# Given data
spot_price <- 3.49
interest_rate <- 0.063
time_to_delivery <- 4/12

# Calculate the delivery price
delivery_price <- spot_price * (1 + interest_rate)^time_to_delivery

# Print the result
cat("The delivery price in the forward contract is: $", round(delivery_price, 2), "\n")

# Given data
spot_price <- 110.70
interest_rate <- 0.058/2
time_to_delivery <- 3/12
No_contract = 20

# Calculate the delivery price
delivery_price <- No_contract* spot_price * (1 + interest_rate)^time_to_delivery

# Print the result
cat("The delivery price in the forward contract is: $", round(delivery_price, 2), "\n")

# Given data
spot_price <- 20.00
interest_rate <- 0.045
time_to_delivery <- 3/12

# Calculate the three-month forward price
forward_price <- spot_price * (1 + interest_rate)^time_to_delivery

# Print the result
cat("The three-month forward price of the asset is: $", round(forward_price, 2), "\n")

# Given data
spot_price <- 10.50
interest_rate <- 0.072
time_to_delivery_1 <- 4/12

# Calculate the four-month forward price
forward_price_1 <- spot_price * exp(interest_rate * time_to_delivery_1)

# Print the result
cat("The four-month forward price of a Bebop share is: £", round(forward_price_1, 2), "\n")

# Given data
time_to_delivery_2 <- 6/12

# Calculate the six-month forward price
forward_price_2 <- spot_price * exp(interest_rate * time_to_delivery_2)

# Print the result
cat("The six-month forward price of a Bebop share is: £", round(forward_price_2, 2), "\n")

# Given data
spot_price <- 35
interest_rate <- 0.048
number_of_periods <- 4/12

# Calculate the delivery price
delivery_price <- spot_price / (1 + (interest_rate / 2))^(number_of_periods)
cat("The delivery price on the forward contract is: £", round(delivery_price, 2), "\n")

# Calculate the four-month forward price
forward_price <- spot_price * (1 + (interest_rate / 2))^number_of_periods
cat("The four-month forward price on the team is: £", round(forward_price, 2), "\n")

# Update the spot price
spot_price_updated <- 32.5

# Calculate the three-month forward price
number_of_periods_2 <- number_of_periods - 1/12
forward_price_2 <- spot_price_updated * (1 + (interest_rate / 2))^number_of_periods_2
cat("The three-month forward price of the team is: £", round(forward_price_2, 2), "\n")

# Given data
spot_price <- 15
interest_rate <- 0.075
time_to_expiry <- 1

# (i) Calculate the initial value of the forward contract
initial_value <- spot_price * exp(interest_rate * time_to_expiry)
cat("The initial value of the forward contract is: £", round(initial_value, 2), "\n")

# (ii) Calculate the one-year forward price on the stock
forward_price <- spot_price * exp(interest_rate * time_to_expiry)
cat("The one-year forward price on the stock is: £", round(forward_price, 2), "\n")

# Update the spot price and time to expiry
spot_price_updated <- 17.70
time_to_expiry_updated <- 0.5

# (iii) Calculate the delivery price on the original forward contract
delivery_price <- spot_price_updated * exp(-interest_rate * time_to_expiry_updated)
cat("The delivery price on the original forward contract is: £", round(delivery_price, 2), "\n")

# Calculate the six-month forward price on the stock
forward_price_updated <- spot_price_updated * exp(interest_rate * time_to_expiry_updated)
cat("The six-month forward price on the stock is: £", round(forward_price_updated, 2), "\n")

# Given data
spot_price <- 18.50
interest_rate <- 0.087
time_to_expiry <- 0.5

# (i) Calculate the six-month forward price on the stock
forward_price_6m <- spot_price * exp(interest_rate * time_to_expiry)
cat("The six-month forward price on the stock is: £", round(forward_price_6m, 2), "\n")

# Update the spot price and time to expiry
spot_price_updated_1m <- 19.98
time_to_expiry_updated_5m <- 0.5 - 1/12

# (ii) Calculate the five-month forward price
forward_price_5m <- spot_price_updated_1m * exp(interest_rate * time_to_expiry_updated_5m)
cat("The five-month forward price on the stock is: £", round(forward_price_5m, 2), "\n")

# Calculate the value of the forward contract today
forward_contract_value_today <- (forward_price_6m - spot_price) * exp(interest_rate * time_to_expiry)
cat("The value of the forward contract today is: £", round(forward_contract_value_today, 2), "\n")

# Update the spot price and time to expiry
spot_price_updated_2m <- 19.50
time_to_expiry_updated_4m <- 0.5 - 2/12

# (iii) Calculate the four-month forward price
forward_price_4m <- spot_price_updated_2m * exp(interest_rate * time_to_expiry_updated_4m)
cat("The four-month forward price on the stock is: £", round(forward_price_4m, 2), "\n")

# Calculate the value of the forward contract after two months
forward_contract_value_2m <- (forward_price_4m - spot_price) * exp(interest_rate * time_to_expiry_updated_4m)
cat("The value of the forward contract after two months is: £", round(forward_contract_value_2m, 2), "\n")

# Given data
dividend_1 <- 5.50
dividend_2 <- 5.50
dividend_times <- c(1/12, 7/12)
asset_price <- 150
interest_rate <- 0.06
time_to_delivery <- 1

# Calculate the present value of dividends
pv_dividend_1 <- dividend_1 * (1 + interest_rate)^(-dividend_times[1])
pv_dividend_2 <- dividend_2 * (1 + interest_rate)^(-dividend_times[2])

# Calculate the delivery price
delivery_price <- (asset_price - pv_dividend_1 - pv_dividend_2) * (1 + interest_rate)^time_to_delivery

# Print the result
cat("The delivery price in the forward contract is: £", round(delivery_price, 3), "\n")

# Given data
share_price <- 10.00
dividend_rate <- 0.05/2
dividend_times <- c(4/12, 10/12)
interest_rate <- 0.06
time_to_delivery <- 14/12

# Calculate the present value of dividends
pv_dividend_1 <- share_price * dividend_rate * exp(-interest_rate * dividend_times[1])
pv_dividend_2 <- share_price * dividend_rate * exp(-interest_rate * dividend_times[2])

# Calculate the delivery price
delivery_price <- (share_price - pv_dividend_1 - pv_dividend_2) * exp(interest_rate * time_to_delivery)

# Print the result
cat("The delivery price in the forward contract is: £", round(delivery_price, 4), "\n")

# Given data
spot_price <- 20.00
dividend_rate <- 0.01
dividend_times <- c(3/12, 6/12)
interest_rate <- 0.065
time_to_delivery <- 10/12

# Calculate the present value of dividends
pv_dividend_1 <- spot_price * dividend_rate * exp(-interest_rate * dividend_times[1])
pv_dividend_2 <- spot_price * dividend_rate * exp(-interest_rate * dividend_times[2])

# Calculate the ten-month forward price and value of the contract today
forward_price_10 <- (spot_price - pv_dividend_1 - pv_dividend_2) * exp(interest_rate * time_to_delivery)
value_today <- 0

# Print the results
cat("The ten-month forward price is: $", round(forward_price_10, 5), "\n")

cat("The value of the contract today is: $", round(value_today, 2), "\n")

# Update the spot price
spot_price_updated <- 17

# Calculate the nine-month forward price and value of the contract
forward_price_9 <- (spot_price_updated - pv_dividend_1 - pv_dividend_2) * exp(interest_rate * (time_to_delivery - 1/12))
value_9 <- forward_price_9 - forward_price_10 * exp(interest_rate * 1/12)

# Print the results
cat("The nine-month forward price is: $", round(forward_price_9, 5), "\n")

cat("The value of the forward contract after one month is: $", round(value_9, 2), "\n")

# Update the spot price
spot_price_updated <- 25

# Calculate the eight-month forward price and value of the contract
forward_price_8 <- (spot_price_updated - pv_dividend_1 - pv_dividend_2) * exp(interest_rate * (time_to_delivery - 2/12))
value_8 <- forward_price_8 - forward_price_10 * exp(interest_rate * 2/12)

# Print the results
cat("The eight-month forward price is: $", round(forward_price_8, 5), "\n")

cat("The value of the forward contract after two months is: $", round(value_8, 2), "\n")

# Given data
spot_price = 1.87
interest_rate_uk = 0.048
interest_rate_us = 0.053
time_to_delivery = 6/12

# Calculate the forward price of the dollar
forward_price = spot_price * (2.71828**(-interest_rate_us*time_to_delivery)) * (2.71828**(interest_rate_uk*time_to_delivery))

# Print the result
print("The six-month forward price of the dollar:", forward_price)

# Given data
interest_rate_london = 0.0435
interest_rate_cyprus = 0.0616
exchange_rate = 1.1981
time_to_delivery = 4 / 12

# Borrowing in London
borrowed_amount = (1 + interest_rate_cyprus)**(-time_to_delivery) * exchange_rate

# Buying CYP
buying_amount = (1 + interest_rate_cyprus)**(time_to_delivery) * 10000

# Value of the portfolio
portfolio_value = -borrowed_amount + buying_amount

# Repaying the loan
repayment_amount = borrowed_amount * (1 + interest_rate_london)**(time_to_delivery)

# Calculate the pound amount
pound_amount = repayment_amount * 10000

pound_amount

# Given data
interest_rate_aud <- 0.0423
interest_rate_usd <- 0.0478
spot_price <- 0.7632
forward_price_1 <- 0.7700
forward_price_2 <- 0.7600

# Borrow AUD in New York
borrowed_amount <- spot_price * exp(interest_rate_aud * (-0.5))

# Buy AUD with the borrowed money
buying_amount <- exp(interest_rate_aud * (-0.5))

# Value of the portfolio
portfolio_value_1 <- forward_price_1 - borrowed_amount
portfolio_value_2 <- forward_price_2 - borrowed_amount

# Repay the loan
repayment_amount <- borrowed_amount * exp(interest_rate_usd * 0.5)

# Calculate the value of the portfolio at T
portfolio_value_T_1 <- repayment_amount - forward_price_1
portfolio_value_T_2 <- repayment_amount - forward_price_2

# Determine the trading position based on portfolio values
if (portfolio_value_T_1 > 0) {
  cat("The six-month forward price of the AUD was $0.7700. The New York dealer should be in a long position.\n")
} else {
  cat("The six-month forward price of the AUD was $0.7700. The New York dealer should be in a short position.\n")
}

if (portfolio_value_T_2 > 0) {
  cat("The six-month forward price of the AUD was $0.7600. The New York dealer should be in a long position.\n")
} else {
  cat("The six-month forward price of the AUD was $0.7600. The New York dealer should be in a short position.\n")
}

# Given data
share_price_today <- 5.70
dividend_rate <- 0.02
interest_rate_quarterly <- 0.045

# Calculate the continuously compounded annual rate for the safe interest rate
interest_rate_continuous <- exp(interest_rate_quarterly) - 1
# Calculate the continuously compounded rate for the two dividend payments
dividend_rate_continuous <- exp(2 * log(1 + dividend_rate)) - 1

# Calculate the one-year forward price
forward_price <- share_price_today * exp(interest_rate_continuous - dividend_rate_continuous)

# Print the result
cat("The one-year forward price of the BBR share is: ", round(forward_price, 4), "\n")

# Given data
share_price_today <- 15.50
dividend_rate_1 <- 0.06/2
dividend_rate_2 <- 0.061/2
dividend_rate_3 <- 0.061/2
interest_rate <- 0.055
time_to_dividend_1 <- 4/12
time_to_dividend_2 <- 10/12
time_to_dividend_3 <- 16/12
time_to_expiry <- 18/12

# Calculate the present value of dividend payments
pv_dividend_1 <- dividend_rate_1 * share_price_today * (1 + interest_rate)^(-time_to_dividend_1)
pv_dividend_2 <- dividend_rate_2 * share_price_today * (1 + interest_rate)^(-time_to_dividend_2)
pv_dividend_3 <- dividend_rate_3 * share_price_today * (1 + interest_rate)^(-time_to_dividend_3)

# Calculate the forward price using discrete dividend formula
forward_price_discrete <- (share_price_today - pv_dividend_1 - pv_dividend_2 - pv_dividend_3) * (1 + interest_rate)^time_to_expiry

# Calculate the continuously compounded rate for the dividend payments
dividend_rate_continuous <- exp(2 * log(1 + dividend_rate_3)) - 1

# Calculate the forward price using continuous dividend formula
forward_price_continuous <- share_price_today * exp(interest_rate - dividend_rate_continuous) * exp(-dividend_rate_continuous * time_to_expiry)

# Print the results
cat("The 18-month forward price on the shares using discrete dividend formula: £", round(forward_price_discrete, 2), "\n")

cat("The 18-month forward price on the shares using continuous dividend formula: £", round(forward_price_continuous, 2), "\n")

# Given data
exchange_rate_today <- 3767.676
forward_rate_six_months <- 3925.831
interest_rate_UK <- 0.0487
time_to_delivery <- 6/12

# Calculate the borrowed amount in BYR
borrowed_amount_BYR <- (1 + interest_rate_UK)^(-time_to_delivery) * exchange_rate_today

# Calculate the interest rate in Belarus
interest_rate_Belarus <- (forward_rate_six_months / borrowed_amount_BYR)^(1/time_to_delivery) - 1

# Print the result
cat("The estimated interest rate in Belarus (annually compounded) is:", round(interest_rate_Belarus, 4), "\n")

# Given data
asset_price_today <- 55.00
dividend_payment <- 2.50
time_to_dividend <- 2/12
interest_rate <- 0.05

# Calculate the present value of the first dividend payment
present_value_dividend_1 <- dividend_payment * exp(-interest_rate * time_to_dividend)

# Calculate the present value of the second dividend payment
present_value_dividend_2 <- dividend_payment * exp(-interest_rate * (time_to_dividend + 6/12))

# Calculate the borrowed amount for the forward contract
borrowed_amount <- asset_price_today - present_value_dividend_1 - present_value_dividend_2

# Calculate the 12-month forward price
forward_price <- borrowed_amount * exp(interest_rate * 1)

# Calculate the value of the forward contract today
forward_contract_value_today <- forward_price - borrowed_amount

# Print the results
cat("The 12-month forward price of the asset is: £", round(forward_price, 2), "\n")

cat("The value of the forward contract today is: £", round(forward_contract_value_today, 2), "\n")