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7CCMFM06 Coursework
Creation date：2024-04-07 15:32:17
Belonging category：计算机computer science
Coursework

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7CCMFM06 Coursework 


General Coursework Instructions
For your coursework you should submit four documents via Keats:
1. A pdf write-up of your coursework. This must be generated using LaTeX.
It should contain a mathematical description of how you answered the
question, together with any plots you have generated and the interpreta-
tion of your results. You should focus on the mathematics used rather
than the details of how it was implemented in Python. For example, you
should explicitly state any difference equations used in your calculations.
You should divide your write-up into sections corresponding to the differ-
ent parts of the question.
2. A Jupyter notebook containing the Python code that calculates any nu-
merical values used in your write-up. This notebook must run on CoCalc
without requiring any additional files or libraries.
3. A pdf version of your Jupyter notebook. This may be generated using the
options on the File menu in the Jupyter notebook.
4. A signed departmental coversheet indicating that this is all your own work.
The pdf file of your coursework should be generated with the default LaTeX
fonts and margins and must not exceed 10 pages. You should not see 10 pages
as a target: if you can express yourself concisely you should do so. You will be
given credit for concise and interesting writing and will lose marks for long and
uninteresting writing and for including irrelevant details.
Be sure to reference all of your sources.
You may discuss the problem with other students but must not share any of
your code or written work with other students.
Specific Question for Shengkai Wang - Corrected
Version
1. You must show how to price a specific knock-out derivative on a stock.
1
The stock price process St for times t ∈ [0, T ] is known to follow the
stochastic differential equation
dSt = St(µdt+ σ(t) dWt)
where Wt is a Brownian motion, S0 = 270.0000, µ = 0.0900 and
σ(t) = 0.16× (1.6667× t)1.5.
A trader may also invest in a risk-free bank account that grows at the
continuously compounded rate r = 0.0425. The units of time for this
question are years and all prices are in dollars.
The contract of this derivative is defined as follows. If the stock ever hits
the barrier level B = 303.0000 on or before the maturity T = 1.0000 of
the option then the payoff of the derivative will be 0. Otherwise the payoff
of the option will be f(ST ) where ST is the stock price at maturity and
the function f is defined by
f(ST ) = max{(0.0033× ST )1.5 × ST − 185, 0}.
You should price this option using the Crank-Nicolson finite difference
method and may assume that the price V (t, S) satisfies the partial differ-
ential equation
∂V
∂t
+
1
2
σ(t)2S2
∂2V
∂S2
+ rS
∂V
∂S
− rV = 0
with boundary condition V (t, B) = 0, plus additional boundary conditions
you should identify. You should use the Crank-Nicolson finite difference
method with a uniform grid containing 1001 time points and 1001 stock
price values. x
Record the price of the derivative at time 0 and the delta of the derivative
at time 0 in the table of results at the end of your essay. [20%]
2. Suppose that a trader attempts to replicate this option using a discrete-
time version of the delta-hedging trading strategy, rehedging at the same
time-points you used when implementing the finite difference method. The
trader uses the value for the price and the value of delta computed by the
finite difference method, using linear interpolation to calculate values at
points which are not in the grid.
Calculate an SDE satisfied by Zt = logSt and simulate Zt using the
Euler scheme for this SDE using the same time points as above. Using
the stock prices arising from this simulation, perform 1000 simulations of
the trader’s strategy and plot a histogram of the error in this replication
strategy. You should compute the 25th and 75th percentiles of the error
and record these values in the table at the end of your essay.[20%]
2
3. Interpret your results. This means that you should make some financially
relevant observations based on your simulation, plotting charts you find
interesting. In order to make interesting observations you might want to
run variations on the simulation, for example varying the barrier. Please
remember to edit your findings and to only comment on the most inter-
esting points. [15%]
4. Describe how you have tested your code is correct, for example explaining
how you have checked that you have priced the derivative correctly. [15%]
5. You must finish your coursework by completing the following table of
results:
Price
Delta
25th percentile
75th percentile
The remaining 10% of your marks will be allocated based on the quality of
your code and your write-up.
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 EMESTER1 MAS8383 ECO 512 STAT 8310 CMN3102 MA577 CMPT 225 COMP0045 Methods Equations MATH 113 Math 3283W ICS-33 EN4302/ENT603 BIA B350F MA318 MTHM506 MECH 5315M ECONOMICS MAS8382 COM 2004 PX3142 XJEL 3662 STAT 231 MGT B399F PX4131 COM2108 30AM MSCI521 ECONM1015 ACFI304 GR5241 MATH10101 ECON 2070 COMS31900 EFIM20011 CSE 250B ACSE-5 STAT4207 SOFT2412 ELEC 331 AY2020 MSIN0209 FIT2094 CS 241L ST404 CS 411 3D CA3 INF4002 COMP3506 SIT718 CS 188 CS 170 MATH 138 CSE 251A CMT118 DATA5207 CMPT307 CMPT459 T1 PGEE11108 COSC 3P32 ME 163 MATH96007 7QQMM203 EE6227 BA 574 STA 4234 ECO206Y1Y ECO2008 MT2300 MATH 11158 CS 527 MACM 316 CSE474 2DI70 ISE 525 COMP3411 EMAT30007 7CCSMBDT MFIN704 MFIN704W21 MfIB ECE 438 CS 436 F36 CS5344 FE 621A FE621 TBA 612 ECM3151 ECMM422 MF1 MSIN0107 ESSMENT CS 5854 MFIT 5008 MIPS R4000 ENG5274 BU52018 ENG2079 BIOA02 STA2570 F0 INF553 STAT 440 STAT3008 COMP9417 COMP6451 6COM1042 BU52006 ST303 HW-1 CISC-235 CS 510 MATH3161 ECN 140 ECE391 Comp 3613 CVEN 9625 PRG455 UESTION 1 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MGMTMFE 405 25579 1ECE 273 M122 COMP4434 1ELEC ELEC5620M STAT0010 BFF2401 MXB361 MATH3811 CS330 CMT307 FIT1033 CptS 583 UP 431 MATH6005 AF5343 CS2435 ECOM30002 ES50061 CS 2506 ECMT6002 CODE 00099F MT4539 ESSAY ICM317 MATH1231 MFIT5010 BMA547 MATH334 CIVL2201 MATH39032 T-04 CIVE97119 EMESTER CAB302 CAB301 59PM STAT802 ISYS3412 RM3 COSC 2123 AcF 311 MATH2022 1FINAL 4CCS1PHC ICM 142 ENVS3023 Math 4023 I1 ACSE8 FIN B385F CS-275 STA 4109-01 A31021 EE140 MT1 EE124 ECO-6004B Inf2-IADS CS126 IS2184 UL18 MATH5092 ECOM009 COMP 6211 ELEC202 MKT3019 IAB230 FIT5046 584-S21 COMP3210 CO250 A29401 MATH 136 MGT6174 ECMT6007 DATA2001 MAT 443 MATH10222 PHDE0071 ELE00123M COSC1295 MAT00045H MATH32032 1004GRC MAS223 COMP10001 DATA3404 CIVL2110 STAT2008 FNCE10002 EEE6431 COM6515 COMP9120 NBS8185 ECTE942 ECON 405 MATH314301 STAT 2011 COMPSCI 350 COMP20007 CMPSC-132 ECON5002 STA 35 MTH6108 FIT5147 MTH6150 100C FINA 5260 DESC9115 ECON4998 NBS8257 GMM ECON 6070 BSA2 ECE599 STATS 102B STA120 INFS601 BFC3241 MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 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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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