How to do a summation

[huanpipt]

Hello, I want to do a summation but I don't know how to do it

Following is my initial code.
I don't know how to write a loop to do the summation.

Could anyone help me?

Code: Select all

dec real L k o sigx
dec series intergral(i)

nonlin L k o sigx varx

compute M=100

frml integral = (1/M)*exp(2*o*sin(2*%pi*(i*L/M)))*exp(-2*k*(t-(i*t/M)))
do i=0,M
compute integral = integral + integral
end do

[TomDoan]

Use SSTATS, though you need to be careful about your integer divides. As you've written it, 1/M is zero---you want 1.0/M, and you'll have similar problems with i*t/M. For SSTATS, the loop index has to be T, so it looks like you'll need to switch the T and I subscripts in your formula. Something like:

SSTATS 0 M (1/M)*exp(2*o*sin(2*%pi*(t*L/M)))*exp(-2*k*(i*(1.0-t)/M)))>>integral

[huanpipt]

Thanks for response.

In fact, I'd like to estimate the four parameters in the equation, as following

L k o sigx are four parameters

equation :
ec = exp(-r*TT)*(S*%cdf(d1)-S*%cdf(d1-(varf^(0.5))))
d1 = (log(S/S)+0.5*varf)/(varf^(0.5))
varf = varx*exp(-2*k*(TT))*integral
integral = summation from t=0 to t=M of (1.0/M)*exp(2*o*sin(2*%pi*(t*L/M)))*exp(-2*k*(ii*(1.0-t)/M))

I run the following code, however there is an error message
## SR10. Missing Values And/Or SMPL Options Leave No Usable Data Points
Could anyone help me with this?

Thanks very much.

Code: Select all

open data TD3monthc2.xls
CALENDAR(irregular)
data(format=xls,org=columns) / ii TT r S A

********************************************************************

dec real L k o sigx varx
dec series intergral
nonlin L k o sigx
compute M = 100


SSTATS 0 M (1.0/M)*exp(2*o*sin(2*%pi*(t*L/M)))*exp(-2*k*(ii*(1.0-t)/M))>>integral

compute varx = sigx**2
frml varf = varx*exp(-2*k*(TT))*integral
frml d1 = (log(S/S)+0.5*varf)/(varf^(0.5))
frml ec = exp(-r*TT)*(S*%cdf(d1)-S*%cdf(d1-(varf^(0.5))))

frml RR = A - ec



nlls(frml=RR,piters=10,iters=100) * 1 99 UU

[TomDoan]

You will need to create a FUNCTION which evaluates the integral at a given value of T. See, for instance, the BONDS.RPF example, which does NLLS using a functional form which, like your integral, isn't closed form. As you have it written, INTEGRAL is computed only once, not once per entry in each function evaluation.

[huanpipt]

Dear Tom,

I follow the BOND.rpf to revise my code while there an error message that I cant solve.

1 part to set an loop of summation

Code: Select all

dec real L k o sigx varx M

nonlin L k o sigx
compute M = 100

function opvalue p
type real opvalue
type integer p

*integral=opvalue

compute pp = 0
while pp<100 {
compute opvalue = (1/M)*exp(2*o*sin(2*%pi*(pp*L/M)))*exp(-2*k*(ii*(1-pp)/M))
compute opvalue = opvalue + opvalue
compute pp=pp+1
}end while

2nd part to sum all things to opvalue and then to estimate parameters
the error message appeared in this part

## SX22. Expected Type REAL, Got MATRIX(REAL) Instead
>>>>f(d1)-S*%cdf(d2)))<<<<

Code: Select all

compute varx = sigx**2
compute varf = varx*exp(-2*k*(TT(p)))*opvalue
compute d1 = (log(S(p)/S(p))+0.5*varf)/(varf^(0.5))
compute d2 = d1-(varf^(0.5))
compute opvalue = exp(-r(p)*TT(p))*(S*(%cdf(d1)-S*%cdf(d2)))

*
frml optionprice A = opvalue(t)

nlls(frml=optionprice,piters=10,iters=100) A 1 99 UU

I'm confused that I didn't set any matrix, why error message inform that.
Thanks for your help

[TomDoan]

nonlin L k o sigx
compute M = 100
function opvalue p
type real opvalue
type integer p

*integral=opvalue

compute pp = 0
while pp<100 {
compute opvalue = (1/M)*exp(2*o*sin(2*%pi*(pp*L/M)))*exp(-2*k*(ii*(1-pp)/M))
compute opvalue = opvalue + opvalue
compute pp=pp+1
}end while

This has all kinds of problems. First, you need to read the message earlier about integer divides. 1/M and 1.0/M aren't the same thing and neither are (1-pp)/M and (1.0-pp)/M. Also, what do you think opvalue = opvalue + opvalue is going to do? What it will do is give you double the pp=99 value of the (1/M)... calculation. You need one variable for the pp-specific calculation, and a different one for the summation across pp.

Is there anything in this which depends upon data, or is this just a function of the non-linear parameters? And what is the argument "P" used for?

2nd part to sum all things to opvalue and then to estimate parameters
the error message appeared in this part

## SX22. Expected Type REAL, Got MATRIX(REAL) Instead
>>>>f(d1)-S*%cdf(d2)))<<<<

Code: Select all

compute varx = sigx**2
compute varf = varx*exp(-2*k*(TT(p)))*opvalue
compute d1 = (log(S(p)/S(p))+0.5*varf)/(varf^(0.5))
compute d2 = d1-(varf^(0.5))
compute opvalue = exp(-r(p)*TT(p))*(S*(%cdf(d1)-S*%cdf(d2)))

*
frml optionprice A = opvalue(t)

nlls(frml=optionprice,piters=10,iters=100) A 1 99 UU

I'm confused that I didn't set any matrix, why error message inform that.
Thanks for your help

What's S. Isn't it a series? If you use it in a COMPUTE, it will be treated as a VECTOR. You're also using OPVALUE for two different purposes, and that entire second calculation is set up for executing just once, not once per function evaluation. That second one needs a different name, and it needs to be a function of the entry number or a FRML since it depends upon the data S.

[huanpipt]

nonlin L k o sigx
compute M = 100
function opvalue p
type real opvalue
type integer p

*integral=opvalue

compute pp = 0
while pp<100 {
compute opvalue = (1/M)*exp(2*o*sin(2*%pi*(pp*L/M)))*exp(-2*k*(ii*(1-pp)/M))
compute opvalue = opvalue + opvalue
compute pp=pp+1
}end while

This has all kinds of problems. First, you need to read the message earlier about integer divides. 1/M and 1.0/M aren't the same thing and neither are (1-pp)/M and (1.0-pp)/M. Also, what do you think opvalue = opvalue + opvalue is going to do? What it will do is give you double the pp=99 value of the (1/M)... calculation. You need one variable for the pp-specific calculation, and a different one for the summation across pp.

Is there anything in this which depends upon data, or is this just a function of the non-linear parameters? And what is the argument "P" used for?

I thought I could use opvalue= opvalue(pp)+opvalue(pp+1) because there is another opvalue above.
I'll revised it again.

2nd part to sum all things to opvalue and then to estimate parameters
the error message appeared in this part

## SX22. Expected Type REAL, Got MATRIX(REAL) Instead
>>>>f(d1)-S*%cdf(d2)))<<<<

Code: Select all

compute varx = sigx**2
compute varf = varx*exp(-2*k*(TT(p)))*opvalue
compute d1 = (log(S(p)/S(p))+0.5*varf)/(varf^(0.5))
compute d2 = d1-(varf^(0.5))
compute opvalue = exp(-r(p)*TT(p))*(S*(%cdf(d1)-S*%cdf(d2)))

*
frml optionprice A = opvalue(t)

nlls(frml=optionprice,piters=10,iters=100) A 1 99 UU

I'm confused that I didn't set any matrix, why error message inform that.
Thanks for your help

What's S. Isn't it a series? If you use it in a COMPUTE, it will be treated as a VECTOR. You're also using OPVALUE for two different purposes, and that entire second calculation is set up for executing just once, not once per function evaluation. That second one needs a different name, and it needs to be a function of the entry number or a FRML since it depends upon the data S.

S is a series. Here I want to simulate the process in BOND.RPF - Add separate values into opvalue- so I add the summation part in the 1st part then add other part in 2nd part.
I thought I might misunderstand the FUNCTION, I'll try to revise it again.

Thanks for your help.

[huanpipt]

Dear Tom,

I revise the code

I use the function to do the summation integral
p I want to set it as different time, just as the code "compute mdate=maturity(bond)" in BONDS.rpf
Because there is only one variable ii in my equation so I only wrote "compute iii=ii(p)"

Code: Select all

dec real L k o sigx M

nonlin L k o sigx
compute M = 100

function integral p
type real integral
type integer p
local real pp

compute integral = 0
compute iii = ii(p)
compute pp = 0
while pp<M {
compute partintegral = (1.0/M)*exp(2*o*sin(2*%pi*(pp*L/M)))*exp(-2*k*(iii*(1.0-pp)/M))
compute integral = integral + partintegral
compute pp = pp + 1
}end while
end

Then, I use SET to set each part of calculation

Code: Select all

frml varf = sigx*exp(-2*k*(TT))*integral(t)
set d1 = (log(S/S)+0.5*varf)/(varf^(0.5))
set d2 = d1-(varf^(0.5))
set opvalue = exp(-r*TT)*(S*(%cdf(d1)-S*%cdf(d2)))

frml optionprice A = opvalue(t)

nlls(frml=optionprice,piters=10,iters=100) A 1 99 UU

However, there is a error message.
## SR10. Missing Values And/Or SMPL Options Leave No Usable Data Points
If I shouldn't end the FUNCTION in the 1st part ?

[huanpipt]

Dear Tom,

I revised the code today. The 2nd part is put into FUNCTION in this code, but the error message still exists.
Would you please help me find which part is wrong?

Thank you very much.

Code: Select all

dec real L k o sigx

nonlin L k o sigx


function opvalue p
type real opvalue
type integer p
local real pp iii M SS rp TTT integral varf d1 d2

compute integral = 0
compute iii = ii(p)
compute M = 100

compute pp = 0
while pp<M {
compute integral = integral + $
(1.0/M)*exp(2*o*sin(2*%pi*(pp*L/M)))*exp(-2*k*(iii*(1.0-pp)/M))

compute pp = pp + 1
}end while


compute TTT=TT(p)
compute varf = sigx*exp(-2*k*(TTT))*integral
compute SS=S(p)
compute d1 = (log(SS/SS)+0.5*varf)/(sqrt(varf))
compute d2 = d1-(sqrt(varf))
compute rp=r(p)
compute opvalue = exp(-rp*TTT)*(SS*(%cdf(d1)-SS*%cdf(d2)))
end

*
frml optionprice A = opvalue(t)

nlls(frml=optionprice,piters=10,iters=100) A 1 99 UU

[TomDoan]

If you tried to run something similar to what you've posted, you should have also gotten warning messages that your non-linear parameters aren't initialized, and that it's trying 0. Zero is a bad number for at least the sigx if not for the others. Start with proper guess values and it should work. If it doesn't, then you probably need to try smaller (closer to zero) guesses for any of the parameters that are in exp(...) functions. With guess values of the wrong size, those could over- or underflow on the initial function evaluation.

[huanpipt]

Dear Tom,

It works.
I'm very Thankful for your help.

[huanpipt]

Dear Tom,

I'm really thankful for your previous help.

Now, I develop the model into a more complicated one and encounter a problem.
I attached the model in the word and following is my code.

Code: Select all

open data TD3monthc2.xls
CALENDAR(irregular)
data(format=xls,org=columns) / TT r S A X

********************************************************************
dec real L k o sigx miu N

nonlin L K o sigx miu



function opvalue p
type real opvalue
type integer p
local real ii M SS rp TTT integral F ppp TTTT pppp F

compute TTT=TT(p)
compute ppp = TTT*360

compute XX=X(p)

***************************************************
**using if function to separate pre- or in-period**
**pppp is the calculation for summation F(t,Ti)  **
***************************************************

if TTT <= 1.0 / 12
 compute pppp = ppp
else
 compute pppp = 30

*****************
**set F initial**
*****************

compute F =0

******************
**set loop for F**
******************

while pppp > 0 {
compute TTTT = ppp / 360

*************************
**set loop for integral**
*************************
	compute M = 100
	compute ii = 0
	compute integral = 0
	while ii<M {
	compute integral = integral + $
	(1.0/M)*exp(2.0*o*sin(2.0*%pi*(ii*TTTT/M+L)))*exp(-2.0*k*(TTTT*(1.0-ii/M)))
	compute ii = ii + 1
	}

*************************
**end loop for integral**
*************************
compute F = F + $
exp(XX*exp(-k*TTTT)+miu*(1-exp(-k*TTTT))+(0.5)*sigx*sigx*integral)*exp(-k*TTTT)
compute ppp = ppp - 1
compute pppp = pppp - 1
}

******************
**end loop for F**
******************

*********************************************
**obtain sigmaF, d1, d2,and finally opvalue**
*********************************************
compute SS=S(p)
compute sigf = (sigx*exp(o*sin(2*%pi*(L)))/N/SS)*F
compute d1 = (log(SS/SS)+0.5*sigf^(2))/(sigf)
compute d2 = d1-(sigf)
compute rp=r(p)
compute opvalue = exp(-rp*TTT)*(SS*(%cdf(d1)-SS*%cdf(d2)))
end

************
**set frml**
************
frml optionprice A = opvalue(t)

********************************************
**set the initial value for each parameter**
********************************************
compute N=30,L=-0.1,k=0.1,o=0.1,sigx=0.1,miu=0.1

**********************************
**using least square to estimate**
**********************************
nlls(frml=optionprice,piters=10,iters=500,trace) A

Indeed, there is no error message but it only shows the result like the following.
---------------------------------------------------------------------------------------------------
Non-Linear Optimization, Iteration 1. Function Calls 281.
Cosine of Angle between Direction and Gradient 0.0000000. Alpha used was 0.000000
Adjusted squared norm of gradient 0
Diagnostic measure (0=perfect) 0.3000
Subiterations 0. Distance scale 0.000000000
Old Function = 633700.642178 New Function = 633700.642178
New Coefficients:
-0.090000 0.100000 0.100000 0.100000 0.100000


Nonlinear Least Squares - Estimation by Gauss-Newton
Convergence in 1 Iterations. Final criterion was 0.0000000 <= 0.0000100
Dependent Variable A
Usable Observations 197 Degrees of Freedom 192
Total Observations 198 Skipped/Missing 1
Centered R**2 -704.178541 R Bar **2 -718.869761
Uncentered R**2 -149.076410 T x R**2 -29368.053
Mean of Dependent Variable 4.107614213
Std Error of Dependent Variable 2.141235790
Standard Error of Estimate 57.450188668
Sum of Squared Residuals 633700.64218
Log Likelihood -1075.02952
Durbin-Watson Statistic 0.012088

Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. L -0.090000000 0.000000000 0.00000 0.00000000
2. K 0.100000000 0.000000000 0.00000 0.00000000
3. O 0.100000000 0.000000000 0.00000 0.00000000
4. SIGX 0.100000000 0.000000000 0.00000 0.00000000
5. MIU 0.100000000 0.000000000 0.00000 0.00000000
---------------------------------------------------------------------------------------------------

I think it's unusual, because I've set the pre-iteration and one data is missed from the sample.
Could you help me with this ?
I hope this may not be too annoying for you.

Thanks.

[TomDoan]

This doesn't look right:

compute d1 = (log(SS/SS)+0.5*sigf^(2))/(sigf)

Why would you have SS/SS?

Your function, at least at the guess values, is obviously way off. You need to first walk through you formulas and make sure that you have them translated into calculations correctly. do

set test = opvalue(t)
print / test a

to see whether this is a general problem or if there are a few data points that are responsible for most of the very high sum of squared errors. If it's the latter, you can focus in on those calculations. If it's more general, than you will have to throw some DISPLAY instructions inside the function to determine where the calculation is going off track.

[huanpipt]

Dear Tom,

I set SS/SS because it's ATM options. In that case, S equals K.

I found one data point has the TT=0, as a result, F=0, sigf=0, opvalue= NA.
However, after I exclude this data, I found it still runs "strangely" ( only one iteration and no pre-iteration).
I'll use a simple data to check if the code for calculation is wrong.

I'm really appreciate your reply and help.