### MFIN6003 安全

MFIN6003 Derivative Securities

Group Project #1

Due date: Session 6

The aim of this project is to get familiar with your group members, the Hang Seng Index

Futures, and the mark-to-market process in futures trading.

Submission of the project: each group is required to submit their write-ups in PDF in the

course Moodle page by the due date.

Include a cover page with the information of all group members (name, university

number, and email address) and the group number.

Only PDF file will be accepted by the system and the submission system closes at

11:59pm on the due date.

The write-up should include three parts.

Part I: Group Introduction

Each group is required to have a group introduction in their write-up. Not only briefly

introduce all group members, but also identify the strengths and weaknesses of the group

and how group member can learn from each other and benefit from group projects.

Part II: Hang Seng Index Futures

Provide contract specification on the Hang Seng Index Futures.

Provide some other relevant information for trading index futures. Be selective. The

purpose is for you to research on information and digest the information. Then

present the information that is more relevant.

Find the daily trading information of ALL short-dated Hang Seng Index Futures

contracts during the following period: August 2 to September 10, 2021. Create a

table presenting the information on open interest and settlement price of all short-

dated futures contracts during the specified period.

Draw a diagram to compare the prices of index futures over time for the specified

period, with the dates for the x-axis and daily settlement price for the y-axis. Note:

Hang Seng Index level should also be included for comparison.

MFIN6003 Derivative Securities Dr. Huiyan Qiu

Group Projects Page 2/4

Part III: Investing in Index Futures and Mark-to-Market

Suppose you opened an investment account with BOCOM International Security Ltd.

on August 5, 2020 and started to take a long position with 8 HSIF0920 contracts. (The Hang

Seng Index Futures expiring in September 2020. Suppose you entered at that day’s

settlement price.) You closed your position on September 9, 2020. Refer to the appendix for

the settlement price of HSIF0920 as well as the level of HSI from August 5, 2020 to

September 9, 2020.

Prepare a table showing your margin account (daily balance, futures price,

gain/loss…) Initial margin and maintenance margin for Hang Seng Index Futures over

the investment period were HK$110,257 and HK$88,205, respectively, per contract.

Assume the annual interest rate on your account is 0.5% with continuous

compounding.

Calculate the annualized rate of return on your investment. For simplicity, assume

that over the period, you met all margin calls if any and you didn’t withdraw money

from your account even when you could. Use the following numbers for transaction

cost matter: $100 BOCOM commission fee, $10 exchange fee, $0.54 commission levy

(these three charges are per side per contract) and $10 settlement fee per contract

(collected only on the final settlement day of the contract).

Is your rate of return higher or lower than 0.5%? What if you invest (superficially) in

HSI directly over the same period? Have some discussion.

Appendix: Settlement price of HSIF0920 and level of HSI

Date HSI HSIF0920 Date HSI HSIF0920

8/5/2020 25,102.54 24,924 8/24/2020 25,551.58 25,416

8/6/2020 24,930.58 24,696 8/25/2020 25,486.22 25,358

8/7/2020 24,531.62 24,275 8/26/2020 25,491.79 25,342

8/10/2020 24,377.43 24,288 8/27/2020 25,281.15 25,131

8/11/2020 24,890.68 24,775 8/28/2020 25,422.06 25,367

8/12/2020 25,244.02 25,119 8/31/2020 25,177.05 25,080

8/13/2020 25,230.67 25,032 9/1/2020 25,184.85 25,076

8/14/2020 25,183.01 24,983 9/2/2020 25,120.09 25,058

8/17/2020 25,347.34 25,201 9/3/2020 25,007.60 24,928

8/18/2020 25,367.38 25,259 9/4/2020 24,695.45 24,678

8/19/2020 25,178.91 25,040 9/7/2020 24,589.65 24,525

8/20/2020 24,791.39 24,581 9/8/2020 24,624.34 24,483

8/21/2020 25,113.84 24,965 9/9/2020 24,468.93 24,415

MFIN6003 Derivative Securities Dr. Huiyan Qiu

Group Projects Page 3/4

Group Project #2

Due date: October 19, Tuesday

This project is to (1) apply binomial option pricing model to price option; (2) apply Black-

Scholes formula to price option over time; (3) understand the market-maker’s delta

hedging.

Submission of the project: each group is required to submit their work in the course

Moodle page by the due date.

The submission of this project should have two parts. The first part is a PDF file

which contains a report of ALL the results. Include a cover page with the information

of all group members (name, university number, and email address) and the group

number. The second part is an excel file with spreadsheets showing your work for

part (c) to (g).

Note that only PDF file and EXCEL file will be accepted by the system and the

submission system closes at 11:59pm on the due date.

Consider a stock with current stock price of $20 and a call option on the stock with strike

price of $21 and 50 days to expire (T = 50/365).

The following information is also available:

The stock is not paying any dividend (δ = 0)

The expected annual rate of return (continuously compounding) on the stock is

20% (α = 20%) and its volatility is 50% ( = 50%).

Annual continuously compounding risk-free interest rate is 5% (r = 5%)

a. Use n = 1, 5, 10, 25, or 50 (correspondingly, h = 50/365, 10/365, 5/365, 2/365, or 1/365)

in binomial option model to calculate the option value. Take the risk-neutral pricing

approach instead of constructing the complete binomial trees.

b. Use the Black-Scholes formula to calculate the option value.

c. Using the functions for option values and option Greeks to calculate the option value (to

confirm the answer above) and four option Greeks (delta, gamma, theta and vega).

MFIN6003 Derivative Securities Dr. Huiyan Qiu

Group Projects Page 4/4

i. To make best use of these functions for this project, install the Add-In

“OptAll2.xla” in your own spreadsheet. Refer to file “excel_functions.pdf” for

instruction.

ii. Both “OptAll2.xla” and “excel_funcations.pdf” are files in the CD-ROM

accompanying the textbook and are made available on the course Moodle page

for students’ use.

d. Generate a random sequence of stock prices for 50 days.

i. Generate a set of 50 random numbers z from the standard normal distribution

and define s = 1/365.

ii. Use the following equation to generate the daily stock prices. (Note the current

stock price is $20. Refer to Chapter 18 of McDonald’s for understanding of the

lognormal model of stock prices.)

e. Based on the stock price series generated in (d), calculate the option value and the four

option Greeks from day 1 to day 50. Note that as time goes by, the maturity of the

option drops to zero. Plot the option value from now to maturity.

f. Assume that you are the market maker who just issued 1 million units of call option. To

hedge your short option position, you take a long position on the synthetic call and

rebalance your account daily (daily delta hedging). Since hedging is not continuous but

daily, there will be resulted hedging profit or loss every day. Prepare a spreadsheet

showing the following information over the entire period: stock price, option value,

option delta, your hedging position (stock position and money market position), and the

hedging profit or loss. Compute the cumulative hedging profit or loss (with interest) over

the entire period and express it as a percentage of the original call premium.

g. Repeat steps (d), (e), and (f) 100 times. Each time, you get the cumulative hedging profit

or loss as a percentage of the original call premium. Compile a list of these numbers and

prepare a table of summary statistics (mean, standard deviation, maximum, etc.). For

this repetition job, show me the list and the table only (not the 100 spreadsheets).

Discuss what you have learned about pricing and risk management from the simulation.

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