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

1.选择您要处理的库存

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：

[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：

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. EasyDue™ 支持PayPal, AliPay, WechatPay, Taobao等各种付款方式!

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