dollar-level

Dollar-level是一种资产定价的方法，通常用于定价高价值的资产，如房地产、艺术品、珠宝等。该方法是指将资产的价格定在整数百万美元的水平上，而不是以小数或千位数的形式报价。例如，如果一栋房子的价值为300万美元，使用dollar-level方法定价后，价格将被报为300万美元，而不是3,000,000美元。这种定价方法可以使买家和卖家更容易理解和比较资产的价格，同时也可以提高资产的知名度和独特性。

相关问题

Obtain a density plot of the daily long returns of Dollar-Euro exchange rate.

To obtain a density plot of the daily long returns of Dollar-Euro exchange rate, you can follow these steps:

1. Collect the daily exchange rate data of Dollar-Euro from a reliable source such as Yahoo Finance or Quandl.
2. Calculate the daily long returns by taking the natural logarithm of the ratio of current exchange rate to the previous day's exchange rate.
3. Use a programming language such as R or Python to plot the density of the daily long returns.
4. Here is an R code example to create a density plot:

library(ggplot2)

# read in exchange rate data
exchange_rate <- read.csv("exchange_rate.csv")

# calculate daily long returns
exchange_rate$log_returns <- log(exchange_rate$rate) - log(lag(exchange_rate$rate))

# plot density
ggplot(exchange_rate, aes(x = log_returns)) +
  geom_density(fill = "blue", alpha = 0.5) +
  labs(title = "Density Plot of Daily Long Returns of Dollar-Euro Exchange Rate")

This will produce a density plot of the daily long returns of Dollar-Euro exchange rate.

Daily foreign exchange rates (spot rates) can be obtained from the Federal Reserve Bank in St Louis (FRED). The data are the noon buying rates in New York City certified by the Federal Reserve Bank of New York. Consider the exchange rates between the U.S. dollar and the Euro from January 4, 1999 to March 8, 2013. See the file d-exuseu.txt. (a) Compute the daily log return of the exchange rate. (b) Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns of the exchange rate. (c) Obtain a density plot of the daily long returns of Dollar-Euro exchange rate. (d) Test H0 : µ = 0 versus Ha : µ ̸= 0, where µ denotes the mean of the daily log return of Dollar-Euro exchange rate.

(a) The daily log return of the exchange rate can be calculated using the following formula:

log return = ln(price[t]) - ln(price[t-1])

where price[t] represents the exchange rate at time t and price[t-1] represents the exchange rate at time t-1.

Using the data in the file d-exuseu.txt, we can calculate the daily log returns as follows (assuming the data is stored in a variable called "exchange_rate"):

import numpy as np

log_returns = np.log(exchange_rate[1:]) - np.log(exchange_rate[:-1])

The first element of "exchange_rate" is excluded from the calculation because there is no previous price to compare it to.

(b) The sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns can be calculated using the following code:

mean = np.mean(log_returns)
std_dev = np.std(log_returns)
skewness = stats.skew(log_returns)
kurtosis = stats.kurtosis(log_returns, fisher=False)
minimum = np.min(log_returns)
maximum = np.max(log_returns)

print("Sample mean:", mean)
print("Standard deviation:", std_dev)
print("Skewness:", skewness)
print("Excess kurtosis:", kurtosis - 3) # convert to excess kurtosis
print("Minimum:", minimum)
print("Maximum:", maximum)

This code requires the "scipy.stats" module to be imported at the beginning of the script. The output will show the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns.

(c) To obtain a density plot of the daily log returns, we can use the following code:

import matplotlib.pyplot as plt

plt.hist(log_returns, bins=50, density=True)
plt.xlabel("Daily log return")
plt.ylabel("Density")
plt.show()

This code will create a histogram of the log returns with 50 bins and normalize it to create a density plot. The output will show the density plot of the log returns.

(d) To test the hypothesis H0 : µ = 0 versus Ha : µ ̸= 0, where µ denotes the mean of the daily log return of Dollar-Euro exchange rate, we can use a t-test. The null hypothesis states that the mean log return is equal to zero, while the alternative hypothesis states that the mean log return is not equal to zero.

from scipy.stats import ttest_1samp

t_stat, p_value = ttest_1samp(log_returns, 0)

print("t-statistic:", t_stat)
print("p-value:", p_value)

This code uses the "ttest_1samp" function from the "scipy.stats" module to calculate the t-statistic and the p-value. The output will show the t-statistic and the p-value of the test. If the p-value is less than the significance level (e.g., 0.05), we can reject the null hypothesis and conclude that the mean log return is significantly different from zero.