SEEM 5840 Term Project Rules
Please choose one of the three topics, independently finish a report by using all the available resources except any help from other people. In the report, you should explain the problem to be resolved, your way to tackle it and the final results. Note that answers may not be unique and additional assumptions may be needed. The length of the report should be in pdf format which is no less than 3 pages but no more than 10 pages (A4 size). The file name should be in the format SID_LastName_FirstName.pdf. You do not need to submit your original programming codes if any. Please submit your report electronically in the Classviva website by 11:59pm May 9th, 2018.
Topic 1 Treasury Bond Futures
Chinese Government Bond (CGB) futures are traded on China Financial Futures Exchange (CFFEX).
a) CFFEX defines the formula to calculate the conversion factor as follows:
Obtain definitions of the parameters in this formula from http://www.cffex.com.cn and derive this formula rigorously from the original idea of setting different conversion factors for bonds in the delivery pool of bond futures.
b) T1806 is the 10 year CGB future to mature in June 2018. For all the deliverable bonds related to this future, use the data in the attached excel sheet to find the cheapest-to-deliver (CTD) bond. Check if the CTD bond has ever changed from January 1 to March 29 of 2018.
c) Assume there is no bid-offer transaction cost, no margin requirement for the CGB futures position, and you may borrow and deposit money freely at FR007 rate as shown in the excel sheet. For the period from April 2nd 2018 to the final delivery date of T1706. Explore if a portfolio with positions in cash, CGB bond and CGB future can be constructed, which creates arbitrage opportunity. If no such arbitrage opportunity exists, then construct a portfolio which most likely to generate positive profit during this period and analyse the scenarios that the portfolio would lose money.
Topic 2 Treasury Bond Yield Curves
Here we consider the yield curve of Chinese Government Bond (CGB).
Recall that a yield curve means a discounting factor function! for any future time t , which denotes the present value of $1 at time t. There is
another zero rate function! with the relationship
Discounting factors and zero rates could be obtained through the bootstrap process from instruments across different maturities.
a) At the last business day of every quarter in 2017 and the first quarter in 2018, build CGB yield curve based on 5 instruments, which are the latest issued 1 year, 3 year, 5 year, 7 year and 10 year CGB at the time. Assume
zero rates are constant within! , and linear functions on time intervals
! ,! ,! ,! respectively, where! are the remaining maturities of the 5 CGB bonds a the time. The relevant bonds basic parameters and pricing information are in the attached excel sheet. b) At chinabond.com.cn, the official CGB yield curve publishes everyday in the format of CGB yield levels for standard tenors. Use your results in a) to calculate 10y CGB yield levels at the 5 quarter ends, and compare them with the official published numbers (which already included the attached excel sheet). c) Suppose you invest in CGB 150023 on March 31, 2017, and redeem it on March 29, 2018. Use your result in a) to derive the purchase and sale prices of this instrument, and calculate the return for such investment. You may compare your result with the 10-year Treasury Bond Total Return Index published by Chinabond.
DF ( t )
z ( t )
DF ( t )= e z ( t ) t
[0, T 1 ]
[ T 1 , T 2 ] [ T 2 , T 3 ] [ T 3 , T 4 ] [ T 4 , T 5 ] Ti ( 1 i 5 )
Topic 3 Equity Index Options
CSI 300 Index is one of the most commonly used equity index in China,
which aims to reflect the price fluctuation and performance of China A share market across both Shanghai Stock Exchange and Shenzhen Stock Exchange. There are a few CSI 300 ETFs traded on the two exchanges, one of them is Huatai-PineBridge CSI 300 ETF (Ticker: 510300). CSI 300 Index Futures (Ticker: IF1806, IF1803, …, etc) are traded on Cffex. The attached excel sheet lists the close prices of CSI 300, CSI 300 ETF and CSI 300 Index Futures since January 2, 2014.
a) At every business day T from February 2, 2014 to now, use the data provided in [ T , T -1month] to calculate the historical annualised volatility of CSI 300 Index, and draw a curve to show your result. Design a way to draw ONE historical volatility curve for CSI 300 Index Futures..
b) For every business day T from January 1, 2014 to March 1, 2018, suppose you are the seller of the 1 month at-the-money spot call option. Use CSI 300 ETF every day from T to T +1month to manage the option risks by the delta-neutral heading strategy. Assume such hedging cost would be just option premium, use the Black-Sholes-Merton model to get the corresponding option volatility. Draw a curve to show your result and compare it with a). Here you may assume there is no dividend for CSI 300 and the risk-free interest rate is based on Shibor 1m.
c) Suppose you are a market maker, and were asked to give price for 1 month at-the-money spot call option on CSI 300 Index, what is the bid and offer price you plan to show and explain your calculation process.