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Matematik simulation and monte carlo with applications in finance and mcmc phần 9

sigma = 0,1,' n '= 16' # bản sao '= 100, đường dẫn cho mỗi nhân rộng' = 2500, tầng lớp nhân dân ước lượng điểm = 100 'giá ước tính' = 0,2023819565, tiêu chuẩn lỗi = 0,00002354664402 13753? ¼ 0:02171666756 'K' = 50, sigma '= 0,1,' n '= 16' # bản sao '= 100 | 266 Appendices with LinearAlgebra with stats Warning these names have been redefined anova describe . fit importdata random statevalf statplots transform basket proc r x sigma q rho T t n npath K local b c1 c2 i1 i2 mean R spot stderr theta w xav xi z global i X2 6 Computes call price for basket option using naive Monte Carlo 6 load STDNORM and Linear Algebra package 6 r risk-free interest rate x i1 i1th. asset price at time t sigma i1 volatility of asset i1 6 q i1 quantity of asset i1 in basket 66 rho correlation matrix for returns between assets 6 T exercise time npath number of paths 66 K strike price 6 spot Transpose x .q 6 b LUDecomposition rho method Cholesky 6 i false z Vector n 6 w Vector n c1 0 c2 0 for i2 from 1 to npath do for i1 from 1 to n do z i1 STDNORM end do w b.z xav 0 for i1 from 1 to n do xi q i1 x i1 exp r-0.5 sigma i1 A2 T-t sigma i1 sqrt T-t w i1 xav xav xi end do theta max 0 xav-K exp -r T-t c1 c1 theta c2 c2 thetaA2 end do mean c1 npath stderr sqrt c2-c1A2 npath npath npath-1 print K K spot spot r r n n t t T T x x q q sigma sigma rho rho print paths npath print point estimate of price mean print estimated standard error stderr end proc Appendices 267 Set up the input data. r 0.04 x Vector 5 2.5 4 3 sigma Vector 0.3 0.2 0.3 0.4 q Vector 20 80 60 40 rho MatriX 1 0.7 0.5 0.3 0.7 1 0.6 0.2 0.5 0.6 1 0.4 0.3 0.2 0.4 1 T 0.5 t 0 n 4 npath 10000 spot Transpose x .q Now price the option with the following strike prices K. K 660 seed randomize 9624651 basket r x sigma q rho T t n npath K K 660 seed 9624651 K 660 spot 660. r 0.04 n 4 t 0 T 0.5 0.3 1 0.7 0.5 0.3 0.2 0.7 1 0.6 0.2 sigma 0.3 rho 0.5 0.6 1 0.4 0.4 0.3 0.2 0.4 1 paths 10000 point estimate of price 47.20505098 estimated standard error 0.7072233067 K 600 seed randomize 9624651 basket r x sigma q rho T t n npath K K 600 seed 9624651 K 600 spot 660. r 0.04 n 4 t 0 T 0.5 x 5 2.5 4 q 3 20 80 60 .