product=60&data_mode=aggregated&period=}{epexspot.com} you can find the real supply-demand curves for every hour, here's an old example for Germany-Austria from 2017:

  \centering
    \includegraphics[width=9cm]{DEAT-170531-14}

\end{frame}

\begin{frame}[fragile]
  \frametitle{Product description}


  \centering
    \includegraphics[height=7.5cm]{epex_product_1.png}


  \source{\hrefc{https://www.epexspot.com/en/product-info/auction/germany-luxembourg}{epexspot.com}}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Product description}


  \centering
    \includegraphics[height=7.5cm]{epex_product_2.png}


  \source{\hrefc{https://www.epexspot.com/en/product-info/auction/germany-luxembourg}{epexspot.com}}
\end{frame}

\begin{frame}[fragile]
  \frametitle{EPEX spot day results}


  \centering
  \includegraphics[height=7.5cm]{epex_day.png}

\end{frame}

\begin{frame}[fragile]
  \frametitle{Not all power is traded on the day-ahead}

  Only around a third of consumed electricity in Germany is traded on the day-ahead spot market. Here are the day-ahead volumes:

  \centering
  \includegraphics[height=5.5cm]{graph-day-ahead-2021.jpg}


  \raggedright
  The rest is traded over the counter (OTC) or on the intraday market.


  \source{\hrefc{https://www.epexspot.com/en/tradingproducts}{epexspot.com}}

\end{frame}

\begin{frame}[fragile]
  \frametitle{Intraday market}

  The \alert{intraday market} reflects a growing need for flexibility close to delivery due to uncertain forecasts for demand and variable renewables.

  The intraday market serves for adjusting trading positions based on corrected forecasts closer to real-time.

  Products:
  \begin{itemize}
    \item uniform price auction for 15-min products; daily at 3 pm (D-1)
      \item continuous intraday market up to delivery for hourly/15-min products
  \end{itemize}

  Continuous: as soon as two entered bid and ask orders match, the trade is executed (cf. shares and bitcoin trading).

\end{frame}

\begin{frame}[fragile]
  \frametitle{Intraday market}

    \centering
  \includegraphics[height=7.5cm]{intraday-brochure.png}

  \source{\hrefc{https://www.epexspot.com/sites/default/files/2021-05/21-03-15_Trading Brochure.pdf}{EPEX Spot brochure}}
\end{frame}


\begin{frame}[fragile]
  \frametitle{Intraday market volumes have been increasing}

  \centering
  \includegraphics[height=7.5cm]{intraday-volumes.png}


  \source{\hrefc{https://www.epexspot.com/en/tradingproducts}{epexspot.com}}

\end{frame}

\section{Balance group concept}

\begin{frame}
  \frametitle{Balancing group: Linking the virtual and physical worlds}
  A \alert{balancing group} (BG) is a virtual energy volume account associated with one or more grid users within a control area.
  \begin{itemize}
  \item   each grid connection point is allocated to one balancing group
  \item example: electricity supplier for a group of customers, or power plant
 \item   \alert{balance responsible party} (BRP) is responsible for balancing its BG's saldo (feed-in and consumption) for each 15 min – incl. through trading on spot markets
  \item   deviations are penalised by imbalance fees
  \end{itemize}
  \begin{columns}[T]
    \begin{column}{3cm}
      \vspace{1cm}
  Analogy to a bank account:
  \end{column}
  \begin{column}{9cm}
  \begin{table}[!t]
    \begin{tabular}{ll}
      \toprule
      TSO & Bank \\
      \midrule
Balance responsible party & Account holder \\
EIC & Account number \\
  Balancing group & Bank account \\
  Energy delivers & Payments\\
      \bottomrule
    \end{tabular}
  \end{table}
  \end{column}
  \end{columns}
\end{frame}


\begin{frame}
  \frametitle{Balancing group: Linking the virtual and physical worlds}

  Trading on transmission grid level, i.e. performing delivery by scheduling to TSO, assumes no physical restrictions within a market area.

  Depending on the nature and composition of a balancing group, the BGR transmits to the TSO forecasted load or generation and/or buy and sell amounts.

  Imbalance fee is uniform for the control area (in Germany: for all four control areas), symmetric and based on actual activation of control power.

  Schedule is power per time
  unit exchanged between
  BCs, fed into or consumed
  from the grid.

    \centering
  \includegraphics[height=3.5cm]{balancing_group.jpg}

\end{frame}

\begin{frame}
  \frametitle{Market roles and processes at TSO level}

    \centering
  \includegraphics[height=7.5cm]{bg-tso.png}

\end{frame}


\begin{frame}
  \frametitle{Market roles and processes at DSO level}

    \centering
  \includegraphics[height=7.5cm]{bg-dso.png}

\end{frame}


\begin{frame}
  \frametitle{Tasks of the balancing group management}

    \centering
  \includegraphics[height=7.5cm]{bg-timeplan.png}

\end{frame}


\begin{frame}
  \frametitle{Reasons for imbalances}
  \begin{itemize}
  \item Unplanned outage of generation units
 \item Unplanned outage or activation of large loads
  \item Forecast gap in variable RES generation
   \item Inaccurate forecast of demand
  \end{itemize}
\end{frame}

\section{Futures, options and hedging}


\begin{frame}
  \frametitle{Trading motives and trader types}

  Trader categories:

  \begin{itemize}
  \item  \alert{asset-backed} – trade to optimise assets / hedge price risk
  \item  \alert{merchant / proprietary} – trade to speculate / gamble
  \end{itemize}


  Generators have a natural net \alert{long position}: their value increases with rising prices.

  Final consumers have a natural net \alert{short position}: they benefit from falling prices.

  Marketers who buy and resell power can be long or short.

  Generators are exposed to volatile fuel prices / fixed selling prices.

  Retailers are exposed to volatile purchase prices / fixed selling prices.
\end{frame}

\begin{frame}
  \frametitle{Trading strategies: Managing price risk}

  \alert{Risk} is a source of \alert{uncertainty} about the future, that could involve a \alert{potential loss}.

  E.g. our business model depends on future prices for what we sell and our material inputs, on interest rates, on demand, on political developments.

  There is a fundamental tradeoff between risk and return.

  E.g. for a higher risk, we expect a higher return to offset the possibility of loss.

  Risk management is identifying and analysing risks and deciding if to accept or mitigate uncertainty.

  The goal is to achieve an optimal risk-return profile of a portfolio.

\end{frame}



\begin{frame}
  \frametitle{Purpose of hedging}

  Hedging is reducing risk (i.e. uncertainty) by taking a position that offsets the risk of the existing position (equal and opposite exposure to the same underlying asset).
  Hedging limits a potential loss and reduces a potential profit.

  Final consumers (industrial and commercial), typically, lack trading capability and sufficient market insight and resort to hedging for better cost planning.

  Traders hedge positions that they are not able or willing to close (e.g. long-term supply contract at a fixed price).

  Generators like wind and solar projects may hedge the price risk via long-term fixed-price power purchase agreements (PPA) to facilitate financing.
\end{frame}


\begin{frame}
  \frametitle{Energy sub-markets: futures and forwards}

  A \alert{forward contract} is a non-standardized contract between two parties to
  buy or to sell an asset at a specified future time at a price agreed upon today. They are bilateral and not exchange-traded.

  A \alert{futures contract} is a standardized contract between two parties to
  buy or sell a specified asset of standardized quantity and quality for a price
  agreed upon today with delivery and payment occurring at a specified future
  date. They are traded on an exchange.


  In 98\% of cases physical delivery of energy futures does not take
  place, and the futures contract is closed financially or by buying or selling
  another futures contract on or near the delivery date.

  The forward and futures markets are key markets for trading,
  speculation, and risk management, allowing market participants
  opportunities to manage or \alert{hedge} price risks.

  In electricity, around 80-90\% of power needs of retailers and other
  consumers are secured through futures and forwards. Less than 20\%
  is covered by the spot market.

\end{frame}


\begin{frame}
  \frametitle{Long and short positions}

  An entity is \alert{long} on a commodity if it benefits from a price increase.

  Example: a generator is long on electricity, since they hope electricity prices will rise.

  An entity is \alert{short} on a commodity if it benefits from a price decrease.

  Example: an electricity consumer is short on electricity, since they hope prices with drop.


  A marketer who buys and resells power can be either long or short. If they have bought fixed-price power before finding a market for that power they are long; if they have sold fixed-price power before securing supply they are short.

\end{frame}



\begin{frame}
  \frametitle{Pricing futures}

  The price of a futures contract is a function of:
  \begin{itemize}
  \item the underlying asset's spot price
  \item interest rates
  \item storage costs
    \item expectations of future supply and demand conditions
  \end{itemize}

  Most important is the current price of the underlying cash commodity.

  Even though actual delivery is quite rare, the possibility of delivery provides the critical link
  between spot and futures markets, enabling arbitragers to profit when prices get too far out
  of line.

  \source{\href{https://eta-publications.lbl.gov/sites/default/files/report-lbnl-41098.pdf}{Stoft et al, 1998}}
\end{frame}


\begin{frame}
  \frametitle{Pricing futures: example}

  A firm expects to need 1000 barrels of oil in 6 months' time. The
  firm can either buy the commodity today and store it for 6 months
  (``buy and store'' approach) or purchase a futures contract for
  delivery in 6 months.

  Suppose the futures price for delivery in 6 months is \$~18/barrel.

  What does ``buy and store'' cost? Spot price today is \$~16/barrel, storage for 6 months is \$~1/barrel and the interest rate is 10\%. Total cost:

    \ra{1.1}
  \begin{table}[!t]
    \begin{tabular}{rl}
      \toprule
      \$ 16.00 & spot price \\
      \$ 0.80 & opportunity cost of investment (\$ 16 $\cdot$ 10\% $\cdot$ 0.5 years) \\
      \$ 1.00 & storage cost\\
      \midrule
      \$ 17.80 & total\\
      \bottomrule
    \end{tabular}
  \end{table}

  $\Rightarrow$ Firm should choose ``buy and store'' approach. Firm could do this for more barrels, then sell a futures contract for riskless profit. If too many firms do this, price of future will come down.

  \source{\href{https://eta-publications.lbl.gov/sites/default/files/report-lbnl-41098.pdf}{Stoft et al, 1998}}
\end{frame}


\begin{frame}
  \frametitle{How electricity generators and consumers use futures to hedge}

  An entity with a long position in the electricity market (e.g. generator) can hedge by selling a future.

  An entity with a short position (e.g. consumer) can hedge by buying a future.

  E.g. if a generator has a marginal cost of 15~\euro/MWh, they may
  choose to sell a future for next month with a price of 20~\euro/MWh
  to lock-in a profit now. By avoiding a loss, they forgo potential
  profit if the spot price is higher than 20~\euro/MWh.

  The generator now has a \alert{short futures position}, i.e. they profit from the future when prices decline below 20~\euro/MWh.

  If a consumer has a marginal benefit of 100~\euro/MWh, they may choose to buy a future with a price of 20~\euro/MWh to lock in the benefit. They forgo benefit if the spot price is lower than 20~\euro/MWh.

  The consumer now has a \alert{long futures position}, i.e. they profit from the future when prices go above 20~\euro/MWh.


\end{frame}

\begin{frame}
  \frametitle{How electricity generators and consumers use futures to hedge}

  Hedgers mitigate risk by taking opposite positions in the physical and futures markets.

    \centering
  \includegraphics[height=5.5cm]{hedging-strategy.png}

  \raggedright
  With a \alert{perfect hedge} the magnitude of the corresponding gains
  and losses in the physical and futures positions will be exactly the
  same.

  \source{\href{https://eta-publications.lbl.gov/sites/default/files/report-lbnl-41098.pdf}{Stoft et al, 1998}}
\end{frame}



\begin{frame}
  \frametitle{Generator hedges price risk}

  \begin{columns}[T]
    \begin{column}{7cm}

  Consider a generator with linear cost function $C(Q) = MC\cdot Q$, capacity $Q \leq Y$.

  It maximises profit:
  \begin{equation*}
    \Pi_G(Q,P) = P \cdot Q - MC \cdot Q
  \end{equation*}
  If $P < MC$ it doesn't run $Q=0$ and if $P > MC$ it runs at maximum capacity $Q = Y$.

\begin{tikzpicture}[
    scale=1.1,
    demand/.style={blue, thick},
    supply/.style={red, thick},
    axis/.style={very thick, ->, >=stealth', line join=miter},
    important line/.style={thick}, dashed line/.style={dashed, thin},
    every node/.style={color=black},
    dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,
      outer sep=-1pt},
  ]
  % axis
  \draw[axis,<->] (2.5,0) node(xline)[right] {$P$ [\euro/MWh]} -|
  (0,1.5) node(yline)[above] {$\Pi$ [\euro/MWh]};
  % demand-supply diagram
  \draw[supply] (0,0) -- (1.5,0) node[below] {$MC$} -- (2.5,1);

  \draw[decorate,decoration={brace},thick] (0,0.1) -- (1.48,0.1);
  \node[above] at (0.75,0.2) {$Q = 0$};
  \draw[decorate,decoration={brace},thick] (1.52,0.1) -- (2.5,1.1);
  \node[left] at (2.05,0.8) {$Q = Y$};
\end{tikzpicture}

 For the sale of its generation, it has a \alert{long} position (i.e. benefits from high $P$).
    \end{column}
    \begin{column}{7cm}

      If it had sold a future for quantity $X$ at price $F$, it
      must settle the future based on the current spot market price
      $P$. Its total income from the future is now:
      \begin{equation*}
        \Pi_F(P) = F \cdot X - P \cdot X
      \end{equation*}

\begin{tikzpicture}[
    scale=1.1,
    demand/.style={blue, thick},
    supply/.style={red, thick},
    axis/.style={very thick, ->, >=stealth', line join=miter},
    important line/.style={thick}, dashed line/.style={dashed, thin},
    every node/.style={color=black},
    dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,
      outer sep=-1pt},
  ]
  % axis
  \draw[axis,<->] (2.5,0) node(xline)[right] {$P$ [\euro/MWh]} -|
  (0,1.5) node(yline)[above] {$\Pi_F$ [\euro/MWh]};
  % demand-supply diagram
  \draw[supply] (0,1) node[left] {$F$} -- (1,0) node[below] {$F$} -- (1.5,-0.5);
\end{tikzpicture}

  For the future it has a \alert{short} position (i.e. benefits from low $P$).

    \end{column}
  \end{columns}

\end{frame}

\begin{frame}
  \frametitle{Futures allow to hedge without distorting real-time incentives}

  Combining the generation income with the future, the generator maximises net income:
  \begin{equation*}
    \Pi_{G+F}(Q,P) = P \cdot Q - MC \cdot Q +  F\cdot X - P \cdot X
  \end{equation*}
  NB: The future only affects the original profit function $\Pi_G(Q,P)$ by a constant that doesn't depend on output $Q$, so its behaviour is still the same! Its real-time incentives remain: if $P < MC$ then don't run $Q=0$ and if $P > MC$ then run at $Q=Y$.  \alert{Futures do not distort real-time incentives.}

  \begin{columns}[T]
    \begin{column}{6cm}
      \vspace{.5cm}
  If the future quantity is equal to the generator's capacity $X=Y$ then the generator is perfectly hedged and can even benefit when prices go below $MC$:
    \end{column}
  \begin{column}{7cm}

    \centering
\begin{tikzpicture}[
    scale=1.1,
    demand/.style={blue, thick},
    supply/.style={red, thick},
    axis/.style={very thick, ->, >=stealth', line join=miter},
    important line/.style={thick}, dashed line/.style={dashed, thin},
    every node/.style={color=black},
    dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,
      outer sep=-1pt},
  ]
  % axis
  \draw[axis,<->] (2.5,0) node(xline)[right] {$P$ [\euro/MWh]} -|
  (0,2) node(yline)[above] {$\Pi_{G+F}$ [\euro/MWh]};
  % demand-supply diagram
  \draw[supply] (0,1.5) node[left] {$F$} -- (1,0.5) -- (2.5,0.5);

  \draw[dashed line]
  (0,0.5)-- (1,0.5) -- (1,0);


  \node[below] at (1,0) {$MC$};
  \node[left] at (0,0.5) {$F-MC$};
  \draw[decorate,decoration={brace},thick] (0.05,1.55) -- (0.98,0.62);
  \node[right] at (0.5,1.2) {$Q = 0$};
  \draw[decorate,decoration={brace},thick] (1.02,0.6) -- (2.5,0.6);
  \node[above] at (1.75,0.6) {$Q = X$};
\end{tikzpicture}

  \end{column}
  \end{columns}
\end{frame}





\begin{frame}
  \frametitle{Consumer hedges price risk}

  \begin{columns}[T]
    \begin{column}{7cm}


  Considerations are similar for consumers. Assume a linear benefit function $B(Q) = MB\cdot Q$, consumption capacity $Q \leq Y$.

  It maximises net benefit:
  \begin{equation*}
    \Pi_B(Q,P) =  MB \cdot Q - P \cdot Q
  \end{equation*}
  If $P > MB$ it doesn't consume $Q=0$ and if $P < MB$ it consumes at max capacity $Q = Y$.

\begin{tikzpicture}[
    scale=1.1,
    demand/.style={blue, thick},
    supply/.style={red, thick},
    axis/.style={very thick, ->, >=stealth', line join=miter},
    important line/.style={thick}, dashed line/.style={dashed, thin},
    every node/.style={color=black},
    dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,
      outer sep=-1pt},
  ]
  % axis
  \draw[axis,<->] (2.5,0) node(xline)[right] {$P$ [\euro/MWh]} -|
  (0,1.8) node(yline)[above] {$\Pi_B$ [\euro/MWh]};
  % demand-supply diagram
  \draw[supply] (0,1.5) node[left]{$MB$} -- (1.5,0) node[below] {$MB$} -- (2.5,0);

  \draw[decorate,decoration={brace},thick] (0.05,1.55) -- (1.48,0.12);
  \node[right] at (0.75,1.2) {$Q = X$};
  \draw[decorate,decoration={brace},thick] (1.52,0.1) -- (2.5,0.1);
  \node[above] at (2,0.2) {$Q = 0$};
\end{tikzpicture}

 For energy consumption, it is \alert{short}.
    \end{column}
    \begin{column}{7cm}

      If it had bought a future for quantity $X$ at price $F$, it
      would receive on expiry the current spot market price
      $P$. Its total income from the future is now:
      \begin{equation*}
        \Pi_F(P) = -F \cdot X  + P \cdot X
      \end{equation*}

      \centering
\begin{tikzpicture}[
    scale=1.1,
    demand/.style={blue, thick},
    supply/.style={red, thick},
    axis/.style={very thick, ->, >=stealth', line join=miter},
    important line/.style={thick}, dashed line/.style={dashed, thin},
    every node/.style={color=black},
    dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,
      outer sep=-1pt},
  ]
  % axis
  \draw[axis,<->] (1.5,0) node(xline)[right] {$P$ [\euro/MWh]} -|
  (0,1.5) node(yline)[above] {$\Pi_F$ [\euro/MWh]};
  % demand-supply diagram
  \draw[supply] (0,-0.5) node[left] {$-F$} -- (0.5,0) node[below] {$F$} -- (1.5,1);
\end{tikzpicture}

  \raggedright
  For the future it has a \alert{long} position (i.e. benefits from high $P$).

    \end{column}
  \end{columns}

\end{frame}




\begin{frame}
  \frametitle{Futures allow to hedge without distorting real-time incentives}

  Combining the consumption net income with the future, the consumer maximises net benefit:
  \begin{equation*}
    \Pi_{B + F}(Q,P) = MB \cdot Q - P \cdot Q +  -F\cdot X + P \cdot X
  \end{equation*}
  NB: The future only affects the original profit function $\Pi_B(Q,P)$ by a constant that doesn't depend on $Q$, so its behaviour is still the same! Its real-time incentives remain: if $P > MB$ then don't consume $Q=0$ and if $P < MB$ then consume at $Q=Y$. \alert{Futures do not distort real-time incentives.}

  \begin{columns}[T]
    \begin{column}{6cm}
      \vspace{.5cm}
  If the future quantity is equal to the consumer's capacity $X=Y$ then the consumer is perfectly hedged and can even benefit when prices go above $MB$:
    \end{column}
  \begin{column}{7cm}

    \centering
\begin{tikzpicture}[
    scale=1.1,
    demand/.style={blue, thick},
    supply/.style={red, thick},
    axis/.style={very thick, ->, >=stealth', line join=miter},
    important line/.style={thick}, dashed line/.style={dashed, thin},
    every node/.style={color=black},
    dot/.style={circle,fill=black,minimum size=4pt,inner sep=0pt,
      outer sep=-1pt},
  ]
  % axis
  \draw[axis,<->] (2.5,0) node(xline)[right] {$P$ [\euro/MWh]} -|
  (0,2) node(yline)[above] {$\Pi_{B+F}$ [\euro/MWh]};
  % demand-supply diagram
  \draw[supply] (0,0.5) node[left] {$MB-F$} -- (1.5,0.5) -- (2.5,1.5);

  \draw[dashed line]
  (1.5,0.5) -- (1.5,0);


  \node[below] at (1.5,0) {$MB$};
  \draw[decorate,decoration={brace},thick] (0,0.6) -- (1.48,0.6);
  \node[above] at (0.75,0.6) {$Q = X$};
  \draw[decorate,decoration={brace},thick] (1.55,0.6) -- (2.5,1.55);
  \node[left] at (2,1.2) {$Q = 0$};
\end{tikzpicture}

  \end{column}
  \end{columns}
\end{frame}





\begin{frame}
  \frametitle{End of futures contract}

  When a futures contract ends you have three options:
  \begin{itemize}
    \item \alert{Settle} the contract by providing the underlying service (physical settlement, e.g. electricity) or cash (financial settlement).
    \item \alert{Offset} position by taking out opposite and equal transaction. E.g. if you sold 2 futures for September, need to buy 2 futures for September. The difference in price between initial and offset position is the profit/loss on trade.
    \item \alert{Rollover}, i.e. offset existing position, buy future for next period. When rolling forward, a trader will simultaneously offset their current position and establish a new position in the next contract month.
  \end{itemize}

  Electricity futures can also \alert{cascade} nearer delivery into shorter-term products.

\end{frame}


\begin{frame}
  \frametitle{Rolling}

  Rolling, i.e. offseting an existing position and buying a future for the next period, enables a trader to maintain the same risk position beyond the initial expiration of the contract.

    \centering
  \includegraphics[height=6cm]{futures-rolling.jpg}

\source{Source: Mack, Energy trading and risk management, 2014}

\end{frame}

\begin{frame}
  \frametitle{Cascading}

  \alert{Cascading}: At the beginning of the delivery period, the initial product splits into a set of equivalent shorter-term products. Longer maturities cascade into corresponding shorter maturities.  For example, a future for year 2022 will cascade in December 2021 into futures for months Jan, Feb, Mar in 2022 and for quarters 2, 3, 4 in 2022.


    \centering
  \includegraphics[height=4.5cm]{phelix-cascade.jpg}

  \source{\hrefc{https://www.tradingtechnologies.com/xtrader-help/eurex-gateway/configuring-market-data/support-for-phelix-products/}{Trading Technologies}}
\end{frame}

\begin{frame}
  \frametitle{Futures market: price development patterns}

  \alert{Contango}: futures price exceeds the spot price.

  \alert{Backwardation}: spot price exceeds the futures price.

  Market participants are driving the futures price up/down in line with their expectations.

    \centering
  \includegraphics[height=4.5cm]{contango-backwardation.png}

\raggedright
  Since producers are less diversified than consumers, they have higher risk and would tolerate lower futures prices, so we expect backwardation to be the norm.

\source{Source: Mack, Energy trading and risk management, 2014}

\end{frame}


\begin{frame}
  \frametitle{Options}

  An \alert{option} gives the holder the right, but not the obligation, to buy or sell a specified quantity of an underlying on (or before) a specified future date, at a predetermined price.

  Excercising the option is buying or selling the underlying.
  \begin{itemize}
  \item \alert{Call option} is a right to buy.
  \item \alert{Put option} is a right to sell.
  \end{itemize}
  Expiry (expiration/maturity date) is the date on (or until) which the option can be excercised.
  \begin{itemize}
  \item European options can be excercised only at expiry.
  \item American options can be excercised at any time up to expiry.
  \end{itemize}

  \alert{Strike (exercise) price} is the pre-agreed buy or sell price.

  Option \alert{premium} is a fixed amount paid by the holder (option buyer) to the writer (option seller) upon concluding an option.

\end{frame}


\begin{frame}
  \frametitle{Options Pricing}

  Suppose a stock costs \euro~34.80 today. Consider the premiums of particular strike prices for call (right to buy) and put (right to sell) options that expire in 1 month:
  \begin{table}[!t]
    \begin{tabular}{lll}
      \toprule
      Strike Price & Call Option Premium & Put Option Premium \\
      \midrule
      30 & 5.00 & 0.01 \\
      35 & 0.53 & 0.60 \\
      40 & 0.01 & 6.00 \\
      \bottomrule
    \end{tabular}
  \end{table}
  The higher the strike price, the lower the call option premium and the higher the put option premium. For an option expiring in 9 months, premiums are higher since there is more risk:
  \begin{table}[!t]
    \begin{tabular}{lll}
      \toprule
      Strike Price & Call Option Premium & Put Option Premium \\
      \midrule
      30 & 6.85 & 1.17 \\
      35 & 3.70 & 2.83 \\
      40 & 1.75 & 5.55 \\
      \bottomrule
    \end{tabular}
  \end{table}

\end{frame}


\begin{frame}
  \frametitle{Put Option Payoff}

  Suppose we purchase a put option (i.e. right to sell) with an exercise price of \$75 and a premium of \$30. If the spot market price at maturity is less than \$75, we can buy at the lower price, then sell at \$75. If the price is more than \$75 then we do not exercise the option.

    \centering
    \includegraphics[height=5.5cm]{put-payoff.png}

\end{frame}

\begin{frame}
  \frametitle{Put Option Profit}

  But remember we still have to pay the option premium which offset the payoff. We will make a loss if the spot price is below \$45.

  Note that the premium will be higher the higher the exercise price is.

    \centering
    \includegraphics[height=5.5cm]{put-profit.png}
\end{frame}

\begin{frame}
  \frametitle{Put Option Writer Payoff}

  For the writer who sold the option, the payoff is opposite.

    \centering
    \includegraphics[height=5.5cm]{put-writer.png}

\end{frame}



\begin{frame}
  \frametitle{Call Option Payoff}


  Suppose we purchase a call option (i.e. right to buy) with an exercise price of \$125 and a premium of \$30. If the spot market price at maturity is more than \$125, we can buy at \$125 and sell for the higher price.  If the price is less than \$125 then we do not exercise the option.

    \centering
    \includegraphics[height=5.5cm]{call-payout.png}

\end{frame}

\begin{frame}
  \frametitle{Call Option Payoff}

  But the payoff needs to be offset against the premium. We will make a loss if the spot market price is below \$155.

    \centering
    \includegraphics[height=5.5cm]{call-payoff.png}
\end{frame}

\begin{frame}
  \frametitle{Call Option Writer Payoff}



  For the writer who sold the option, the payoff is opposite.

    \centering
    \includegraphics[height=5.5cm]{call-writer.png}

\end{frame}

\begin{frame}
  \frametitle{Further Option Terminology}

  \alert{In-the-money}: positive payoff in case of option excercise.

  \alert{At-the-money}: zero payoff in case of option excercise.

  \alert{Out-of-the-money}: negative payoff in case of option excercise.

  A call option is in-the-money if strike price $<$ spot price.

  A put option is in-the-money if strike price $>$ spot price.

  \vspace{.8cm}

  \alert{NB}: Options allow you to keep choices open.

  \alert{NB}: Options have an asymmetric payoff (unlike perfect hedging with futures).

\end{frame}

\begin{frame}
  \frametitle{Generator hedging with put options}

A power generator uses put options to guarantee a minimum selling price for its generated electricity. Suppose the electricity futures contract price is \$25/MWh. The power generator wishes to receive at least \$25/MWh for the physical sale of power. To accomplish this, the power generator purchases a put option for a premium of \$1/MWh.

    \centering
    \includegraphics[height=5.5cm]{generator-put.jpg}

\source{Source: Mack, Energy trading and risk management, 2014}
\end{frame}
\begin{frame}
  \frametitle{Consumer hedging with call options}

  A power consumer can hedge against price increases by purchasing a call option. Suppose the electricity futures contract price is \$25/MWh. The end user wishes to pay no more than \$25/MWh. To accomplish this, the end user purchases a call option for a premium of \$0.75/MWh.

    \centering
    \includegraphics[height=5.5cm]{consumer-call.jpg}

\source{Source: Mack, Energy trading and risk management, 2014}
\end{frame}



\begin{frame}
  \frametitle{Swaps}


  A forward contract locks in the terms of a single future transaction right now.

  A \alert{swap} is similar, but applies for a \alert{series} of future transactions. E.g. An electricity swap is equivalent to a strip of forward contracts with multiple settlement dates and identical forward price for each settlement.

  It replaces a risky variable floating transaction for a risk-free fixed transaction. Price exposures are \alert{swapped} between the parties.

  E.g. mobile phone fixed monthly contract for unlimited calls.

  Swaps are bilateral and traded over-the-counter (OTC).


\end{frame}

\begin{frame}
  \frametitle{Contracts for Difference and Virtual Power Purchase Agreements}

  \alert{Contracts for Difference} (CfDs) and \alert{Virtual Power
    Purchase Agreements} (VPPAs), common ways of financing renewable
  energy, are financial swaps.

  In a CfD or VPPA agreement, the generator receives a fixed amount per MWh for their electricity (the \alert{strike price}) from the purchaser.

  If the market price is below the strike price, the generators receives the difference from the purchaser; if the market price is above the strike price, the generators pays the difference to the purchaser. Price risk is transferred from the generator to the purchaser.

  Consider a CfD (common in UK for renewables, also used for planned nuclear plant Hinkley Point C) with a strike price of \pounds~50/MWh.

  If the market price is \pounds~20/MWh, the generator receives the difference, \pounds~30/MWh, from the CfD purchaser.

  If the market price is \pounds~100/MWh, the generator pays the difference, \pounds~50/MWh, to the CfD purchaser.

\end{frame}



\begin{frame}
  \frametitle{Contracts for Difference and Virtual Power Purchase Agreements}

  \alert{Contracts for Difference} (CfDs) and \alert{Virtual Power
    Purchase Agreements} (VPPAs), common ways of financing renewable
  energy, are financial swaps.

  In a CfD or VPPA agreement, the generator receives a fixed amount per MWh for their electricity (the \alert{strike price}) from the purchaser.


  \vspace{.3cm}

  \begin{columns}[T]
    \begin{column}{8cm}
    \centering
    \includegraphics[width=8cm]{Strike-Price-Graph-V3.png}
    \end{column}
    \begin{column}{6cm}
  If the market price is below the strike price, the generators receives the difference from the purchaser; if the market price is above the strike price, the generators pays the difference to the purchaser. Price risk is transferred from the generator to the purchaser.
    \end{column}
  \end{columns}

  \source{\hrefc{https://lgegroup.com/contract-for-difference/}{LGEnergy}}

\end{frame}

\end{document}
