etrm: Energy Trading and Risk Management

Description

Tools for energy market risk management (forward curves and trading strategies)

Author(s)

Anders D. Sleire <sleire@gmail.com>

References

F. E. Benth, S. Koekkebakker, and F. Ollmar. Extracting and applying smooth forward curves from average-based commodity contracts with seasonal variation.The Journal of Derivatives, 15(1):52–66,2007b. https://doi.org/10.3905/jod.2007.694791

F. E. Benth, J. S. Benth, and S. Koekebakker. Stochastic modelling of electricity and related markets,volume 11. World Scientific, 2008. https://doi.org/10.1142/6811

F. Black. The pricing of commodity contracts.Journal of financial economics, 3(1):167–179, 1976. https://doi.org/10.1016/0304-405X(76)90024-6

T. Bjork. Arbitrage Theory in Continuous Time. Oxford University Press, 3 edition, 2009. https://EconPapers.repec.org/RePEc:oxp:obooks:9780199574742

F. Black and R. W. Jones. Simplifying portfolio insurance. The Journal of Portfolio Management, 14(1):48–51, 1987. https://doi.org/10.3905/jpm.1987.409131

H. E. Leland. Who should buy portfolio insurance? The Journal of Finance, 35(2):581–594, 1980. http://www.jstor.org/stable/2327419

An S4 class for the CPPI hedging strategy

Description

An S4 class for the CPPI hedging strategy

Slots

RiskFactor

The risk factor (cushion) used in the CPPI model

An S4 class for the DPPI hedging strategy

Description

An S4 class for the DPPI hedging strategy

Slots

TargetPercent

A percentage of first trading day's market price used to set target price (cap or floor)

RiskFactor

The risk factor (cushion) used in the DPPI model

An S4 VIRTUAL parent class for the hedging strategy classes in etrm

Description

An S4 VIRTUAL parent class for the hedging strategy classes in etrm

Slots

Name

A string with the portfolio insurance strategy name

Volume

The quantity to be hedged

TargetPrice

The target price(s) for the portfolio (cap or floor)

TransCost

Transaction costs pr unit traded

TradeisInt

TUE/FALSE integer restriction on tradable volume, TRUE sets smallest transacted unit to 1

Results

Data frame with strategy results, daily values for market price, transactions, exposure, position, hedge and portfolio price

An S4 class for the Maximum Smoothness Forward Curve (MSFC) in etrm

Description

An S4 class for the Maximum Smoothness Forward Curve (MSFC) in etrm

Slots

Name

A string with the acronym for Maximum Smoothness Forward Curve, "MSFC"

TradeDate

The trading date

BenchSheet

A data frame with futures contracts selected for calculation with MSFC computed prices

Polynomials

The number of polynomials in the MSFC spline

PriorFunc

A numeric vector with the prior function values

Results

A data frame with daily values for the calculated MSFC and contracts in "BenchSheet"

SplineCoef

List with coefficients for the polynomials in the MSFC spline

KnotPoints

Vector with spline knot points

CalcDat

Data frame extending "Results" with daily values for time vectors and polynomial coefficients used in calculation

An S4 class for the OBPI hedging strategy

Description

An S4 class for the OBPI hedging strategy

Slots

StrikePrice

Strike price for the synthetic option hedging

AnnVol

Annualized volatility for the contract to be traded

InterestRate

Risk-free rate of interest

TradingDays

The number of trading days per year

An S4 class for the SHPI hedging strategy

Description

An S4 class for the SHPI hedging strategy

An S4 class for the SLPI hedging strategy

Description

An S4 class for the SLPI hedging strategy

Constant Proportion Portfolio Insurance (CPPI)

Description

Implements CPPI strategy for commodity price risk management

Usage

cppi(q, tdate, f, tper, rper, tcost = 0, int = TRUE)

Arguments

Value

instance of the CPPI class

Examples

# CPPI for a buyer (seller), where stop loss is set 10% above (below) initial market price.

set.seed(5)
# GBM price process parameters
mu <- 0.2
sigma <- 0.1
S0 <- 100

# time
Y <- 2
N <- 500
delta <- Y/N
t <- seq (0, 1, length = N + 1)

# price process and date vector
W <- c(0, cumsum ( sqrt(delta) * rnorm (N)))
f_gbm <- S0 * exp(mu * t + sigma * W)
tr_dates <- seq(Sys.Date(), Sys.Date()+500, by = "day")

# implement cppi strategy for buyer
cppi_b <- cppi(q = 10,
tdate = tr_dates,
f = f_gbm,
tper = 0.1,
rper = 0.1,
tcost = 0,
int = TRUE)

# implement cppi strategy for seller
cppi_s <- cppi(q = - 10,
tdate = tr_dates,
f = f_gbm,
tper = - 0.1,
rper = 0.1,
tcost = 0,
int = TRUE)

Dynamic Proportion Portfolio Insurance (DPPI)

Description

Implements DPPI strategy for commodity price risk management

Usage

dppi(q, tdate, f, tper, rper, tcost = 0, int = TRUE)

Arguments

Value

instance of the DPPI class

Examples

# DPPI for a buyer (seller), where stop loss is set 10% above (below) initial market price.

set.seed(5)
# GBM price process parameters
mu <- 0.2
sigma <- 0.1
S0 <- 100

# time
Y <- 2
N <- 500
delta <- Y/N
t <- seq (0, 1, length = N + 1)

# price process and date vector
W <- c(0, cumsum ( sqrt(delta) * rnorm (N)))
f_gbm <- S0 * exp(mu * t + sigma * W)
tr_dates <- seq(Sys.Date(), Sys.Date()+500, by = "day")

# implement dppi strategy for buyer
dppi_b <- dppi(q = 10,
tdate = tr_dates,
f = f_gbm,
tper = 0.1,
rper = 0.1,
tcost = 0,
int = TRUE)

# implement dppi strategy for seller
dppi_s <- dppi(q = - 10,
tdate = tr_dates,
f = f_gbm,
tper = - 0.1,
rper = 0.1,
tcost = 0,
int = TRUE)

Maximum Smoothness Forward Curve (MSFC)

Description

Creates a smooth forward curve from futures prices for a flow delivery

Usage

msfc(tdate, include, contract, sdate, edate, f, prior = 0)

Arguments

Value

instance of the MSFC class

Examples

# calculate forward curve for synthetic futures contracts, without prior

# date for curve calculation and contract information
tdate <- as.Date("2021-06-17")
include <- rep(TRUE, 10)
contract <- c("JUL-21", "AUG-21", "SEP-21", "OCT-21", "NOV-21", "DEC-21",
"Q1-22", "Q2-22", "Q3-22", "Q4-22")

sdate <- as.Date(c("2021-07-01", "2021-08-01", "2021-09-01", "2021-10-01",
"2021-11-01", "2021-12-01", "2022-01-01", "2022-04-01", "2022-07-01", "2022-10-01"))

edate <- as.Date(c("2021-07-30", "2021-08-31", "2021-09-30", "2021-10-31",
"2021-11-30", "2021-12-31", "2022-03-31", "2022-06-30", "2022-09-30", "2022-12-31"))

f <- c(32.55, 32.50, 32.50, 32.08, 36.88, 39.80, 39.40, 25.20, 21.15, 29.50)

fwd_curve <- msfc(tdate = tdate,
include = include,
contract = contract,
sdate = sdate,
edate = edate,
f = f)

Option Based Portfolio Insurance (OBPI)

Description

Implements OBPI strategy for commodity price risk management

Usage

obpi(
  q,
  tdate,
  f,
  k = f[1],
  vol,
  r = 0,
  tdays = 250,
  daysleft,
  tcost = 0,
  int = TRUE
)

Arguments

Value

instance of the OBPI class

Examples

# OBPI for a buyer (seller), where stop loss is set 10% above (below) initial market price.

set.seed(5)
# GBM price process parameters
mu <- 0.2
sigma <- 0.1
S0 <- 100

# time
Y <- 2
N <- 500
delta <- Y/N
t <- seq (0, 1, length = N + 1)

# price process and date vector
W <- c(0, cumsum ( sqrt(delta) * rnorm (N)))
f_gbm <- S0 * exp(mu * t + sigma * W)
tr_dates <- seq(Sys.Date(), Sys.Date()+500, by = "day")

#implement obpi strategy for buyer
obpi_b <- obpi(q = 10,
tdate = tr_dates,
f = f_gbm,
k = f_gbm[1],
vol = 0.2,
r =  0,
tdays = 250,
daysleft = length(f_gbm),
tcost = 0,
int = TRUE)

# implement obpi strategy for seller
obpi_s <- obpi(q = - 10,
tdate = tr_dates,
f = f_gbm,
k = f_gbm[1],
vol = 0.2,
r =  0,
tdays = 250,
daysleft = length(f_gbm),
tcost = 0,
int = TRUE)

S4 method for the plot generic for portfolio insurance strategy classes

Description

S4 method for the plot generic for portfolio insurance strategy classes

Usage

## S4 method for signature 'GenericStrat'
plot(
  x,
  y = NULL,
  title = "Strategy plot",
  xlab = "",
  ylab.1 = "Price",
  ylab.2 = "Hedge %",
  pcols = c("#F8766D", "steelblue3", "gray60", "gray80"),
  legend = "bottom"
)

Arguments

Value

a two-panel chart with daily values for (top panel) target price, market price and portfolio price and (bottom) portfolio hedge rate

S4 method for the plot generic for class "MSFC"

Description

S4 method for the plot generic for class "MSFC"

Usage

## S4 method for signature 'MSFC'
plot(
  x,
  y = NULL,
  plot.prior = FALSE,
  title = "",
  xlab = "",
  ylab = "Price",
  legend = "right"
)

Arguments

Value

a chart with daily values for the forward curve and contracts used in calculation

Historical daily closing prices for 11 calendar year power futures contracts

Description

A synthetic dataset containing the closing prices and other attributes of 11 power futures contracts for calendar year delivery for 2006 - 2016.

Usage

powcal

Format

A data frame with 3253 rows and 12 columns:

Date

the trading date

CAL-06

the closing price for the 2006 futures contract

CAL-07

the closing price for the 2007 futures contract

CAL-08

the closing price for the 2008 futures contract

CAL-09

the closing price for the 2009 futures contract

CAL-10

the closing price for the 2010 futures contract

CAL-11

the closing price for the 2011 futures contract

CAL-12

the closing price for the 2012 futures contract

CAL-13

the closing price for the 2013 futures contract

CAL-14

the closing price for the 2014 futures contract

CAL-15

the closing price for the 2015 futures contract

CAL-16

the closing price for the 2016 futures contract

Closing prices for power futures contracts at trading date 2013-05-13

Description

A synthetic dataset containing the closing prices and other attributes of 38 power futures contracts.

Usage

powfutures130513

Format

A data frame with 38 rows and 5 columns:

Include

boolean variable to determine if contract should be included in forward curve calculation

Contract

the name of the futures contract

Start

delivery start date for the futures contract

End

delivery start date for the futures contract

Closing

the futures contract closing price

Example priors at trading date 2015-05-13

Description

An example of two simple priors for forward market price to be used with powfutures130513

Usage

powpriors130513

Format

A data frame with 3885 rows and 3 columns:

Date

vector of dates ranging from 2013-05-13 to final end date of contracts in powfutures130513

trig.prior

a simple smooth trigonometric prior describing power price seasonality

mod.prior

a trigonometric prior adjusted for typical calendar effects

S4 method for the show generic for portfolio insurance strategy classes

Description

S4 method for the show generic for portfolio insurance strategy classes

Usage

## S4 method for signature 'GenericStrat'
show(object)

Arguments

Value

a data frame with daily observations for market price, transactions, exposed volume, forward positions, hedge rate, target price and portfolio price

S4 method for the show generic for class "MSFC"

Description

S4 method for the show generic for class "MSFC"

Usage

## S4 method for signature 'MSFC'
show(object)

Arguments

Value

data frame with daily values for forward curve and forward contracts used in calculation

Step Hedge Portfolio Insurance (SHPI)

Description

Implements SHPI strategy for commodity price risk management

Usage

shpi(q, tdate, f, daysleft, tper, tcost = 0, int = TRUE)

Arguments

Value

instance of the SHPI class

Examples

# SHPI for a buyer (seller), where stop loss is set 10% above (below) initial market price.

set.seed(5)
# GBM price process parameters
mu <- 0.2
sigma <- 0.1
S0 <- 100

# time
Y <- 2
N <- 500
delta <- Y/N
t <- seq (0, 1, length = N + 1)

# price process and date vector
W <- c(0, cumsum ( sqrt(delta) * rnorm (N)))
f_gbm <- S0 * exp(mu * t + sigma * W)
tr_dates <- seq(Sys.Date(), Sys.Date()+500, by = "day")

# implement step-hedge strategy for buyer
shpi_b <- shpi(q = 10,
tdate = tr_dates,
f = f_gbm,
daysleft = length(tr_dates),
tper = 0.1,
tcost = 0,
int = TRUE)

# implement step-hedge strategy for seller
shpi_s <- shpi(q = - 10,
tdate = tr_dates,
f = f_gbm,
daysleft = length(tr_dates),
tper = - 0.1,
tcost = 0,
int = TRUE)

Stop Loss Portfolio Insurance (SLPI)

Description

Implements SLPI strategy for commodity price risk management

Usage

slpi(q, tdate, f, tper, tcost = 0, int = TRUE)

Arguments

Value

instance of the SLPI class

Examples

# SLPI for a buyer (seller), where stop loss is set 10% above (below) initial market price.

set.seed(5)
# GBM price process parameters
mu <- 0.2
sigma <- 0.1
S0 <- 100

# time
Y <- 2
N <- 500
delta <- Y/N
t <- seq (0, 1, length = N + 1)

# price process and date vector
W <- c(0, cumsum ( sqrt(delta) * rnorm (N)))
f_gbm <- S0 * exp(mu * t + sigma * W)
tr_dates <- seq(Sys.Date(), Sys.Date()+500, by = "day")

# implement stop-loss strategy for buyer
slpi_b <- slpi(q = 10,
tdate = tr_dates,
f = f_gbm,
tper = 0.1,
tcost = 0,
int = TRUE)

# implement stop-loss strategy for seller
slpi_s <- slpi(q = - 10,
tdate = tr_dates,
f = f_gbm,
tper = - 0.1,
tcost = 0,
int = TRUE)

S4 method for the summary generic for portfolio insurance strategy classes

Description

S4 method for the summary generic for portfolio insurance strategy classes

Usage

## S4 method for signature 'GenericStrat'
summary(object)

Arguments

Value

a list with five elements. 1) A string describing the type of portfolio insurance trading strategy and number of observations, 2) volume to be hedged, calculated churn rate (numer of times volume to be hedged has been traded) and 5) a data frame with summary statistics for achieved results

S4 method for the summary generic for class "MSFC"

Description

S4 method for the summary generic for class "MSFC"

Usage

## S4 method for signature 'MSFC'
summary(object)

Arguments

Value

a list with three elements. 1) A string describing length of forward curve, number of polynomials used in spline and trading date, 2) a vector with a sample of the prior used via head(prior) and 3) a data frame with all forward contracts used in the calculation along with computed forward curve prices