FIN311: If 𝑍𝑍 = 𝑋𝑋 + 2𝑌𝑌 and 𝑋𝑋 and 𝑌𝑌 are Independent Random Variables that are Formulated to be Normally Distributed with 𝑋𝑋: Mathematics and Programming for Finance Assignment, SUSS, Singapore

Question 1
If 𝑍𝑍 = 𝑋𝑋 + 2𝑌𝑌 and 𝑋𝑋 and 𝑌𝑌 are independent random variables that are formulated to be normally distributed with 𝑋𝑋 ∼ 𝑁𝑁(𝜇𝜇𝑥𝑥, 𝜎𝜎𝑥𝑥) and 𝑌𝑌 ∼ 𝑁𝑁(𝜇𝜇𝑦𝑦, 𝜎𝜎𝑦𝑦),
(a) What is the mean and standard deviation of 𝑍𝑍?

(b) Write down the Python function that allows you to evaluate the probability that Z < 2.0, given that you know the mean and variance of Z as 1.5 and 0.6 respectively

Question 2
Given the following information, assess and show the differences of each data structure listed below.

• pandas data frame
• pandas Series

If the bank saves the above trading information into a single data frame data where the I column is the index, write down the Python code to retrieve all transactions that involved Bank X in May 2019.

Question 3

If you are bullish about stock T, discuss and appraise whether each of the following strategies is appropriate for yielding the greatest return if you are correct.

Strategy A: Buy stock T

Strategy B: Buy call options on stock T

Question 4

Appraise each of the following statements about the use of hashing in Bitcoin in regards to whether it is correct or incorrect and why it is so.

Statement A: Hashing is used to encrypt the transaction information in a block so that it can later be decrypted.

Statement B: Hashing is used to hide a user’s identity in a transaction.

Question 5

a. Describe and distinguish the differences between a call and a put option. What is an investor’s outlook if he buys a call option? How does his view change when he buys a put option?

• A straddle is a combination of an ATM call and ATM put.

Given:

stock price = $40,

volatility = 45%,

maturity = 6 months,

risk free rate = 3%,

b. Calculate the price of a straddle.

c. Draw the payoff profile of a straddle. What is your market outlook if you buy a straddle?

d. You need to fund the purchase of a straddle with a bank loan charging a rate of 15%. The payment to the bank is made at the maturity date of the options. What must be the stock price at maturity in order for you to profit from your straddle purchase?.

Question 6

Mark has a trading account in crypto exchange and he has 1.25 bitcoins in his account. When Mark trades using his account, a fixed transaction fee of $5 is imposed if the transaction amount is less than $500. If the transaction is greater than $500, the fee will be 1.0% of the transaction amount. The number of bitcoins he trades is determined by the transaction amount less the transaction fee and the traded price of Bitcoin.

a. Analyze what will the miners do when such a transaction is presented in the blockchain

The prices of Bitcoin, on different dates, are given in a pandas prices data frame as shown, where the date is the index and information is stored in np.datetime64 format. btc and volume give the traded price and volume of bitcoin respectively on the date.

b. If Mark transacted $900 to buy bitcoins on the 3-June-2018, calculate

• the transaction price (txn_price) of bitcoin
• the transaction cost (txn_cost) and
• the number of units of bitcoins (txn_units) he has bought after paying for the transaction fee

c. If the transaction of Mark is stored in the following dictionary,

trade = {‘id’ : ‘bvd-294’,

‘txn_date’ : np.datetime64(‘2018-06-03’),

‘txn_amt’ : 900,

‘txn_direction’ : ‘buy’}

include the information calculated in (a) into the trade dictionary. The calculated fields should be derived using information given in the question, data from prices, trade, and suitable Python functions/operations.

Question 7

You are carrying out the automation of the following investment strategy in Python. An initial investment amount of $50,000 is used to acquire Stock A.

Every month, you are prepared to fork out a monthly amount of $1,000. The average price of Stock A in the portfolio is defined as the amount of cash put into the portfolio divided by the total number of units of Stock Anetin the portfolio.

Only integer units of stock can be purchased. Any remaining cash is used together with the monthly amount of $1,000 for the subsequent stock purchase.

a. For Month 1, show clearly that 12 units of stocks is purchased, the cash remaining is $70 and the average price of the stock in the portfolio is $94.67.

b. Given the following initialization in Python for your examination, design and write down Python code to calculate the integer units of A purchased with the given initial investment amount. Store the results in a Python list.

init_invt = 50000 monthly_invt = 1000 init_price = 95

c. Given the following Python list of the market price of the stock,

prices = [80, 102, 84, 41, 74, 55, 32, 77, 92, 40, 91, 26]

use a Python _for_ loop to implement and experiment with the investment strategy by composing suitable data structures. Report the final observed average price of A in the portfolio.