悉尼大学FINC6005 assignment

෪ If market is arbitrage free, the payoff from all states of A ଴ should be greater than zero: ൅ >0
௉ ଼
‫ۍ‬ସ଼ ൅ ଼ ‫ې‬ ‫ ଻ ێ‬௉‫ۑ‬ ‫ێ‬ଵଶ െ ଶ ‫ۑ‬ ‫ ێ‬௉ ‫ۑ‬ ‫ ۏ‬ଶ ‫ے‬
-2-
FINC6005 Group Assignment
1. a）state contigent payoff matrix Call Put Stock
ିଵ ்ܵ =൥ 1
4
K=8, when stock price is 12 at T, call option will exercise and generate payoff=(X-K)+=(12-8)=4, but put will not exercise,payoff=0. when stock price at middle state=9, call option still can exercise and earn payoff=( X-K)+=(9-8)=1,put will not exercise. When stock price=6 at down state, call option will not exercise, put option will exercise and get payoff=(K-X)=(8-6)=2.
ଵ
This strategy implies that short 1/8 units in call option, and long 1/8 units in both the put option and the stock. As the payoff is the zero coupon bond, therefore the final strategy is the added up amout of the three AD securities strategies.
12 9൩ 6
det(்ܵ ) = 4*(0*6-2*9)+0*(1*6-0*9)+12*(1*2+0*0) = -48 ≠0. Then, the market is complete under this result.
-3-
FINC6005 Group Assignment
b)
ିଵ to determine the trading strategy for Arrow-Debreau security, firstly, calculate ்ܵ . ିଵ ்ܵ = 1/det(்ܵ )* adjusted (்ܵ )
ଵଵ ௉
P>-11/6
-5-
FINC6005 Group Assignment
଻
ଵଶ ௉ ଶ
െ >0
௉ ଶ
P< 14/12
0<P<
ଵସ ଵଶ
c) The A-D price are given by: െ ‫ ې‬ଷ ‫଼ ۍ‬ ଼ ଶସ ଵ ଵ ଵ ‫ۑ‬ ଶ ‫ێ‬ ିଵ ෪ A * ቎ ଴ =ሾ்ܵ ሿ′ ‫ܵ כ‬଴ =‫ێ‬െ ଶ െ ଶ ܲ቏= ଺ ‫ۑ‬ ‫ێ‬ ‫ۑ‬ ଵ 0 ‫ ے‬8 ‫ۏ‬0 ଶ
ଷ ଵ ଵ
ଵଵ ସ଼
By filling out and using this cover sheet, you approve of the information contained. Filling out and then using this coversheet as part of an electronic submission operates in the same way as if you had physically signed a paper copy of the cover sheet.
-4-
FINC6005 Group Assignment
‫଼ ۍ‬ ଶ ଵ ଵ ‫ێ‬ ିଵ െ Θ=்ܵ *்ܷ = ‫଼ ێ‬ ଶ ‫ ێ‬ଵ ଵ ‫ۏ‬െ ଶସ ଺
ଷ
െ
ଵ
0‫ې‬ 1 ଵ‫ۑ‬ * ൥1൩= ଶ‫ۑ‬ ‫ ۑ‬1 0‫ے‬
‫ۍ‬െ ଼‫ې‬ ‫ ێ‬ଵ ‫ۑ‬ ‫ۑ ଼ ێ‬ ‫ ێ‬ଵ ‫ۑ‬ ‫ے ଼ ۏ‬
FINC6005 Group Assignment
Faculty of Economics and Business
The University of Sydney
Group Assessment Cover Sheet Electronic submission
Group Name: ________Group 1______________________________________________________________ Assessment title:______FINC6005 Group Assignment __________________________________________________ Word limit of assessment:____no_____________ Word count: _________________no_______________ Unit of Study code & name:_____FINC 6005____________________________________________________ Lecturer/Tutor’s name:___Hamish Malloch_____ Due date:____31/05/2011____________________ After marking, this assignment will be collected Academic Honesty All forms of plagiarism and unauthorised collusion are regarded as academic dishonesty by the University, resulting in penalties including failure of the unit of study and possible disciplinary action. If you are in doubt about academic honesty, please consult with the unit coordinator. Lecture/Tutorial day/time:_____Tuesday __5 PM____________ Time and date submitted:____31/05/2011_______________ by: ________________________________________
ଷ
‫ۍ‬െ ଶ‫ې‬ ‫ ێ‬ଵ‫ۑ‬ ߆௠ = ‫ێ‬െ ଶ‫ۑ‬ ‫ ێ‬ଵ ‫ۑ‬ ‫ے ଺ ۏ‬
ଵ
߆ௗ = ቎ ଶ ቏ 0
0
ଵ
These are the payoffs of AD-Security which respectively at upper state, median state and at down state when market is in each one given state. The strategy with production of zero coupon bond payoff would be:
Declaration – (Tick each box and fill in details)
-1-
FINC6005 Group Assignment
√We have read and understood the University of Sydney Student Plagiarism: Coursework Policy and Procedure; √ We understand that failure to comply with the above can lead to the University commencing proceedings against me for potential student misconduct under Chapter 8 of the University of Sydney By-Law 1999 (as amended). √ We certify that this work is substantially our own, and where any part of this work is not our own, we have indicated as such by acknowledging the source of that part or those parts of the work. √ We have completed the online academic honesty module (if applicable) √ The assessment has not been submitted previously for assessment in another unit √ The assessment conforms to the requirements in the Unit of Study Outline. √ We have retained a duplicate copy of the assessment √ The Faculty may reproduce this assignment, provide a copy to another member of faculty, and/or communicate a copy of this assignment to a plagiarism checking service (which may then retain a copy of the assignment on its database for the purpose of future plagiarism checking). Student Name Jingwen WANG Ruyi JIAO Xingwen WU Liwei JIANG SID 310092191 310290961 310300010 309133696 Email jwan6042@uni.sydney.edu.au rjia6790@uni.sydney.edu.au xiwu6521@uni.sydney.edu.au ljia1634@uni.sydney.edu.au Contact number 0402529851 0425600150 0402581720 0416363899 Signature Jingwen WANG Ruyi JIAO Xingwen WU Liwei JIANG
െ 0‫ې‬ ‫଼ ۍ‬ ଶ 18 െ24 0 ଵ ଵ‫ۑ‬ ଵ ‫ ێ‬ଵ ିଵ െ ்ܵ =െ *൥ 6 െ24 െ24൩=‫଼ ێ‬ ଶ ଶ‫ۑ‬ ସ଼ ‫ ێ‬ଵ ‫ۑ‬ െ2 8 0 ଵ ‫ۏ‬െ ଶସ ଺ 0‫ے‬
ଷ ଵ
So, the AD-security strategy would be: ‫ې ଼ ۍ‬ ‫ ێ‬ଵ ‫ۑ‬ ߆௨ Leabharlann Baidu‫ۑ ଼ ێ‬ ‫ ێ‬ଵ‫ۑ‬ ‫ۏ‬െ ଶସ‫ے‬
ିଵ ିଵ exists, the market is complete. We can compute the determinate (்ܵ ). if determinate(்ܵ )≠0, ்ܵ exists, If there is ்ܵ market is complete.
0
0 0 2