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Question: why i can not get the picture?

Question:why i can not get the picture?

fbb 0 Maple 15
student
September 26 2012
0

CEV_calloption.mw

> 

NULL
> 

K := 'K'; sigma := .2; tau := .25; s := 1; r := 0

1

  

.2

  

.25

  

1

  

0

 (1)
> 

d1 := proc (sigma) options operator, arrow; (ln(s/K)+(r+(1/2)*sigma^2)*tau)/(sigma*sqrt(tau)) end proc;

proc (sigma) options operator, arrow; (ln(s/K)+(r+(1/2)*sigma^2)*tau)/(sigma*sqrt(tau)) end proc

 (2)
> 

d1(.2);

0.5000000000e-1

 (3)
> 

d2 := proc (sigma) options operator, arrow; d1(sigma)-sigma*sqrt(tau) end proc;

proc (sigma) options operator, arrow; d1(sigma)-sigma*sqrt(tau) end proc

 (4)
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d2(.2);

-0.5000000000e-1

 (5)
> 

Phi := proc (x) options operator, arrow; (int(exp(-(1/2)*t^2), t = -infinity .. x))/sqrt(2*Pi) end proc;

proc (x) options operator, arrow; (int(exp(-(1/2)*t^2), t = -infinity .. x))/sqrt(2*Pi) end proc

 (6)
> 

f := proc (sigma) options operator, arrow; s*Phi(d1(sigma))-K*exp(-r*tau)*Phi(d2(sigma)) end proc;

proc (sigma) options operator, arrow; s*Phi(d1(sigma))-K*exp(-r*tau)*Phi(d2(sigma)) end proc

 (7)
> 

upsilon := proc (sigma) options operator, arrow; s*sqrt(tau)*exp(-(1/2)*d1(sigma)^2)/sqrt(2*Pi) end proc

proc (sigma) options operator, arrow; s*sqrt(tau)*exp(-(1/2)*d1(sigma^2))/sqrt(2*Pi) end proc

 (8)
> 

evalf(f(.2));

0.3987761168e-1

 (9)
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y := 1;

1

 (10)
> 

tau1 := sigma^2*tau/(2*y^2);

0.5000000000e-2

 (11)
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c := 1/tau1;

200.0000000

  

200.0000000

 (12)
> 

``
> 

CEVfunc := proc (x, a, y, n) options operator, arrow; evalf(int(exp(-(1/4)*z^2/x)*z^n*BesselI(y, z), z = a .. infinity)) end proc;

proc (x, a, y, n) options operator, arrow; evalf(int(exp(-(1/4)*z^2/x)*z^n*BesselI(y, z), z = a .. infinity)) end proc

 (13)
> 

``
> 

``
> 

V := exp(-r*t-x)*(CEVfunc(x, 2*sqrt(c*x*K^(1/y)), y, y+1)/(x*c^y*2^(y+1))-K*(2*x)^(y-1)*CEVfunc(x, 2*sqrt(c*x*K^(1/y)), y, 1-y));

0.3988175536e-1

 (14)
> 

``
> 

NULL
> 

newton := proc (sigma) options operator, arrow; sigma-(f(sigma)-V)/upsilon(sigma) end proc;

proc (sigma) options operator, arrow; sigma-(f(sigma)-V)/upsilon(sigma) end proc

 (15)
> 

``
> 

``
> 

evalf((newton@@5)(.2));

.2000207955

 (16)
> 

plot((newton@@5)(.2), K = .7 .. 2)

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

  

 
> 

``

 

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