这个作业是用R语言蒙特卡洛模拟期权走势收益

MFIT5011 Course Project

主题1:蒙特卡洛模拟的增强
回想一下,蒙特卡洛模拟是一种有效的算法,可用来估计期望值
随机变量的函数值(即𝔼[𝑓(𝑋1,𝑋2,…,𝑋𝑛
)])。但是,准确
估算需要大量的仿真路径(即大样本量),并且
算法可能很耗时。因此,有人想修改蒙特卡洛
模拟,这样就可以在不增加数量的情况下提高精度
模拟路径。这种技术被称为方差减少技术。
在这个项目中,您需要探索两种流行的方法来提高效率。
算法:(i)对立变量方法和(ii)重要抽样方法。详细
可以在以下参考书中找到这两种方法:
[1] Glasserman,P.(2003),“金融工程中的蒙特卡洛方法”,施普林格
(*您可以使用ITSC帐户并通过科大访问参考书的电子副本
图书馆。)
我们将重点关注使用布莱克-斯科尔斯模型的欧洲期权的定价,并研究如何
这两种方差减少方法可以提高估计的准确性。

Topic 2: Examining effectiveness of a dynamic trading strategy using Monte-Carlo simulation
In the lecture, we have demonstrated that Monte-Carlo simulation is also effective in
evaluating the profitability/return of a dynamic trading strategy. In this project, you are asked
to extend this analysis to the case when there are multiple risky assets.
Assumption: Assume that the investment period is 30 trading days.
Working Elements:
1. The first step is to construct a mathematical model that describe the future movement
of the asset stock.
 Collect historical data of several stocks (4~5 stocks) in the market over the
period 1st Jan, 2014 – 31st, Dec, 2019. You can consider the stock in United States,
Hong Kong or China etc.
 Based on the data that you obtained, fit a distribution/model to model the daily
return (as percentage return or of the stock (multivariate normal distribution,
multivariate 𝑡-distribution or linear regression model etc.). Provide justification
to your model.
(😊Hint: You are advised to choose the stock with high trading volume (e.g. composite
stocks in major index such as Dow jones index (US), Nasdaq index (US), Hang Seng Index
(HK) or Shanghai composite index etc.)
(😊Hint 2: There is no specific requirement on the choice of the stocks. You may
consider a group of stocks that are suitable to a particular model.)
2. Consider two dynamic trading strategies (you can use the existing trading strategy used
in financial community or create your own trading strategy). Provide specific details to
each of the trading strategies (i.e. how do you do the trading over the entire investment
period) and briefly explain the motivation of each of the trading strategy.
3. Based on the model constructed in Step 1, examine the performance of the trading
strategies (e.g. the distribution of the portfolio return, the probability of achieving
certain return) identified in Step 2 using Monte Carlo simulation.


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