本次金融代写主要是计算金融方向进行量化分析金融股票数据

CMSC 5718 Introduction to Computational Finance Assignment 3: Derivative trading strategies (40% of total grade)

介绍

在本作业的第一部分中,我们利用恒生指数中某些股票的历史价格来测试三角套期保值策略。这些测试可能不太现实,因为某些交易条件已被忽略。特别是不包括股息和交易成本,但我们的目的是证明理论框架的有效性。第二部分考察了衍生策略的一些理论关系。

第一部分:期权对冲(50%)
1.选择您要处理的库存

对于此部分,请使用您的学生编号来确定执行分析所必须使用的股票。用您的学生编号的最后两位数字,使用49模获得订单号,并从给定的数据表中查找股票代码。例如,如果您的学生编号以18结尾,则订单号为(18 mod 49 = 18),因此库存为腾讯控股有限公司(股票代码700)。如果您的学生编号以84结尾,则订单号为(84 mod 49 = 35),库存为Sands China Ltd.(股票代码1928)。如果您的学生编号以00、49或98结尾,则选择阿里巴巴集团控股有限公司(股票代码9988)。该股票在以下问题中称为X股票,您的分析应基于该股票和恒生指数。

2.波动率计算和期权定价(12%)

i)使用2019年12月31日至2020年12月31日的每日数据计算恒生指数(HSI)和股票X的已实现波动率。

ii)使用已实现的波动率(以上计算)和给出的隐含波动率以及Black-Scholes公式为恒指和股票X的以下期权定价:

欧洲看涨期权(平价)(截至2019年12月31日),连续复利= 1.25%,期限= 1年(2020年12月31日)。

[请参阅作业2中的公式]
[无股息欧洲看涨期权的差额:N(d1)]

3.检验三角套期保值策略(38%​​)

i)假设您按照(2(ii))中所述,在HSI上做空M个看涨期权,在股票X上做N个看涨期权。此外,假设指数HSI可以作为股票进行买卖。使用电子表格中提供的每日价格数据,为2019年12月31日至2020年12月31日之间的两个头寸中的每个头寸构建增量套期保值策略(格式在电子表格中给出)。每天的帐户余额是通过将以下部分相加得出的:

以前的帐户余额。

利息费用(假设必须借入帐户余额,

并且每天计算利息,即产生的利息=借入金额x利率x num_days / 365; num_days是从前一个日期到当前日期的天数,因此它可以是一天或一天​​以上,具体取决于是否有节假日。

股份交易所需/收到的现金。 2个

在此练习中,可以忽略每手交易量,您可以交易小数股,并且可以假设可以按照给定的方式使用连续复利利率。您必须为两个基础分别执行两组计算。在第一组中,使用给定的隐含波动率来计算Black-Scholes框架下的增量。在第二组中,使用您在上面2(i)中计算的2019年12月31日至2020年12月31日之间的已实现波动率来生成增量。在您的报告中,在此表中包括几行(但无需包括所有日期)。到期日,如果期权是价内期权,则需要在股票账户中累积正确数量的股份,并且该头寸将以执行价格出售给期权持有人。如果期权价格不菲,则无需进行此类交易。在这四种情况下,到期日的最终帐户余额是多少?

ii)于2019年12月31日,您将从做空看涨期权(如上文2(ii)中所述)所收到的钱存入一个存款账户,连续年复利为1.25%。存款的到期日为2020年12月31日。计算您将在到期时获得的金额。将这四个金额与上面3(i)中获得的最终帐户余额进行比较。帐户中的总金额是否与存款帐户中的总金额匹配?

Instructions

  1. 1)  Submit a copy of your report together with supporting programs and/or data files (as a zipped file) by uploading to Blackboard on or before April 22, 2021, 11:59pm. The file name of the zipped file or your report should include your surname and have the following format, e.g. Assign3. [If uploading to Blackboard is not successful, you may consider sending a email, but submission through Blackboard is preferred.]
  2. 2)  No late submission is allowed.
  3. 3)  This is an INDIVIDUAL assignment. Each student should submit one report.
  4. 4)  Please observe the university’s plagiarism guidelines.

Introduction

In the first part of this assignment, we make use of historical prices of some stocks in the Hang Seng Index to test the delta hedging strategy. These tests may not be too realistic as some trading conditions have been ignored. In particular, dividends and transaction costs are not included, but our aim is to show the validity of the theoretical framework. Part two examines some theoretical relationships of derivative strategies.

Part I: Option Hedging (50%)
1. Choose the stock that you have to work on

For this part, use your student number to decide which stock you have to use to perform the analysis. Take the last two digits of your student number and use modulo 49 to obtain the order number, and look up the stock code from the given data sheet. For example, if your student number ends with 18, the order number is (18 mod 49 = 18), and the stock is thus Tencent Holdings Ltd. (stock code 700). If your student number ends with 84, the order number is (84 mod 49 = 35), and the stock is Sands China Ltd. (stock code 1928). If your student number ends with 00, 49 or 98, then select Alibaba Group Holdings Ltd (stock code 9988). This stock is known as stock X in the questions below, and your analysis should be based on this stock and the Hang Seng Index.

2. Volatility calculation and option pricing (12%)

  1. i)  Calculate the realized volatilities of the Hang Seng Index (HSI) and stock X, using the daily data of December 31, 2019 to December 31, 2020.
  2. ii)  Use the realized volatilities (calculated above) and the implied volatilities given and the Black-Scholes equation to price the following options for HSI and stock X: European call option, at-the-money (as of December 31, 2019), continuously compounded interest rate = 1.25%, maturity = 1 year (December 31, 2020).

    [refer to the formulas in assignment 2]
    [delta for a European call option with no dividend:
    N(d1)]

3. Testing of delta hedging strategy (38%)

i) Assume that you are short M call options on HSI and N call options on stock X as described in (2(ii)). Furthermore, assume that the index HSI can be bought or sold as a stock. Using the daily price data given in the spreadsheet, construct a delta hedging strategy for each of the two positions for the period between December 31, 2019 to December 31, 2020 (the format is given in the spreadsheet). The account balance on each day is calculated by summing the following components:

  • Previous account balance.
  • Interest cost (assume that the account balance has to be borrowed, and interest is calculated daily, i.e. interest incurred = borrowed_amount x interest_rate x num_days/365; num_days is the number of days from the previous date to the current date, so it can be one day or more than one day, depending on whether there are holidays).
  • Cash required / received from share transaction. 2

In this exercise, board lots can be ignored and you can trade fractional shares, and you can assume that the continuously compounded interest rate can be used as given. You have to perform two sets of calculations for each of the two underlyings. In the first set, use the given implied volatilities to calculate the deltas under the Black-Scholes framework. In the second set, use the realized volatilities between December 31, 2019 to December 31, 2020 that you calculate in 2(i) above to generate the deltas. In your report, include a few lines of this table (but no need to include all the dates). On maturity date, if the option is in-the-money, you need to accumulate the correct number of shares in the share account, and this position is to be sold to the option holder at the strike price. No such transactions are needed if the option is out-of-the-money. What is the final account balance on the maturity date in each of the four cases?

ii) On December 31, 2019, you have deposited the money that you received from shorting the call options (as in 2(ii) above) into a deposit account, earning a continuously compounded interest of 1.25% p.a. The maturity of the deposit is December 31, 2020. Calculate the amounts that you would obtain at maturity. Compare these four amounts with the final account balances obtained in 3(i) above. Does the total amount in the account match the total amount in the deposit account? Comment briefly on the result.


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