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Exam Time Table Code FIN9007
Creation date：2024-04-08 17:41:07
Belonging category：金融Finance
Tag FIN9007
FINANCE

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FIN9007

Exam Time Table Code FIN9007
Normal answer book
Approved calculators only permitted
EXAMINATION FOR THE DEGREE OF
MASTER OF SCIENCE (FINANCE) AND OTHER DEGREES
DERIVATIVES
and the internal examiners
Write on both sides of the answer paper
Answer any THREE questions
All questions carry equal marks
Allocation of marks within questions is shown in brackets
You have TWO HOURS to complete the paper
Answer any THREE questions
1 (a) With reference to the Black Scholes model explain the concept of risk
neutral valuation. Outline the Monte Carlo valuation procedures.
(30%)
(b) Demonstrate the manner in which the Black-Scholes model is adapted to
accommodate European futures options, i.e. the Black’s model for futures
options.
(40%)
(c) Explain the exponentially weighted moving average (EWMA) model for
estimating volatility from historical data. Explain how to apply the GARCH
methodology to derive and forecast an asset’s volatility.
(30%)

2 Consider ONE of the following articles. Briefly document the key elements
of the paper, the methodology used in the investigation, and provide a
commentary on the ramifications of the main findings highlighted in the
article.
(100%)
(i) “Understanding VIX”, by Whaley R. (2009), Journal of Portfolio
Management, 35, 98–105.
(ii) “Time series momentum”, by Moskowitz, T., Ooi, Y. H. and
Pedersen, L. H. (2012), Journal of Financial Economics 104, 228-
250.
3 (a) Stock A has a daily volatility of 1.2% and stock B has a daily volatility of
1.8%. The correlation between the two stock price returns is 0.2.
I. What is the 99%, 5-day VaR for 1 million dollar investment in
stock A?
II. What is the 99%, 5-day VaR for 1 million dollar investment in
stock B?
III. What is the 99%, 5-day VaR for 1 million dollar investment in
stock A and 1 million dollar investment in stock B?
IV. What is the benefit of diversification for the 99% VaR?
(50%)
(b) Explain why the futures price tF of a stock (without paying dividend) with
price tS satisfies
( ) ,r T tt tF S e
 where r is the risk-free rate, and T is
the maturing date. Can you use the same arguments to price all other
types of futures contracts? Furthermore, if the stock price tS follows a
Geometric Brownian Motion, what is the process followed by the futures
price ?tF Interpret your result.

(50%)
4 (a) Outline the mean-variance approach to hedge ratio construction. What
are the speculative demand and the hedging demand? Interpret them
economically.
(50%)
(b) What is the implied volatility? Explain how the Bisection OR the Newton-
Raphson procedure is utilized to calculate the implied volatility of options
priced according to the Black-Scholes model.
(50%)
5 (a) Detail the basic concepts of Value at Risk (VaR); explain how to use
historical simulation to estimate VaR. Comment on the advantages and
disadvantages of this method.

(40%)

(b) What are volatility smiles, describe the key features of volatility smiles,
and why do you think they exist?
(30%)

(c) What is credit risk? Explain the risk-neutral and real-world default
probabilities and the difference between them. Which should be used for
(i) valuation and (ii) scenario analysis? How are recovery rates usually
defined and how is the recovery rate used to approximately calculate
default probability?
Case category
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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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