`etrm`

is an R package with tools for trading and financial risk management in energy markets. The package currently offer tools for two main activities:

- Construction of forward market curves
- Portfolio insurance trading strategies for energy price risk management

The development version can be installed from GitHub with:

The following sections provide examples using some of the synthetic data sets included in the package.

A typical characteristic of energy commodities such as electricity and natural gas is that delivery takes place over a period in time, not on a single date. Listed futures contracts cover standardized periods, such as “Week”, “Month”, “Quarter”, “Season” or “Year”. The forward curve is an essential tool for pricing non-standard OTC contracts having any settlement period. An example of such standard energy market contracts can be found in the package data set `powfutures130513`

.

```
#> Include Contract Start End Closing
#> 1 TRUE W21-13 2013-05-20 2013-05-26 33.65
#> 2 TRUE W22-13 2013-05-27 2013-06-02 35.77
#> 3 TRUE W23-13 2013-06-03 2013-06-09 36.58
#> 4 TRUE W24-13 2013-06-10 2013-06-16 35.93
#> 5 TRUE W25-13 2013-06-17 2013-06-23 33.14
#> 6 TRUE W26-13 2013-06-24 2013-06-30 34.16
#> 7 FALSE MJUN-13 2013-06-01 2013-06-30 35.35
#> 8 TRUE MJUL-13 2013-07-01 2013-07-31 33.14
#> 9 TRUE MAUG-13 2013-08-01 2013-08-31 35.72
#> 10 TRUE MSEP-13 2013-09-01 2013-09-30 38.41
#> 11 TRUE MOCT-13 2013-10-01 2013-10-31 38.81
#> 12 TRUE MNOV-13 2013-11-01 2013-11-30 40.94
#> 13 FALSE Q3-13 2013-07-01 2013-09-30 35.72
#> 14 TRUE Q4-13 2013-10-01 2013-12-31 40.53
#> 15 TRUE Q1-14 2014-01-01 2014-03-31 42.40
#> 16 TRUE Q2-14 2014-04-01 2014-06-30 33.39
#> 17 TRUE Q3-14 2014-07-01 2014-09-30 31.78
#> 18 TRUE Q4-14 2014-10-01 2014-12-31 38.25
#> 19 TRUE Q1-15 2015-01-01 2015-03-31 40.73
#> 20 TRUE Q2-15 2015-04-01 2015-06-30 32.64
#> 21 TRUE Q3-15 2015-07-01 2015-09-30 30.87
#> 22 TRUE Q4-15 2015-10-01 2015-12-31 37.22
#> 23 FALSE CAL-14 2014-01-01 2014-12-31 36.43
#> 24 FALSE CAL-15 2015-01-01 2015-12-31 35.12
#> 25 TRUE CAL-16 2016-01-01 2016-12-31 34.10
#> 26 FALSE CAL-17 2017-01-01 2017-12-31 35.22
#> 27 FALSE CAL-18 2018-01-01 2018-12-31 36.36
#> 28 FALSE CAL-19 2019-01-01 2019-12-31 37.44
#> 29 FALSE CAL-20 2020-01-01 2020-12-31 38.58
#> 30 FALSE CAL-21 2021-01-01 2021-12-31 39.73
#> 31 FALSE CAL-22 2022-01-01 2022-12-31 40.93
#> 32 FALSE CAL-23 2023-01-01 2023-12-31 42.15
```

The function `msfc()`

will create an instance of the S4 class `MSFC`

with generic methods `plot()`

, `summary()`

and `show()`

. In addition to the arguments from the list of contracts, the user may also provide a prior function to the calculation. This is relevant for markets with strong seasonality, such as power markets. The default value is `prior = 0`

, but the user can provide any vector expressing a belief regarding the market to be combined with the observed prices. In the example below we have used a simple seasonal prior from the package `powpriors130513`

data set.

```
fwd_fut_wpri <- msfc(tdate = as.Date("2013-05-13"), # trading date
include = powfutures130513$Include, # vector with TRUE/FALSE, include contract?
contract = powfutures130513$Contract, # vector with contract names
sdate = powfutures130513$Start, # vector with contract start dates
edate = powfutures130513$End, # vector with contract end dates
f = powfutures130513$Closing, # vector with contract closing prices
prior = powpriors130513$mod.prior # prior function
)
plot(fwd_fut_wpri, legend = "", title = "MSFC with prior for power futures 2013-05-13")
```

The forward curve is calculated with the function

*f*(*t*) = *λ*(*t*) + *ϵ*(*t*)

where *λ*(*t*) is the prior supplied by the user and *ϵ*(*t*) is an adjustment function taking the observed prices into account. The `msfc()`

function finds the smoothest possible adjustment function by minimizing the mean squared value of a spline function, while ensuring that the average value of the curve *f*(*t*) is equal to contract prices used in the calculation for the respective time intervals. The number of polynomials used in the spline along with `head(prior)`

and computed prices based on the curve are available with the `summary()`

method:

```
summary(fwd_fut_wpri)
#> $Description
#> [1] "MSFC of length 1329 built with 41 polynomials at trade date 2013-05-13"
#>
#> $PriorFunc
#> [1] 30.10842 30.16396 30.19572 30.16144 29.06268 28.93272
#>
#> $BenchSheet
#> Include Contract From To Price Comp
#> 1 TRUE W21-13 2013-05-20 2013-05-26 33.65 33.65
#> 2 TRUE W22-13 2013-05-27 2013-06-02 35.77 35.77
#> 3 TRUE W23-13 2013-06-03 2013-06-09 36.58 36.58
#> 4 TRUE W24-13 2013-06-10 2013-06-16 35.93 35.93
#> 5 TRUE W25-13 2013-06-17 2013-06-23 33.14 33.14
#> 6 TRUE W26-13 2013-06-24 2013-06-30 34.16 34.16
#> 8 TRUE MJUL-13 2013-07-01 2013-07-31 33.14 33.14
#> 9 TRUE MAUG-13 2013-08-01 2013-08-31 35.72 35.72
#> 10 TRUE MSEP-13 2013-09-01 2013-09-30 38.41 38.41
#> 11 TRUE MOCT-13 2013-10-01 2013-10-31 38.81 38.81
#> 12 TRUE MNOV-13 2013-11-01 2013-11-30 40.94 40.94
#> 14 TRUE Q4-13 2013-10-01 2013-12-31 40.53 40.53
#> 15 TRUE Q1-14 2014-01-01 2014-03-31 42.40 42.40
#> 16 TRUE Q2-14 2014-04-01 2014-06-30 33.39 33.39
#> 17 TRUE Q3-14 2014-07-01 2014-09-30 31.78 31.78
#> 18 TRUE Q4-14 2014-10-01 2014-12-31 38.25 38.25
#> 19 TRUE Q1-15 2015-01-01 2015-03-31 40.73 40.73
#> 20 TRUE Q2-15 2015-04-01 2015-06-30 32.64 32.64
#> 21 TRUE Q3-15 2015-07-01 2015-09-30 30.87 30.87
#> 22 TRUE Q4-15 2015-10-01 2015-12-31 37.22 37.22
#> 25 TRUE CAL-16 2016-01-01 2016-12-31 34.10 34.10
```

The calculation without prior function, for comparison:

```
fwd_fut_npri <- msfc(tdate = as.Date("2013-05-13"), # trading date
include = powfutures130513$Include, # vector with TRUE/FALSE, include contract?
contract = powfutures130513$Contract, # vector with contract names
sdate = powfutures130513$Start, # vector with contract start dates
edate = powfutures130513$End, # vector with contract end dates
f = powfutures130513$Closing, # vector with contract closing prices
prior = 0 # no prior function
)
plot(fwd_fut_npri, legend = "", title = "MSFC excluding prior for power futures 2013-05-13")
```

The daily forward curve values can be found along with the prior function and contracts used in the calculation with the `show()`

method. An instance of `MSFC`

is a rather rich object, and further details regarding the calculation, spline coefficients, etc. can be found in the slots:

```
slotNames(fwd_fut_wpri)
#> [1] "Name" "TradeDate" "BenchSheet" "Polynomials" "PriorFunc"
#> [6] "Results" "SplineCoef" "KnotPoints" "CalcDat"
```

Futures trading strategies for price risk management, for commercial hedgers with long or short exposure. All models below aim to achieve a favorable unit price for the energy portfolio, while preventing it from breaching a pre defined cap (floor).

The functions

`cppi()`

- Constant Proportion Portfolio Insurance

`dppi()`

- Dynamic Proportion Portfolio Insurance

`obpi()`

- Option Based Portfolio Insurance

`shpi()`

- Step Hedge Portfolio Insurance

`slpi()`

- Stop Loss Portfolio Insurance

implement alternative approaches to achieve this goal. They return S4 objects of type `CPPI`

, `DPPI`

, `OBPI`

, `SHPI`

and `SLPI`

respectively, with methods `plot()`

, `summary()`

and `show()`

.

In our example, we will consider the CAL-06 contract in the synthetic `powcal`

data set, and start trading 500 days prior to the contract expiry. For the `OBPI`

strategy presented below, the target price is calculated as an expected cap (floor) given by the option premium-adjusted strike price selected for the delta hedging scheme within a standard Black-76 option pricing framework. The default strike price is set at-the-money. The user may express a view regarding future market development by deviating from this level.

```
cal06_obpi_b <- obpi(q = 30, # volume 30 MW (buyer)
tdate = dat06$Date, # vector with trading days until expiry
f = dat06$CAL06, # vector with futures price
k = dat06$CAL06[1], # default option strike price at-the-money
vol = 0.2, # annualized volatility, for the Black-76 delta hedging
r = 0, # default assumed risk free rate of interest
tdays = 250, # assumed trading days per year
daysleft = 500, # number of days to expiry
tcost = 0, # transaction cost
int = TRUE # integer restriction, smallest transacted unit = 1
)
plot(cal06_obpi_b, legend = "bottom", title = "OBPI strategy buyer CAL-06")
```

The `summary()`

method:

```
summary(cal06_obpi_b)
#> $Description
#> [1] "Hedging strategy of type OBPI and length 500"
#>
#> $Volume
#> [1] 30
#>
#> $Target
#> [1] 29.83626
#>
#> $ChurnRate
#> [1] 4.333333
#>
#> $Stats
#> Market Trade Exposed Position Hedge Target Portfolio
#> First 26.82 17 13 17 0.5666667 29.83626 26.82000
#> Max 39.01 17 17 30 1.0000000 29.83626 29.29433
#> Min 25.60 -3 0 13 0.4333333 29.83626 26.46833
#> Last 37.81 0 0 30 1.0000000 29.83626 29.29433
```

The `show()`

method provide details regarding daily values for market price, transactions, exposed volume, futures contract position, the target price and the calculated portfolio price. Further details for a specific instance of a trading strategy can be found in the slots, see for example:

```
slotNames(cal06_obpi_b)
#> [1] "StrikePrice" "AnnVol" "InterestRate" "TradingDays" "Name"
#> [6] "Volume" "TargetPrice" "TransCost" "TradeisInt" "Results"
```

The CAL-06 OBPI strategy from a sellers point of view:

```
cal06_obpi_s <- obpi(q = - 30, # volume -30 MW (seller)
tdate = dat06$Date, # vector with trading days until expiry
f = dat06$CAL06, # vector with futures price
k = dat06$CAL06[1], # default option strike price at-the-money
vol = 0.2, # annualized volatility, for the Black-76 delta hedging
r = 0, # default assumed risk free rate of interest
tdays = 250, # assumed trading days per year
daysleft = 500, # number of days to expiry
tcost = 0, # transaction cost
int = TRUE # integer restriction, smallest transacted unit = 1
)
plot(cal06_obpi_s, legend = "bottom", title = "OBPI strategy seller CAL-06")
```