金融计算方法代写 Computational Methods in Finance代写
931Homework 2 FE621 Computational Methods in Finance 金融计算方法代写 For all the problems in this assignment you need to write computer programs an For all the problems in this assignment you ...
View detailsSearch the whole station
波动率预测代写 1.You will estimate the parameters of a few GARCH-type models using about ten years of data (from Jan 1, 2013 to Nov 30, 2022) for SPY
You will estimate the parameters of a few GARCH-type models using about ten years of data (from Jan 1, 2013 to Nov 30, 2022) for SPY (the S&P 500 ETF). I would like you to build this from scratch, rather than use a package. As I demonstrated in class, it’s easy to do in Excel, which has a built-in solver, but you can code it in Python and use its optimization library as well. I used the scipy.optimize.minimize function with method=’SLSQP’, which allows you to specify bounds on thevariables.
Estimate the parameters of a GARCH(1,1) model.
Estimate a GARCH(1,1) model with conditional returns having a Generalized Error Distribution.
Estimate a TGARCH(1,1) model with conditional returns having a normal distribution.
Compare the maximum value of the likelihood function for the models in parts (a), (b), and (c) to rank the three models. The maximum value of the likelihood function for parts (b) and (c) can be compared directly since they have the same number of parameters. Use the Schwartz Bayesian Criteria to compare likelihood functions when the number of parameters is different.
One way to download historical prices for SPY in Python is to pip install the yfinance library, import the library using
import yfinance as yf
and download the data with
df = yf.download(“SPY”, start=”2013-01-01″, end=”2022-11-30″)
Use the ”Adj Close” column, which adjusts for dividends.
The figure below lists prices and implied volatilities for puts and calls on SPY options as of the close on Wednesday, November 30, 2022. The middle column in the figure are the strikes, and the data on the left side are for the call options, and the data on the right side are for the put options. The column ”IVM” is the midmarket implied volatility. Thecolumn ”DM” is the midmarket delta of the options. The closing price for SPY on November 30, 2022 was 407.68. Use the TGARCH(1,1) model from part (c) above to price two options: the 416 strike call options (the delta is approximately 0.25), and the 400 put options (the delta is approximately -0.25). You should price these using a Monte Carlo simulation. These options expire on Friday, December 9, 2022, which is 7 trading days from Wednesday, November 30. Assume that the annual risk-free rate, rf , is 4.71% and there are no dividends.
Figure 1: Option Prices at the Close on Nov 30, 2022 for expiration Dec 9, 2022
What are the prices, and the corresponding Black-Scholes implied volatilities, for the two options?
There have been several stories in the news recently that the skewness in the volatility smile, as measured by the difference in volatilities between out-of-money put options and out-of-the-money call options, is the lowest it’s been since 2009.
The figure below shows a graph of the CBOE SKEW Index. Is that reduction in the skew justified, according to the results above? In other words, given the current difference in implied vols for 0.25 delta puts and calls of 18.88 − 17.01 = 1.87 Would your TGARCH model prefer to buy the puts and sell the calls, or sell the puts and buy the calls? A one-sentence explanation is sufficient.
Figure 2: The CBOE SKEW Index over the past 20 years
Consider the stochastic volatility (SV) model we discussed in class,given by:
rt= µ + σtϵt
ln(σt) = α + ϕ(ln(σt−1) − α) + ηt
You can use the class notes to find the expectations above. Just like with the first exercise, I would like you to estimate the parameters from scratch, rather than using a package. Also, to make things easier, you can choose to do two-step GMM rather than iterated GMM, and you can compute the weighting matrix assuming the data are uncorrelated so you don’t have to compute the Newey-West adjustment if you would like.
更多代写:Matlab作业 在家考gre作弊 英国找代写会被发现吗 如何写英文论文 多伦多代写作业 英国论文代写
合作平台:essay代写 论文代写 写手招聘 英国留学生代写
Homework 2 FE621 Computational Methods in Finance 金融计算方法代写 For all the problems in this assignment you need to write computer programs an For all the problems in this assignment you ...
View detailsSTAD57 Time Series Analysis Final Examination 时间序列分析代写 Duration: 3hours Examination aids allowed: Non-programmable scientific calculator, open book/notes Instructions: • Read the...
View detailsPython2 Python算法代写 测试数据 工单数量自由设定,先设定为 20 机器数量自由设定,先设定为 6,编号为[1 2 3 4 5 6] 工人数量自由设定,先设定为 2,编号为[1 2] PTq[5 10 15 20 25 5 10 15 20 25 5 10 15 20 2...
View detailsCS579/ECE599 Assignment Homework 1 物理攻击与对策代写 Please complete this assignment (100 pts total) and submit your report/program code on Canvas (all files compressed in one .zip witho...
View details