2012 금융수학 겨울학교 - fm 210 mhz
TRANSCRIPT
February, 3 2012
FM 210 Mhz
과제결과발표2012.02.03.
금융수학 겨울학교
Contents
1 Option (1) Implicit method
(2) Stability by Von Neumann analysis
2. Network (1) Asset MST
(2) 3D simulation
3. Creative project (1) Paper introduction
(2) Future research
금융수학 겨울학교
PROF ILE
조이름
주소
창립 년도
직원 수
UNIST 테경관 210 호
2012. 2. 2.
총 4 명 | 수학 자갈 2 명 | 재무 천재 1 명 | 막내 ^.^
Staff
남자 1 호응용수학전공
여자 1 호응용수학전공
FM 210 (Finance & Math meet at Technomanagement building 210 class )
여자 2 호재무관리전공
여자 3 호테크노경영학부
(1)American
ca l l op t i on -
(2)Stability
(3)American
optionsVon Neumann analysis Operator splitting method
Mathmatical approach to op-tion
implicit method
(1) Discretize the Black-Scholes equation on n+1 time level using Taylor series expansion. Approximate the first-order spatial derivative at m-th grid point using m-1 and m grid points. Keyword : Taylor expansion
Taylor expansion
(1) Discretize the Black-Scholes equation on n+1 time level using Taylor series expansion. Approximate the first-order spatial derivative at m-th grid point using m-1 and m grid points. Keyword : Discretize
EU call option
Mathmatical approach to op-tion
(1)Ameri -can ca l l op t ion -
(2)Stability
(3)American
optionsVon Neumann analysis Operator splitting method implicit method
(2) Check stability in the sense the Von Neumann analysis.
Ke y w o rd : subst i tu t ing i n ex p l i c i t m e t h o d
(2) Check stability in the sense the Von Neumann analysis.
Ke y w o rd : s tab i l i t y i n ex p l i c i t m e t h o d
(2) Check stability in the sense the Von Neumann analysis.
Ke y w o rd : subst i tu t ing i n i m p l i c i t m e t h o d
(2) Check stability in the sense the Von Neumann analysis.
Ke y w o rd : expans ion
(2) Check stability in the sense the Von Neumann analysis.
Ke y w o rd : s tab i l i t y i n i m p l i c i t m e t h o d
Mathmatical approach to op-tion
(1)Ameri -can ca l l op t ion -
(2)Stability
(3)American op-
tions
Von Neumann analysis Operator splitting method implicit method
Asset t ree -
3D simula-tion
Paper in-troduction
Network approach to Finance
Net-work
with mathlab code Future research with mathlab code
Asset t ree -
3D simula-tion
Paper intro-duction
Network approach to Finance
Net-work
with mathlab code Future research with mathlab code
Int roduc t i on o f paper
1. The clustering of companies using the correlation matrix of asset returns,
2. Transforming correlations into distances,
3. Selecting a subset with the minimum spanning tree(MST) criterion.
-A s s e t Tre e s a n d A s s e t G r a p h s i n Fi n a n c i a l M a r ke t
Ma in theme o f paper
-A s s e t Tre e s a n d A s s e t G r a p h s i n Fi n a n c i a l M a r ke t
Asset Tree Asset Graph
Construction
Differences
Determining the minimum span-ning tree(MST) of the distances
Extracting the N(N-1)/2 distinct distance ele-ments from the upper triangular part of the
Order : fixed No cycles
Order : unfixed Cycles
Conc lus ion o f paper
-A s s e t Tre e s a n d A s s e t G r a p h s i n Fi n a n c i a l M a r ke t
In general, the tree and graph behave very similarly.
Second region – a straight line on the log-log plot G should decay more faster than T.
First region - in early timeT faster than G(∵G shows exponential de-cay)
G are far more optimal (shorter) than the T.
Log log g raph
-B a s e d o n Kosp i da ta
Network approach to Finance
Asset t ree -3D simula-
tionPaper in-
troduction
Net-work
with mathlab code Future research with mathlab code
Asset MST
Return = importdata('US_200001032008_STOCKReturn.mat'); Corr = corrcoef(Return); Dist = sqrt(2*(1-Corr)); Dist = triu(Dist) + triu(Dist)'; SDist = sparse(Dist); [out1 out2 out3 ] = mst(SDist); MST = [out1 out2 out3 ]; MST_Geometric_SUB02_Application(MST,'a');
Asset MST
Asset MST
과독점에 대한정부 규제 방법 ?
Network approach to Finance
Asset t ree -
3D simulationPaper in-troduction
Net-work
with mathlab code Future research with mathlab code
3D simulation
3D simulation
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0
0.5
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2003
2004
2005
2006
2007
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-1012002 2002.5 2003 2003.5 2004 2004.5 2005 2005.5 2006 2006.5
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3D simulation
Clear all; close all; clf;
SAME CODE
Futu re Research
-A s s e t Tre e s a n d A s s e t G r a p h s i n Fi n a n c i a l M a r ke t
1. 다른 주식과 많은 연결개수를 갖는 주식의 시장지수에 따른 공통속성의 정도와 개별속성의 정도 차이 .
2. 주식 간의 연결개수에 영향을 미치는 요인에 대한 분석 ( 연구 )
3. 주식들과의 연결개수에 따라 2 가지 이상의 집단으로 구분 후 , 평균비교 T 검정과 ANOVA 를 이용하여 집단간 통계적 유의한 차이를 보이는 특징에 대해 분석한다 .
4. 기업의 연결개수에 따른 수익성을 예측하기 위해서 회귀분석을 실시하여 , 베타 값에 따라 큰 영향을 미칠 수 있는지에 대한 분석 .
감사합니다