Please help to solve Question d,e,f,g on the last page of the attached file

MFIN6003 Derivative Securities Dr. Huiyan Qiu Group Project #1 Due: September 12, Wednesday 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 email their write-ups to hqiu@hku.hk no later than September 12, 2012. Include a cover page with the information of all group members (name, university ID, and email address) and the group number. The file submitted has to be in PDF format and with name Project1_GroupXX. (XX refers to the group number. For example, 01 for group number 1.) Only after you receive an acceptance email from me, the submission can be considered as complete. It is the student's responsibility to contact me again if there is no such email response within one week. 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 your group and how each 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 any other relevant information for trading index futures. Find the daily trading information for the currently existing Hang Seng Index Futures contracts. Create a table containing information on open interest and settlement price of each contract on each trading day from August 1 to September 7, 2012. Draw a diagram to compare the prices of index futures over time, 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. 1 MFIN6003 Derivative Securities Dr. Huiyan Qiu Part III: Investing in Index Futures and Mark-to-Market Suppose you opened an investment account with BOCOM International Security Ltd. on August 2, 2010 and started to take a long position with 8 HSIF0910 contracts. (The Hang Seng Index Futures expiring in September 2010. Suppose you entered at that day's settlement price.) You closed your position on September 2, 2010. Refer to the appendix for the settlement price of HSIF0910 as well as the level of HSI from August 2, 2010 to September 2, 2010. 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$65,150 and HK$52,100, respectively, per contract. Assume the annual interest rate on your account is 0.1% 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, $0.80 commission levy (these three charges are per side per contract) and $10 settlement fee per contract (collected on the settlement day of the contract). Is your rate of return higher or lower than 0.1%? What if you invest (superficially) in HSI directly over the same period? Have some discussion. Appendix: Settlement price of HSIF0910 and level of HSI Date 8/2/2010 8/3/2010 8/4/2010 8/5/2010 8/6/2010 8/9/2010 8/10/2010 8/11/2010 8/12/2010 8/13/2010 8/16/2010 8/17/2010 HSI HSIF0910 21412.79 21330 21457.66 21393 21549.88 21442 21551.72 21442 21678.80 21542 21801.59 21690 21473.60 21375 21294.54 21213 21105.71 20874 21071.57 20939 21112.12 20890 21137.43 21004 Date 8/18/2010 8/19/2010 8/20/2010 8/23/2010 8/24/2010 8/25/2010 8/26/2010 8/27/2010 8/30/2010 8/31/2010 9/1/2010 9/2/2010 HSI HSIF0910 21022.73 20870 21072.46 20914 20981.82 20860 20889.01 20782 20658.71 20490 20634.98 20550 20612.06 20541 20597.35 20448 20737.22 20671 20536.49 20320 20623.83 20474 20868.92 20832 2 MFIN6003 Derivative Securities Dr. Huiyan Qiu Group Project #2 Due: October 10, Wednesday This project is to (1) apply binomial option pricing model to price option; (2) apply BlackScholes formula to price option over time; (3) understand the market-maker's delta hedging. Submission of the project: each group is required to email their write-ups to hqiu@hku.hk no later than October 10, 2012. 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 ID, and email address) and the group number. The second part is an excel file with spreadsheets showing your work for part (c) to (g). Both files should have name Project2_GroupXX. (XX refers to the group number.) Only after you receive an acceptance email from me, the submission can be considered as complete. It is the student's responsibility to contact me again if there is no such email response within one week. 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 ( = 0) The expected annual rate of return (continuously compounding) on the stock is 20% ( = 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 available in the CD-ROM accompanying the textbook, calculate the option value (to confirm the answer above) and four option Greeks (delta, gamma, theta and vega). 3 MFIN6003 Derivative Securities Dr. Huiyan Qiu 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. 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.) S 1 ln t 2 s s z 2 St 1 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) 50 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 50 spreadsheets). Discuss what you have learned about pricing and risk management from the simulation. 4