英国理工课件：（计算金融：资产定价模型）computational finance：asset pricing models

1、Computational Finance 1/34 Asset Pricing Models381 Computational FinanceComputational Finance 2/34Computational Finance 3/34Computational Finance 4/34Computational Finance 5/34Computational Finance 6/34Computational Finance 7/34Computational Finance 8/34Computational Finance 9/34MfMfrrrrrE)(Expected

2、 Value of market rate of return Standard Deviation of market rate of returnComputational Finance 10/34fMififMifirrrrrrErrE 2MiMiComputational Finance 11/34fMifirrrrdescribes relationship between risk and expected return of assetComputational Finance 12/34fMirr1)(),(22MMMMMMrVarrrCovComputational Fin

3、ance 13/34niiipw1niiiprwr1niMiiMprrwrr1),cov(),cov(Computational Finance 14/34ifMifierrrr)(0),cov( and 0)(MiireeErisk specific2 risk ystematic22risk total2 iesMiiComputational Finance 15/34risk specific2 risk ystematic22risk total2 iesMiiMfMfrrrr2 whereMiMifMifirrrrComputational Finance 16/34rrfrfr)

4、,cov(Mrr2M1Capital Market LineSecurity Market LineMMMfMfrrrr2MiMifMifirrrrComputational Finance 17/34CAPMin asset of Price 1formula CAPM return of Rate fMffMfrrrSPrrrPPSPPSrComputational Finance 18/34CAPMin asset an of Price 1fMfrrrSP rate interest adjusted-risk factor discount case, randomthe In fa

5、ctor discount case,tic deterministhe In)(1111fMffrrrrComputational Finance 19/34niefbariiii, 2 , 1 RandomConstantConstantInterceptFactor LoadingsError 0ieE0ifeEjieeEij ,0Computational Finance 20/34niefbfbariiiii, 2 , 12211 RandomConstantConstantConstantniefbarikjjjiii, 2 , 11 Computational Finance 2

6、1/34Computational Finance 22/34iiiMMiiMiMifMiifiifMiiifMifiifiiMiiiiiiibrrrbrbrrrrEbrrEerrberrbrbarrerbarefbar0 and var,covvar,cov)()()()1 (Computational Finance 23/34Single Index Model applied to Lloyds-0.1-0.0500.050.10.15-0.04-0.03-0.02-0.0100.010.020.030.040.05Market ReturnsReturns on Llloydsslo

7、pe = Beta = 1.77intercept = alpha = 0 (approx)Single factor model equation defines a linear fit to data Imagine several independent observations of the rate of return and factor Straight line defined by single factor model equation is fitted through these points such that average value of errors is

8、zero. Error is measured by the vertical distance from a point to the lineComputational Finance 24/34Computational Finance 25/34Computational Finance 26/34BABAwww w120100 :2 statein 3050 :1 statein 112120100 383050 BABAwww wComputational Finance 27/34The outcome of forming an arbitrage portfolio of 1mComputational Finance 28/34Computational Finance 29/34Computational Finance 30/34nifbariii, 2 , 1for Computational Finance 31/34jibb fbwwbawwarjijip)1 ()1 (jiijijjipjiijjbbbabbbarbwwbbbbw0)1 ( and Computational Finance 32/34cbacbabababbbabbbaiiiiiijjjiijijji00000ai and bi a