demo/Bank_Structure_Example.R
In wbreymann/FEMS: R Package for Financial Enterprise Modelling and Simulation
# Model of the bank of practice sheet 9 in FEMS.
# This is the basis in order to compute problems 1 to 5 of homework 2
# The script contains comments that should allow you to understand what is done.
# An additional script for the further tasks will follow.
## Preparation --------------
rm(list=ls())
devtools::load_all()
#library(FEMS)
options(warnings=-1)
#rm(list=ls())
## Initialization -----------
t0 <- "2021-01-01"
# Start date of the contracts. Should already exist at analysis date
tstart <- "2020-12-31" #
# scale for the amount of capital (in Mio CHF)
scale <- 1000000
### Modeling the bank --------
## The structure of the bank -----
bank <- institution("Bank")
# Create additional accounts
# Assets
bank$Assets$AddChild("LT.default")
bank$Assets$AddChild("FixedAssets")
# Liabilities
bank$Liabilities$Debt$AddChild("ShortTerm")
bank$Liabilities$Debt$AddChild("LongTerm")
# Operations
# bank$Operations$AddChild("Revenues")
# Commissions, fees, etc.
bank$Operations$Revenues$AddChild("Commissions")
# Revenue from rent
bank$Operations$Revenues$AddChild("Rent")
# Expenses
# bank$Operations$AddChild("Expenses")
bank$Operations$Expenses$AddChild("Salaries")
# Other expenses
bank$Operations$Expenses$AddChild("Other")
#bank$Operations$AddChild("Profit/loss before taxes")
bank
# risk factor model -------
spot.rates <- c(0.01, 0.02, 0.03, 0.04)
yc <- YieldCurve(label = "YC",
ReferenceDate = t0,
Tenors = c("1M", "2Y", "5Y", "10Y"),
Rates = spot.rates)
yc
plot(yc)
rf <- RFConn(yc)
## The contracts: Assets --------
# # Cash
# # a) Bank account
# # Time series of transactions:
# (cashflows <- timeSeries(
# 0, units="CHF",
# timeSequence(from=t0, by="year", length.out=1)))
#
# # Construction of the bank account
#
# # balance.init <- 100*scale
# # (my.account <- bankAccount("2013-12-31", balance=balance.init,
# # ext_transactions = cashflows, ir=0.03))
# Liquid assets -------
# We assume that the amount stays constant and model them as a bond.
# But the interest rate is set to market rates periodically.
# We choose a period of 1 year (1 quarter would also be good ("P3ML0"))
# We could also model them as a bank account.
assets.liquid.value <- 100*scale
assets.liquid <- bond(ContractID="Liquid", start = tstart, maturity = "10 years",
nominal = assets.liquid.value, coupon = yc$Rates[1], role="long",
CycleOfRateReset="P3YL0", MarketObjectCodeOfRateReset="YC")
addContracts(list(assets.liquid), FindNode(bank$Assets, "ShortTerm"))
# events(assets.liquid, t0, rf)
# Long term assets ---------
ir.spread.assets <- 0.03
mortgage.value <- 300*scale
mtg.mat.short = "2 years"
mtg.mat.med = "5 years"
mtg.mat.long = "10 years"
mortgage.long1 <- bond(start = tstart, maturity = mtg.mat.short,
nominal = mortgage.value, coupon = spot.rates[2]+ir.spread.assets,
role="long", ContractID="mg1")
mortgage.long2 <- bond(start = tstart, maturity = mtg.mat.med,
nominal = mortgage.value, coupon = spot.rates[3]+ir.spread.assets,
role="long", ContractID="mg2")
mortgage.long3 <- bond(start = tstart, maturity = mtg.mat.long,
nominal = mortgage.value, coupon = spot.rates[4]+ir.spread.assets,
role="long", ContractID="mg3")
addContracts(list(mortgage.long1, mortgage.long2, mortgage.long3),
FindNode(bank$Assets, "LongTerm"))
# plot(mortgage.long1, tstart)
# Modeling of default ----------
# We add contracts with a negative value on the asset side by chosing 'role="short"'
# For each mortgage, we must add every year a contract that has 1% of its value.
# (4% default rate with 75% recovery rate and assumption that recovery happens immediately)
times.default <- timeSequence(from = timeDate(tstart), by = "1 years", length.out = 26)
default.rate <-0.04
recovery <- 0.75
p.disc <- (1-recovery)*default.rate
mortgage.long1.df1 <- bond(start = as.character(times.default[2]), maturity = "1 years",
nominal = default.rate*mortgage.value,
PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[2]+ir.spread.assets,
role="short", ContractID="mg1-df1")
# events(mortgage.long1.df1, t0)
mortgage.long1.df2 <- bond(start = "2022-12-30", maturity = "1 day",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[2]+ir.spread.assets,
role="short", ContractID="mg1-df2")
events(mortgage.long1.df2, t0)
mortgage.long2.df1 <- bond(start = as.character(times.default[2]), maturity = "4 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df1")
mortgage.long2.df2 <- bond(start = as.character(times.default[3]), maturity = "3 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df2")
mortgage.long2.df3 <- bond(start = as.character(times.default[4]), maturity = "2 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df3")
mortgage.long2.df4 <- bond(start = as.character(times.default[5]), maturity = "1 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df4")
mortgage.long2.df5 <- bond(start = "2025-12-30", maturity = "1 day",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df5")
mortgage.long3.df1 <- bond(start = as.character(times.default[2]), maturity = "9 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df1")
mortgage.long3.df2 <- bond(start = as.character(times.default[3]), maturity = "8 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df2")
mortgage.long3.df3 <- bond(start = as.character(times.default[4]), maturity = "7 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df3")
mortgage.long3.df4 <- bond(start = as.character(times.default[5]), maturity = "6 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df4")
mortgage.long3.df5 <- bond(start = as.character(times.default[6]), maturity = "5 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df5")
mortgage.long3.df6 <- bond(start = as.character(times.default[7]), maturity = "4 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df6")
mortgage.long3.df7 <- bond(start = as.character(times.default[8]), maturity = "3 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df7")
mortgage.long3.df8 <- bond(start = as.character(times.default[9]), maturity = "2 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df8")
mortgage.long3.df9 <- bond(start = as.character(times.default[10]), maturity = "1 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df9")
mortgage.long3.df10 <- bond(start = "2030-12-30", maturity = "1 day",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df10")
addContracts(list(
mortgage.long1.df1,mortgage.long1.df2,
mortgage.long2.df1,mortgage.long2.df2,mortgage.long2.df3,mortgage.long2.df4,mortgage.long2.df5,
mortgage.long3.df1,mortgage.long3.df2,mortgage.long3.df3,mortgage.long3.df4,mortgage.long3.df5,
mortgage.long3.df6,mortgage.long3.df7,mortgage.long3.df8,mortgage.long3.df9,mortgage.long3.df10
), FindNode(bank$Assets, "LT.default"))
# events(mortgage.long1.df1, t0)
# Fixed assets -----------
# must be modeled with Investment contract because of depreciation
asset.fixed.value <- 200*scale
# Define time pattern of depreciation
# yearly time steps 50 years into the future
times.re <- timeSequence(from = timeDate(tstart), by = "1 years", length.out = 51)
asset.fixed.func <- function(times) {
timeSeries(seq(asset.fixed.value, 0, length.out=51), times)
}
asset.fixed.func(times.re)
# Define Investments contract
asset.fixed <- Investments(pattern=asset.fixed.func,
args=list(times=times.re
), Currency="CHF", ContractID="RE01")
addContracts(list(asset.fixed), FindNode(bank$Assets, "FixedAssets"))
# The rent must be modeled separately as operational revenue, cf. below.
## Liabilities -----------------------
#
# Debt ---------------------
# Savings -----------------
savings <- bond(ContractID="svg", start = tstart, maturity = "10 years",
nominal = 600*scale, coupon = yc$Rates[1], role="short",
CycleOfRateReset="P1YL0", MarketObjectCodeOfRateReset="YC")
addContracts(list(savings), FindNode(bank$Liabilities, "ShortTerm"))
#
# savings1 <- bond(ContractID="svg-delta", start = "2021-12-31", maturity = "9 years",
# nominal = 50*scale, coupon = yc$Rates[1], role="long",
# CycleOfRateReset="P1YL0", MarketObjectCodeOfRateReset="YC")
# addContracts(list(savings, savings1), FindNode(bank$Liabilities, "ShortTerm"))
# Long term debt ----------
ir.spread.liab <- 0.01
loan.long <- bond(ContractID="dlg1", start = tstart, maturity = "10 years",
nominal = 500*scale, coupon = spot.rates[4]+ir.spread.liab, role="short")
addContracts(list(loan.long), FindNode(bank$Liabilities, "LongTerm"))
plot(loan.long, t0)
### Operational cash flows ---------------
# Operations modeled 10 years into the future,
# with the exception of rent for real estate, which is modeled for the lifetime
# of the real estate investment, i.e. 50 years
times.ops <- timeSequence(tstart, by="1 years", length.out=11)
## Revenues ------------------
# Rent -----------------------
asset.fixed.rent <- 0.05 * asset.fixed.value
rent.yearly <- rep(asset.fixed.rent, 50)
#
rent.fun <- function(rent, times) {
timeSeries(data=rent, charvec=times)
}
rent.fun(rent.yearly, times.re[-51])
Rent <- OperationalCF(ContractID="RE-Rent", Currency="CHF", # Define contract
pattern=rent.fun,
args=list(rent=rent.yearly, times=times.re[-51]) )
# Test
# events(Rent, t0, rf)
addContracts(list(Rent), FindNode(bank$Operations, "Rent"))
# Commissions, Fees, etc. -----------------------
commissions <- 20*scale
# asset.fixed <- bond(start = tstart, maturity = "50 years",
# nominal = 200, coupon = asset.fixed.rent, role="long")
commissions.yearly <- rep(commissions, 10)
#
commissions.fun <- function(commissions, times) {
timeSeries(data=commissions, charvec=times)
}
Commissions <- OperationalCF(ContractID="Comm", Currency="CHF", # Define contract
pattern=commissions.fun,
args=list(commissions=commissions.yearly, times=times.ops[-1]) )
# Test
# events(Commissions, t0, rf)
addContracts(list(Commissions), FindNode(bank$Operations, "Commissions"))
## Expenses ------------------
# Salaries --------------
salaries.yearly <- rep(20*scale, 10)
#
salaries.fun <- function(times, expenses) {
timeSeries(-expenses, times)
}
Salaries <- OperationalCF(ContractID="Salaries", Currency="CHF", # Define contract
pattern=salaries.fun, args=list(
expenses=salaries.yearly,
times=times.ops[-1]) )
# Test
# events(Salaries, t0, rf)
addContracts(list(Salaries), FindNode(bank$Operations$Expenses, "Salaries"))
# Other -------------------
other.yearly <- rep(9*scale, 10)
#
other.fun <- function(times, expenses) {
timeSeries(-expenses, times)
}
Other <- OperationalCF(ContractID="Other", Currency="CHF", # Define contract
pattern=other.fun, args=list(
expenses=other.yearly,
times=times.ops[-1]) )
# Test
# events(Other, t0, rf)
addContracts(list(Other), FindNode(bank$Operations$Expenses, "Other"))
# Test: Which contracts are in the model? ----------
showContracts(bank)
# Performing the simulation ------
# calculate events
system.time({events(bank, t0, rf, end_date="2031-01-01")})
showEvents(bank)
### Analysis -------------------
# construction of time bucket
# t2 = "2021-01-02"
by <- timeSequence(t0, by="1 years", length.out=6)
(tb <- timeBuckets(by, bucketLabs=2021:2025,
breakLabs=substr(as.character(by),3,10)))
(val.nom <- value(bank, tb, scale=scale, digits=2)[,1:2])
# (val.nom <- value(bank, tb, scale=scale, digits=2)[,1,drop=FALSE])
(liq <- liquidity(bank, tb, scale=scale, digits=2)[,1:2])
(inc.nom <- income(bank, tb, scale=scale, digits=2)[,1:2])
(liq - inc.nom)[,1:2]
## Problem 1: ---------
## Problem 2 ----
# Create the current balance sheet of the bank -> cf.above
# Compute the equity capital ratio (equity / balance sheet total) -> 1/12 = 8.3%
# Equity ratio:
eq.ratio <- round(100*(-val.nom[12,]/val.nom[2,]),2)
rownames(eq.ratio) <- "eq.ratio"
eq.ratio
# Compute the ration of the liquid assets over the short term liabilities
# Compute the same way
## Problem 3: Analysis with shifted interest rates ---------
# Rerun the simulation with the shifted yield curve.
# Define new market environment with shifted rates
spot.rates.shifted <- c(0.01, 0.02, 0.03, 0.04)+0.01
yc.shifted <- YieldCurve(label = "YC",
ReferenceDate = t0,
Tenors = c("1M", "2Y", "5Y", "10Y"),
Rates = spot.rates)
rf1 <- RFConn(yc.shifted)
rf1[["YC"]]
# Change rates for contracts with variable interest rates
bank$Assets$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <- spot.rates.shifted[1]
bank$Liabilities$Debt$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <- spot.rates.shifted[1]
# Rerun simulation
events(bank, t0, rf1, end_date="2031-01-01")
### Analysis
# # construction of time bucket
# # t2 = "2021-01-02"
# by <- timeSequence(t0, by="1 years", length.out=6)
# (tb <- timeBuckets(by, bucketLabs=2021:2025,
# breakLabs=substr(as.character(by),3,10)))
(val.nom <- value(bank, tb, scale=scale, digits=2)[,1:2])
# (val.nom <- value(bank, tb, scale=scale, digits=2)[,1,drop=FALSE])
(liq <- liquidity(bank, tb, scale=scale, digits=2)[,1:2])
(inc.nom <- income(bank, tb, scale=scale, digits=2)[,1:2])
(liq - inc.nom)[,1:2]
## Problem 5 ----------------------
# Compute present value, future value, internal rate of return and duration of
# the cash flows resulting from real estate.
# Make the simplifying assumption that rent is paid yearly in advance
# and use the following interest rates for discounting:
# - 2 years spot rates for terms of 1-3 years
# - 5 years spot rates for terms of 4-6 years
# - 10 years spot rates for terms > 6 years
# Here we use the yield curve for discounting
re.rent <- bank$Operations$Revenues$Rent$contracts[[1]]
cfs <- cashFlows(re.rent, from=as.character(t0), to=as.character(times.re[51]))
(pv <- presentValue(cfs, yield=yc, by=times.re[1])/scale)
(futureValue <- pv * 1.04^50)
# To compute the internal rate of return, the initial investment of 200 mio
# must be added to cfs
cfs[1] <- cfs[1] - 200*scale
# Internal rate of return
irr(cfs)
# duration
duration(re.rent, type="fisher-weil", yield=yc, price=200*scale, from=t0)
## Problem 6 -------------------
# This cannot be solved naturally with FEMS
# because the capitalization of the net rent (rent - maintenance expenditure)
# can currently not be modeled with any existing contract
## Problem 7 --------------------
# The interest curve is randomly shifted
#
# We first set the interest rate of the variable contracts to the original values
bank$Assets$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <- spot.rates[1]
bank$Liabilities$Debt$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <- spot.rates[1]
# Simulation with original values
events(bank, t0, rf, end_date="2023-01-01")
# Analysis
by <- timeSequence(t0, by="1 years", length.out=6)
(tb <- timeBuckets(by, bucketLabs=2021:2025,
breakLabs=substr(as.character(by),3,10)))
# Lists for storing the analytical results
liq <- list()
val.nom <- list()
inc.nom <- list()
val.nom[["0"]] <- value(bank, tb, scale=scale, digits=2)[,1:2]
liq[["0"]] <- liquidity(bank, tb, scale=scale, digits=2)[,1:2]
inc.nom[["0"]] <- income(bank, tb, scale=scale, digits=2)[,1:2]
# Extract particular values of interest
shift <- numeric()
shift["0"] <- 0
profit <- numeric()
profit["0"] <- inc.nom[["0"]][1,1]
eq <- numeric()
eq["0"] <- -val.nom[["0"]][12,2]
liq.assets <- numeric()
liq.assets["0"] <- sum(val.nom[["0"]][3:4,2])
# loop over random shift of yield curve
# The simulation is pretty slow
# You can grow the simulated sample by setting ns.new <- nn.old
ns <- 1
nn <- 10
for (i in ns:nn) {
i.ch <- as.character(i)
# create random shift
shift[i.ch] <- rnorm(1, 0, 0.01)
spot.rates.shifted <- c(0.01, 0.02, 0.03, 0.04)+shift[i.ch]
print(c(i, as.numeric(shift[i.ch])))
yc.shifted <- YieldCurve(label = "YC",
ReferenceDate = t0,
Tenors = c("1M", "2Y", "5Y", "10Y"),
Rates = spot.rates.shifted)
rf1 <- RFConn(yc.shifted)
rf1[["YC"]]
# Change rates for contracts with variable interest rates
bank$Assets$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <-
spot.rates.shifted[1]
bank$Liabilities$Debt$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <-
spot.rates.shifted[1]
# Rerun simulation
events(bank, t0, rf1, end_date="2023-01-01")
# Store analysis
liq[[i.ch]] <- liquidity(bank, tb, scale=scale, digits=2)[,1:2]
inc.nom[[i.ch]] <- income(bank, tb, scale=scale, digits=2)[,1:2]
val.nom[[i.ch]] <- value(bank, tb, scale=scale, digits=2)[,1:2]
# Extract particular values
profit[i.ch] <- inc.nom[[i.ch]][1,1]
eq[i.ch] <- -val.nom[[i.ch]][12,2]
liq.assets[i.ch] <- sum(val.nom[[i.ch]][3:4,2])
}
res <- cbind(shift, profit, eq, liq.assets)
res[order(res[,1]),]
hist(res[,"shift"])
hist(res[,"profit"])
hist(res[,"eq"])
hist(res[,"liq.assets"])
## Problem 8 -------------------
# We model the fluctuation of the savings by a new contract in the
# Liabilities$Debt$ShortTerm account
# The changes occur at the last day of 2021.
# First, the contract is created with nominal 0
bank$Liabilities$Debt$ShortTerm$contracts <- NULL
savings1 <- bond(ContractID="svg-delta", start = "2021-12-31", maturity = "9 years",
nominal = 0*scale, coupon = yc$Rates[1], role="long",
CycleOfRateReset="P1YL0", MarketObjectCodeOfRateReset="YC")
addContracts(list(savings, savings1), FindNode(bank$Liabilities, "ShortTerm"))
# Now we randomly choose the changes of the savings.
# According to problem 8 in practice sheet 9, the volume should be a normally
# distributed random variable with mean 0 and stdev. 50.
# Since the nominal cannot be negative, we must distinguish two cases:
# - If the volume decreases we need a long contract
# - If the volume increases we need a short contract
nn <- 10
savings.delta <- rnorm(nn, 0, 50)
role <- rep("RPA", nn) # Real Position Asset = "long"
role[savings.delta<0] <- "RPL" # Real Position Liability = "short"
role
# Initialization
savings.delta <- numeric()
savings.delta["0"] <- 0
role <- character()
role["0"] <- "RPA"
liq <- list()
inc.nom <- list()
val.nom <- list()
fcf <- numeric()
current <- numeric()
bank$Liabilities$Debt$ShortTerm$contracts[[2]]$ContractTerms$NotionalPrincipal <- 0
bank$Liabilities$Debt$ShortTerm$contracts[[2]]$ContractTerms$ContractRole <- "RPA"
events(bank, t0, rf, end_date="2022-01-01")
# events(bank$Liabilities$Debt$ShortTerm, t0, rf, end_date="2022-01-01")
liq[["0"]] <- liquidity(bank, tb, scale=scale, digits=2)[,1:2]
inc.nom[["0"]] <- income(bank, tb, scale=scale, digits=2)[,1:2]
val.nom[["0"]] <- value(bank, tb, scale=scale, digits=2)[,1:2]
fcf["0"] <- liq[["0"]][1,1]
current["0"] <- sum(val.nom[["0"]][3:4,2])
# Loop over random changes of savings
ns <- 1
nn <- 10
system.time({
for (i in ns:nn) {
i.ch <- as.character(i)
savings.delta[i] <- rnorm(1, 0, 50)
if ( savings.delta[i]>=0 )
role[i] <- "RPA"
else
role[i] <- "RPL"
print(paste(i, savings.delta[i], role[i]))
bank$Liabilities$Debt$ShortTerm$contracts[[2]]$ContractTerms$NotionalPrincipal <- abs(savings.delta[i])*scale
bank$Liabilities$Debt$ShortTerm$contracts[[2]]$ContractTerms$ContractRole <- role[i]
# events(bank$Liabilities$Debt$ShortTerm, t0, rf, end_date="2022-01-01") # This doesn't work properly
events(bank, t0, rf, end_date="2022-01-01")
liq[[i.ch]] <- liquidity(bank, tb, scale=scale, digits=2)[,1:2]
inc.nom[[i.ch]] <- income(bank, tb, scale=scale, digits=2)[,1:2]
val.nom[[i.ch]] <- value(bank, tb, scale=scale, digits=2)[,1:2]
fcf[i.ch] <- liq[[i.ch]][1,1]
current[i.ch] <- sum(val.nom[[i.ch]][3:4,2]) # should be the sum of lines 3 and 4
}
})
res <- cbind(c(0,-round(savings.delta,2)), fcf, current)
colnames(res) <- c("d-savings", "free cf", "liq. assets")
res
hist(res[,1])
hist(res[,2])
## Problem 9 ------------------------
# We simulate the discovery rates and adjust the volume of the contracts that
# simulated the default accordingly
# construction of time bucket over 10 years
by <- timeSequence(t0, by="1 years", length.out=11)
(tb <- timeBuckets(by, bucketLabs=2021:2030,
breakLabs=substr(as.character(by),3,10)))
# Computation for 4% default rate of the remaining assets
default.rate <- rep(0.04,10)
default.rate.cum <- default.rate*c(1,cumprod(1-default.rate)[-10])
recovery <- 0.75
p.disc <- (1-recovery)*default.rate.cum
for(j in 1:2) {
i <- j
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
print(paste(i, j,
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["ContractID"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]]
))
}
for (j in 1:5) {
i <- j+2
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
print(paste(i, j,
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["ContractID"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]]
))
}
for (j in 1:10) {
i <- j+7
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
print(paste(i, j,
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["ContractID"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]]
))
}
system.time({events(bank, t0, rf, end_date="2032-01-01")})
showEvents(bank)
liq <- list()
inc.nom <- list()
val.nom <- list()
liq[["0"]] <- liquidity(bank, tb, scale=scale, digits=2)
inc.nom[["0"]] <- income(bank, tb, scale=scale, digits=2)
val.nom[["0"]] <- value(bank, tb, scale=scale, digits=2)
eq <- numeric()
eq["0"] <- val.nom[["0"]][12,10]
def.rates <- default.rate
dim(def.rates) <- c(1,10)
rownames(def.rates) <- "0"
colnames(def.rates) <- 1:10
# loop over random defaults rates
ns <- 1
nn <- 10
for (ctr in ns:nn) {
ctr.ch <- as.character(ctr)
default.rate <- runif(10, 0, 0.08)
default.rate.cum <- default.rate*c(1,cumprod(1-default.rate)[-10])
recovery <- 0.75
p.disc <- (1-recovery)*default.rate.cum
def.rates <- rbind(def.rates, default.rate)
rownames(def.rates)[ctr+1] <- ctr.ch
print(paste(ctr, default.rate))
for(j in 1:2) {
i <- j
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
}
for (j in 1:5) {
i <- j+2
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
}
for (j in 1:10) {
i <- j+7
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
}
system.time({events(bank, t0, rf, end_date="2032-01-01")})
liq[[ctr.ch]] <- liquidity(bank, tb, scale=scale, digits=2)
inc.nom[[ctr.ch]] <- income(bank, tb, scale=scale, digits=2)
val.nom[[ctr.ch]] <- value(bank, tb, scale=scale, digits=2)
eq[ctr.ch] <- val.nom[[ctr.ch]][12,10]
}
res <- cbind(
apply(def.rates, 1, function(x) 1-prod(1-x)),
-eq
)
colnames(res) <- c("total def", "equity")
# The second line shows equity. It should not be negative.
res[order(res[,2]),]
# histogram for equity
hist(res[,2])
# Liquidity cannot really be investigated with this model.
# We need a rule of how to reinvest the recovered money
wbreymann/FEMS documentation built on May 6, 2024, 2:19 p.m.
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# Model of the bank of practice sheet 9 in FEMS.
# This is the basis in order to compute problems 1 to 5 of homework 2
# The script contains comments that should allow you to understand what is done.
# An additional script for the further tasks will follow.
## Preparation --------------
rm(list=ls())
devtools::load_all()
#library(FEMS)
options(warnings=-1)
#rm(list=ls())
## Initialization -----------
t0 <- "2021-01-01"
# Start date of the contracts. Should already exist at analysis date
tstart <- "2020-12-31" #
# scale for the amount of capital (in Mio CHF)
scale <- 1000000
### Modeling the bank --------
## The structure of the bank -----
bank <- institution("Bank")
# Create additional accounts
# Assets
bank$Assets$AddChild("LT.default")
bank$Assets$AddChild("FixedAssets")
# Liabilities
bank$Liabilities$Debt$AddChild("ShortTerm")
bank$Liabilities$Debt$AddChild("LongTerm")
# Operations
# bank$Operations$AddChild("Revenues")
# Commissions, fees, etc.
bank$Operations$Revenues$AddChild("Commissions")
# Revenue from rent
bank$Operations$Revenues$AddChild("Rent")
# Expenses
# bank$Operations$AddChild("Expenses")
bank$Operations$Expenses$AddChild("Salaries")
# Other expenses
bank$Operations$Expenses$AddChild("Other")
#bank$Operations$AddChild("Profit/loss before taxes")
bank
# risk factor model -------
spot.rates <- c(0.01, 0.02, 0.03, 0.04)
yc <- YieldCurve(label = "YC",
ReferenceDate = t0,
Tenors = c("1M", "2Y", "5Y", "10Y"),
Rates = spot.rates)
yc
plot(yc)
rf <- RFConn(yc)
## The contracts: Assets --------
# # Cash
# # a) Bank account
# # Time series of transactions:
# (cashflows <- timeSeries(
# 0, units="CHF",
# timeSequence(from=t0, by="year", length.out=1)))
#
# # Construction of the bank account
#
# # balance.init <- 100*scale
# # (my.account <- bankAccount("2013-12-31", balance=balance.init,
# # ext_transactions = cashflows, ir=0.03))
# Liquid assets -------
# We assume that the amount stays constant and model them as a bond.
# But the interest rate is set to market rates periodically.
# We choose a period of 1 year (1 quarter would also be good ("P3ML0"))
# We could also model them as a bank account.
assets.liquid.value <- 100*scale
assets.liquid <- bond(ContractID="Liquid", start = tstart, maturity = "10 years",
nominal = assets.liquid.value, coupon = yc$Rates[1], role="long",
CycleOfRateReset="P3YL0", MarketObjectCodeOfRateReset="YC")
addContracts(list(assets.liquid), FindNode(bank$Assets, "ShortTerm"))
# events(assets.liquid, t0, rf)
# Long term assets ---------
ir.spread.assets <- 0.03
mortgage.value <- 300*scale
mtg.mat.short = "2 years"
mtg.mat.med = "5 years"
mtg.mat.long = "10 years"
mortgage.long1 <- bond(start = tstart, maturity = mtg.mat.short,
nominal = mortgage.value, coupon = spot.rates[2]+ir.spread.assets,
role="long", ContractID="mg1")
mortgage.long2 <- bond(start = tstart, maturity = mtg.mat.med,
nominal = mortgage.value, coupon = spot.rates[3]+ir.spread.assets,
role="long", ContractID="mg2")
mortgage.long3 <- bond(start = tstart, maturity = mtg.mat.long,
nominal = mortgage.value, coupon = spot.rates[4]+ir.spread.assets,
role="long", ContractID="mg3")
addContracts(list(mortgage.long1, mortgage.long2, mortgage.long3),
FindNode(bank$Assets, "LongTerm"))
# plot(mortgage.long1, tstart)
# Modeling of default ----------
# We add contracts with a negative value on the asset side by chosing 'role="short"'
# For each mortgage, we must add every year a contract that has 1% of its value.
# (4% default rate with 75% recovery rate and assumption that recovery happens immediately)
times.default <- timeSequence(from = timeDate(tstart), by = "1 years", length.out = 26)
default.rate <-0.04
recovery <- 0.75
p.disc <- (1-recovery)*default.rate
mortgage.long1.df1 <- bond(start = as.character(times.default[2]), maturity = "1 years",
nominal = default.rate*mortgage.value,
PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[2]+ir.spread.assets,
role="short", ContractID="mg1-df1")
# events(mortgage.long1.df1, t0)
mortgage.long1.df2 <- bond(start = "2022-12-30", maturity = "1 day",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[2]+ir.spread.assets,
role="short", ContractID="mg1-df2")
events(mortgage.long1.df2, t0)
mortgage.long2.df1 <- bond(start = as.character(times.default[2]), maturity = "4 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df1")
mortgage.long2.df2 <- bond(start = as.character(times.default[3]), maturity = "3 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df2")
mortgage.long2.df3 <- bond(start = as.character(times.default[4]), maturity = "2 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df3")
mortgage.long2.df4 <- bond(start = as.character(times.default[5]), maturity = "1 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df4")
mortgage.long2.df5 <- bond(start = "2025-12-30", maturity = "1 day",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[3]+ir.spread.assets,
role="short", ContractID="mg2-df5")
mortgage.long3.df1 <- bond(start = as.character(times.default[2]), maturity = "9 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df1")
mortgage.long3.df2 <- bond(start = as.character(times.default[3]), maturity = "8 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df2")
mortgage.long3.df3 <- bond(start = as.character(times.default[4]), maturity = "7 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df3")
mortgage.long3.df4 <- bond(start = as.character(times.default[5]), maturity = "6 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df4")
mortgage.long3.df5 <- bond(start = as.character(times.default[6]), maturity = "5 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df5")
mortgage.long3.df6 <- bond(start = as.character(times.default[7]), maturity = "4 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df6")
mortgage.long3.df7 <- bond(start = as.character(times.default[8]), maturity = "3 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df7")
mortgage.long3.df8 <- bond(start = as.character(times.default[9]), maturity = "2 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df8")
mortgage.long3.df9 <- bond(start = as.character(times.default[10]), maturity = "1 years",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df9")
mortgage.long3.df10 <- bond(start = "2030-12-30", maturity = "1 day",
nominal = default.rate*mortgage.value, PremiumDiscountAtIED=-p.disc*mortgage.value,
coupon = spot.rates[4]+ir.spread.assets,
role="short", ContractID="mg3-df10")
addContracts(list(
mortgage.long1.df1,mortgage.long1.df2,
mortgage.long2.df1,mortgage.long2.df2,mortgage.long2.df3,mortgage.long2.df4,mortgage.long2.df5,
mortgage.long3.df1,mortgage.long3.df2,mortgage.long3.df3,mortgage.long3.df4,mortgage.long3.df5,
mortgage.long3.df6,mortgage.long3.df7,mortgage.long3.df8,mortgage.long3.df9,mortgage.long3.df10
), FindNode(bank$Assets, "LT.default"))
# events(mortgage.long1.df1, t0)
# Fixed assets -----------
# must be modeled with Investment contract because of depreciation
asset.fixed.value <- 200*scale
# Define time pattern of depreciation
# yearly time steps 50 years into the future
times.re <- timeSequence(from = timeDate(tstart), by = "1 years", length.out = 51)
asset.fixed.func <- function(times) {
timeSeries(seq(asset.fixed.value, 0, length.out=51), times)
}
asset.fixed.func(times.re)
# Define Investments contract
asset.fixed <- Investments(pattern=asset.fixed.func,
args=list(times=times.re
), Currency="CHF", ContractID="RE01")
addContracts(list(asset.fixed), FindNode(bank$Assets, "FixedAssets"))
# The rent must be modeled separately as operational revenue, cf. below.
## Liabilities -----------------------
#
# Debt ---------------------
# Savings -----------------
savings <- bond(ContractID="svg", start = tstart, maturity = "10 years",
nominal = 600*scale, coupon = yc$Rates[1], role="short",
CycleOfRateReset="P1YL0", MarketObjectCodeOfRateReset="YC")
addContracts(list(savings), FindNode(bank$Liabilities, "ShortTerm"))
#
# savings1 <- bond(ContractID="svg-delta", start = "2021-12-31", maturity = "9 years",
# nominal = 50*scale, coupon = yc$Rates[1], role="long",
# CycleOfRateReset="P1YL0", MarketObjectCodeOfRateReset="YC")
# addContracts(list(savings, savings1), FindNode(bank$Liabilities, "ShortTerm"))
# Long term debt ----------
ir.spread.liab <- 0.01
loan.long <- bond(ContractID="dlg1", start = tstart, maturity = "10 years",
nominal = 500*scale, coupon = spot.rates[4]+ir.spread.liab, role="short")
addContracts(list(loan.long), FindNode(bank$Liabilities, "LongTerm"))
plot(loan.long, t0)
### Operational cash flows ---------------
# Operations modeled 10 years into the future,
# with the exception of rent for real estate, which is modeled for the lifetime
# of the real estate investment, i.e. 50 years
times.ops <- timeSequence(tstart, by="1 years", length.out=11)
## Revenues ------------------
# Rent -----------------------
asset.fixed.rent <- 0.05 * asset.fixed.value
rent.yearly <- rep(asset.fixed.rent, 50)
#
rent.fun <- function(rent, times) {
timeSeries(data=rent, charvec=times)
}
rent.fun(rent.yearly, times.re[-51])
Rent <- OperationalCF(ContractID="RE-Rent", Currency="CHF", # Define contract
pattern=rent.fun,
args=list(rent=rent.yearly, times=times.re[-51]) )
# Test
# events(Rent, t0, rf)
addContracts(list(Rent), FindNode(bank$Operations, "Rent"))
# Commissions, Fees, etc. -----------------------
commissions <- 20*scale
# asset.fixed <- bond(start = tstart, maturity = "50 years",
# nominal = 200, coupon = asset.fixed.rent, role="long")
commissions.yearly <- rep(commissions, 10)
#
commissions.fun <- function(commissions, times) {
timeSeries(data=commissions, charvec=times)
}
Commissions <- OperationalCF(ContractID="Comm", Currency="CHF", # Define contract
pattern=commissions.fun,
args=list(commissions=commissions.yearly, times=times.ops[-1]) )
# Test
# events(Commissions, t0, rf)
addContracts(list(Commissions), FindNode(bank$Operations, "Commissions"))
## Expenses ------------------
# Salaries --------------
salaries.yearly <- rep(20*scale, 10)
#
salaries.fun <- function(times, expenses) {
timeSeries(-expenses, times)
}
Salaries <- OperationalCF(ContractID="Salaries", Currency="CHF", # Define contract
pattern=salaries.fun, args=list(
expenses=salaries.yearly,
times=times.ops[-1]) )
# Test
# events(Salaries, t0, rf)
addContracts(list(Salaries), FindNode(bank$Operations$Expenses, "Salaries"))
# Other -------------------
other.yearly <- rep(9*scale, 10)
#
other.fun <- function(times, expenses) {
timeSeries(-expenses, times)
}
Other <- OperationalCF(ContractID="Other", Currency="CHF", # Define contract
pattern=other.fun, args=list(
expenses=other.yearly,
times=times.ops[-1]) )
# Test
# events(Other, t0, rf)
addContracts(list(Other), FindNode(bank$Operations$Expenses, "Other"))
# Test: Which contracts are in the model? ----------
showContracts(bank)
# Performing the simulation ------
# calculate events
system.time({events(bank, t0, rf, end_date="2031-01-01")})
showEvents(bank)
### Analysis -------------------
# construction of time bucket
# t2 = "2021-01-02"
by <- timeSequence(t0, by="1 years", length.out=6)
(tb <- timeBuckets(by, bucketLabs=2021:2025,
breakLabs=substr(as.character(by),3,10)))
(val.nom <- value(bank, tb, scale=scale, digits=2)[,1:2])
# (val.nom <- value(bank, tb, scale=scale, digits=2)[,1,drop=FALSE])
(liq <- liquidity(bank, tb, scale=scale, digits=2)[,1:2])
(inc.nom <- income(bank, tb, scale=scale, digits=2)[,1:2])
(liq - inc.nom)[,1:2]
## Problem 1: ---------
## Problem 2 ----
# Create the current balance sheet of the bank -> cf.above
# Compute the equity capital ratio (equity / balance sheet total) -> 1/12 = 8.3%
# Equity ratio:
eq.ratio <- round(100*(-val.nom[12,]/val.nom[2,]),2)
rownames(eq.ratio) <- "eq.ratio"
eq.ratio
# Compute the ration of the liquid assets over the short term liabilities
# Compute the same way
## Problem 3: Analysis with shifted interest rates ---------
# Rerun the simulation with the shifted yield curve.
# Define new market environment with shifted rates
spot.rates.shifted <- c(0.01, 0.02, 0.03, 0.04)+0.01
yc.shifted <- YieldCurve(label = "YC",
ReferenceDate = t0,
Tenors = c("1M", "2Y", "5Y", "10Y"),
Rates = spot.rates)
rf1 <- RFConn(yc.shifted)
rf1[["YC"]]
# Change rates for contracts with variable interest rates
bank$Assets$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <- spot.rates.shifted[1]
bank$Liabilities$Debt$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <- spot.rates.shifted[1]
# Rerun simulation
events(bank, t0, rf1, end_date="2031-01-01")
### Analysis
# # construction of time bucket
# # t2 = "2021-01-02"
# by <- timeSequence(t0, by="1 years", length.out=6)
# (tb <- timeBuckets(by, bucketLabs=2021:2025,
# breakLabs=substr(as.character(by),3,10)))
(val.nom <- value(bank, tb, scale=scale, digits=2)[,1:2])
# (val.nom <- value(bank, tb, scale=scale, digits=2)[,1,drop=FALSE])
(liq <- liquidity(bank, tb, scale=scale, digits=2)[,1:2])
(inc.nom <- income(bank, tb, scale=scale, digits=2)[,1:2])
(liq - inc.nom)[,1:2]
## Problem 5 ----------------------
# Compute present value, future value, internal rate of return and duration of
# the cash flows resulting from real estate.
# Make the simplifying assumption that rent is paid yearly in advance
# and use the following interest rates for discounting:
# - 2 years spot rates for terms of 1-3 years
# - 5 years spot rates for terms of 4-6 years
# - 10 years spot rates for terms > 6 years
# Here we use the yield curve for discounting
re.rent <- bank$Operations$Revenues$Rent$contracts[[1]]
cfs <- cashFlows(re.rent, from=as.character(t0), to=as.character(times.re[51]))
(pv <- presentValue(cfs, yield=yc, by=times.re[1])/scale)
(futureValue <- pv * 1.04^50)
# To compute the internal rate of return, the initial investment of 200 mio
# must be added to cfs
cfs[1] <- cfs[1] - 200*scale
# Internal rate of return
irr(cfs)
# duration
duration(re.rent, type="fisher-weil", yield=yc, price=200*scale, from=t0)
## Problem 6 -------------------
# This cannot be solved naturally with FEMS
# because the capitalization of the net rent (rent - maintenance expenditure)
# can currently not be modeled with any existing contract
## Problem 7 --------------------
# The interest curve is randomly shifted
#
# We first set the interest rate of the variable contracts to the original values
bank$Assets$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <- spot.rates[1]
bank$Liabilities$Debt$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <- spot.rates[1]
# Simulation with original values
events(bank, t0, rf, end_date="2023-01-01")
# Analysis
by <- timeSequence(t0, by="1 years", length.out=6)
(tb <- timeBuckets(by, bucketLabs=2021:2025,
breakLabs=substr(as.character(by),3,10)))
# Lists for storing the analytical results
liq <- list()
val.nom <- list()
inc.nom <- list()
val.nom[["0"]] <- value(bank, tb, scale=scale, digits=2)[,1:2]
liq[["0"]] <- liquidity(bank, tb, scale=scale, digits=2)[,1:2]
inc.nom[["0"]] <- income(bank, tb, scale=scale, digits=2)[,1:2]
# Extract particular values of interest
shift <- numeric()
shift["0"] <- 0
profit <- numeric()
profit["0"] <- inc.nom[["0"]][1,1]
eq <- numeric()
eq["0"] <- -val.nom[["0"]][12,2]
liq.assets <- numeric()
liq.assets["0"] <- sum(val.nom[["0"]][3:4,2])
# loop over random shift of yield curve
# The simulation is pretty slow
# You can grow the simulated sample by setting ns.new <- nn.old
ns <- 1
nn <- 10
for (i in ns:nn) {
i.ch <- as.character(i)
# create random shift
shift[i.ch] <- rnorm(1, 0, 0.01)
spot.rates.shifted <- c(0.01, 0.02, 0.03, 0.04)+shift[i.ch]
print(c(i, as.numeric(shift[i.ch])))
yc.shifted <- YieldCurve(label = "YC",
ReferenceDate = t0,
Tenors = c("1M", "2Y", "5Y", "10Y"),
Rates = spot.rates.shifted)
rf1 <- RFConn(yc.shifted)
rf1[["YC"]]
# Change rates for contracts with variable interest rates
bank$Assets$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <-
spot.rates.shifted[1]
bank$Liabilities$Debt$ShortTerm$contracts[[1]][["ContractTerms"]][["NominalInterestRate"]] <-
spot.rates.shifted[1]
# Rerun simulation
events(bank, t0, rf1, end_date="2023-01-01")
# Store analysis
liq[[i.ch]] <- liquidity(bank, tb, scale=scale, digits=2)[,1:2]
inc.nom[[i.ch]] <- income(bank, tb, scale=scale, digits=2)[,1:2]
val.nom[[i.ch]] <- value(bank, tb, scale=scale, digits=2)[,1:2]
# Extract particular values
profit[i.ch] <- inc.nom[[i.ch]][1,1]
eq[i.ch] <- -val.nom[[i.ch]][12,2]
liq.assets[i.ch] <- sum(val.nom[[i.ch]][3:4,2])
}
res <- cbind(shift, profit, eq, liq.assets)
res[order(res[,1]),]
hist(res[,"shift"])
hist(res[,"profit"])
hist(res[,"eq"])
hist(res[,"liq.assets"])
## Problem 8 -------------------
# We model the fluctuation of the savings by a new contract in the
# Liabilities$Debt$ShortTerm account
# The changes occur at the last day of 2021.
# First, the contract is created with nominal 0
bank$Liabilities$Debt$ShortTerm$contracts <- NULL
savings1 <- bond(ContractID="svg-delta", start = "2021-12-31", maturity = "9 years",
nominal = 0*scale, coupon = yc$Rates[1], role="long",
CycleOfRateReset="P1YL0", MarketObjectCodeOfRateReset="YC")
addContracts(list(savings, savings1), FindNode(bank$Liabilities, "ShortTerm"))
# Now we randomly choose the changes of the savings.
# According to problem 8 in practice sheet 9, the volume should be a normally
# distributed random variable with mean 0 and stdev. 50.
# Since the nominal cannot be negative, we must distinguish two cases:
# - If the volume decreases we need a long contract
# - If the volume increases we need a short contract
nn <- 10
savings.delta <- rnorm(nn, 0, 50)
role <- rep("RPA", nn) # Real Position Asset = "long"
role[savings.delta<0] <- "RPL" # Real Position Liability = "short"
role
# Initialization
savings.delta <- numeric()
savings.delta["0"] <- 0
role <- character()
role["0"] <- "RPA"
liq <- list()
inc.nom <- list()
val.nom <- list()
fcf <- numeric()
current <- numeric()
bank$Liabilities$Debt$ShortTerm$contracts[[2]]$ContractTerms$NotionalPrincipal <- 0
bank$Liabilities$Debt$ShortTerm$contracts[[2]]$ContractTerms$ContractRole <- "RPA"
events(bank, t0, rf, end_date="2022-01-01")
# events(bank$Liabilities$Debt$ShortTerm, t0, rf, end_date="2022-01-01")
liq[["0"]] <- liquidity(bank, tb, scale=scale, digits=2)[,1:2]
inc.nom[["0"]] <- income(bank, tb, scale=scale, digits=2)[,1:2]
val.nom[["0"]] <- value(bank, tb, scale=scale, digits=2)[,1:2]
fcf["0"] <- liq[["0"]][1,1]
current["0"] <- sum(val.nom[["0"]][3:4,2])
# Loop over random changes of savings
ns <- 1
nn <- 10
system.time({
for (i in ns:nn) {
i.ch <- as.character(i)
savings.delta[i] <- rnorm(1, 0, 50)
if ( savings.delta[i]>=0 )
role[i] <- "RPA"
else
role[i] <- "RPL"
print(paste(i, savings.delta[i], role[i]))
bank$Liabilities$Debt$ShortTerm$contracts[[2]]$ContractTerms$NotionalPrincipal <- abs(savings.delta[i])*scale
bank$Liabilities$Debt$ShortTerm$contracts[[2]]$ContractTerms$ContractRole <- role[i]
# events(bank$Liabilities$Debt$ShortTerm, t0, rf, end_date="2022-01-01") # This doesn't work properly
events(bank, t0, rf, end_date="2022-01-01")
liq[[i.ch]] <- liquidity(bank, tb, scale=scale, digits=2)[,1:2]
inc.nom[[i.ch]] <- income(bank, tb, scale=scale, digits=2)[,1:2]
val.nom[[i.ch]] <- value(bank, tb, scale=scale, digits=2)[,1:2]
fcf[i.ch] <- liq[[i.ch]][1,1]
current[i.ch] <- sum(val.nom[[i.ch]][3:4,2]) # should be the sum of lines 3 and 4
}
})
res <- cbind(c(0,-round(savings.delta,2)), fcf, current)
colnames(res) <- c("d-savings", "free cf", "liq. assets")
res
hist(res[,1])
hist(res[,2])
## Problem 9 ------------------------
# We simulate the discovery rates and adjust the volume of the contracts that
# simulated the default accordingly
# construction of time bucket over 10 years
by <- timeSequence(t0, by="1 years", length.out=11)
(tb <- timeBuckets(by, bucketLabs=2021:2030,
breakLabs=substr(as.character(by),3,10)))
# Computation for 4% default rate of the remaining assets
default.rate <- rep(0.04,10)
default.rate.cum <- default.rate*c(1,cumprod(1-default.rate)[-10])
recovery <- 0.75
p.disc <- (1-recovery)*default.rate.cum
for(j in 1:2) {
i <- j
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
print(paste(i, j,
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["ContractID"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]]
))
}
for (j in 1:5) {
i <- j+2
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
print(paste(i, j,
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["ContractID"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]]
))
}
for (j in 1:10) {
i <- j+7
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
print(paste(i, j,
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["ContractID"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]],
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]]
))
}
system.time({events(bank, t0, rf, end_date="2032-01-01")})
showEvents(bank)
liq <- list()
inc.nom <- list()
val.nom <- list()
liq[["0"]] <- liquidity(bank, tb, scale=scale, digits=2)
inc.nom[["0"]] <- income(bank, tb, scale=scale, digits=2)
val.nom[["0"]] <- value(bank, tb, scale=scale, digits=2)
eq <- numeric()
eq["0"] <- val.nom[["0"]][12,10]
def.rates <- default.rate
dim(def.rates) <- c(1,10)
rownames(def.rates) <- "0"
colnames(def.rates) <- 1:10
# loop over random defaults rates
ns <- 1
nn <- 10
for (ctr in ns:nn) {
ctr.ch <- as.character(ctr)
default.rate <- runif(10, 0, 0.08)
default.rate.cum <- default.rate*c(1,cumprod(1-default.rate)[-10])
recovery <- 0.75
p.disc <- (1-recovery)*default.rate.cum
def.rates <- rbind(def.rates, default.rate)
rownames(def.rates)[ctr+1] <- ctr.ch
print(paste(ctr, default.rate))
for(j in 1:2) {
i <- j
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
}
for (j in 1:5) {
i <- j+2
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
}
for (j in 1:10) {
i <- j+7
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["NotionalPrincipal"]] <-
round(default.rate.cum[j]*mortgage.value,0)
bank$Assets$LT.default$contracts[[i]][["ContractTerms"]][["PremiumDiscountAtIED"]] <-
-round(p.disc[j]*mortgage.value,0)
}
system.time({events(bank, t0, rf, end_date="2032-01-01")})
liq[[ctr.ch]] <- liquidity(bank, tb, scale=scale, digits=2)
inc.nom[[ctr.ch]] <- income(bank, tb, scale=scale, digits=2)
val.nom[[ctr.ch]] <- value(bank, tb, scale=scale, digits=2)
eq[ctr.ch] <- val.nom[[ctr.ch]][12,10]
}
res <- cbind(
apply(def.rates, 1, function(x) 1-prod(1-x)),
-eq
)
colnames(res) <- c("total def", "equity")
# The second line shows equity. It should not be negative.
res[order(res[,2]),]
# histogram for equity
hist(res[,2])
# Liquidity cannot really be investigated with this model.
# We need a rule of how to reinvest the recovered money
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