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Re: st: Solving simultaneous equations


From   Rohit Sonika <net@rsonika.me>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Solving simultaneous equations
Date   Fri, 3 May 2013 19:31:51 +0100

Thanks for your response.

It seems to be working for me now, although I am not sure how I can simulate this like 10000 times, each time saving some variables like price, strike, val, vol, etc.

Thanks!
Rohit

On 3 May 2013, at 18:54, Aljar Meesters <aljar.meesters@gmail.com> wrote:

> Dear Rohit,
> 
> Your program works for me after some minor adjustments but I am using
> Stata 12.1 so you may need to update (see -help update-).
> The adjustments that I need to make are replacing set obs 10000 with
> set obs 2 and add scalar n = 1.
> You have two equations that you want to solve and thus you only need
> two observations, one for each equation. The scalar n = 1 is needed
> since you multiply by n by generating your a variable.
> Best,
> 
> Aljar
> 
> Best,
> 
> Aljar
> 
> 
> 
> 2013/5/3 Rohit Sonika <net@rsonika.me>:
>> Hi,
>> 
>> I have never programmed in Stata, so I am reaching out to the community for some help. Here is my problem:
>> 
>> I have two equations, with two unknowns as follows:
>> 
>> 1. price = val - (a/b)*(val*normal(price/strike) - strike*normal(price/strike))
>> 2. sd = vol * (val/price) * (1-(a/b)*strike*normal(price/strike))
>> 
>> The two unknowns in the above equations are 'val' and 'vol' while the other variables are observed.
>> 
>> I am taking a numerical approach to trying to solve for above equations. Since, I create a dataset and declare variables as follows:
>> 
>> set obs 10000
>> gen double price = (100-1)*runiform()+1
>> gen double strike = (100-1)*runiform()+1
>> gen rate = 0.0025*int(60*runiform())
>> gen double b = 100
>> gen double a = (0.15-0.0001)*runiform()*n
>> gen double sd = (0.30-0.05)*runiform()+0.05
>> 
>> The program I created to populate values of 'val' and 'vol' is as follows:
>> 
>> program nlwar
>>        syntax varlist(min=1 max=1) [if], at(name)
>> 
>>        tempname val vol
>>        scalar `val' = `at'[1,1]
>>        scalar `vol' = `at'[1,2]
>> 
>>        tempvar abc
>>        gen double `abc' = `val' - (a/b)*(`val'*normal(`val'/strike * `vol') - strike*normal(`val'/strike)) - price + 1 in 1
>>        replace `abc' = (`vol'/sd) * (`val'/price) * (1-(a/b)*strike*normal(`val'/strike)) - 1 in 2
>> 
>>        replace `varlist' = `abc'
>> end
>> 
>> gen y = 0
>> replace y = 1 in 1
>> nl war @ y, parameters(val vol) initial(val 1 vol 1)
>> 
>> When I run the above program, Stata gives me an error stating 'verify that nlwar is a function evaluator program'.
>> 
>> Any help on this query would be appreciated. I am using Stata version 12.
>> 
>> Thanks!
>> Rohit
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