simulation

Faster still will be:

rets <- cumsum(rnorm(n, sd=sd))

If you want to change that from returns to
prices, then do

init.price * c(0, exp(rets))

Pat

On 29/12/2012 15:12, Dominykas Grigonis wrote:

Well the simplest but most inefficient approach is a "for" loop.
However the best ant kinda sophisticated approach is to use "Reduce".

I did not analyse your problem as it would take some time for dubious
knowledge, but here is a simple random walk simulation presented in
both ways.

Reduce(function(x,eps) {x+eps},rnorm(100,sd=2.5),accumulate=TRUE)

a=numeric();a[1]=1
for (i in 2:100){a[i]=a[i-1]+rnorm(1,sd=2.5)}

If you can present me with the paper I might be able to simulate the
ones you need. As I am not going to analyse something what I doubt it
will have any value to me.

Also for efficiency:
Unit: microseconds
     expr      min       lq   median        uq      max
1  sim() 1074.634 1100.702 1120.667 1172.0290 4291.588
2 sim2()  499.730   507.990   527.797  582.7205 1516.850


where sim2 is Reduce function.



Kind regards,--
Dominykas Grigonis


On Saturday, 29 December 2012 at 13:33, Simone Gogna wrote:

Dear R users,
suppose we have a random walk such as:

v_t+1 = v_t + e_t+1

where e_t is a normal IID noise pocess with mean = m and standard
deviation = sd and v_t is the fundamental value of a stock.

Now suppose I want a trading strategy to be:

x_t+1 = c(v_t ??? p_t)

where c is a costant.
I know, from the paper where this equations come from (Farmer and
Joshi, The price dynamics of common trading strategies, 2001) that
the induced price dynamics is:

r_t+1 = ???a*r_t + a*e_t + theta_t+1

and

p_t+1 = p_t +r_t+1

where r_t = p_t ??? p_t-1 , e_t = v_t ??? v_t-1 and a = c/lambda
(lambda is another constant).

How can I simulate the equations I have just presented?
I have good confidence with R for statistical analysis, but not for
simulation therefore I apologize for my ignorance.
What I came up with is the following:

##general settings
c<-0.5
lambda<-0.3
a<-c/lambda
n<-500

## Eq.12 (the v_t random walk)
V_init_cond<-0
Et<-ts(rnorm(n+100,mean=0,sd=1))
Vt<-Et*0
Vt[1]<-V_init_cond+Et[1]
for(i in 2:(n+100)) {
Vt[i]<-Vt[i-1]+Et[i]
}
Vt<-ts(Vt[(length(Vt)-n+1):length(Vt)])
plot(Vt)

## Eq.13 (the strategy)
Xt_init_cond<-0
Xt<-Xt_init_cond*0
Xt[2]<-c(Vt[1]-Pt[1])
for(i in 2:(n)){
Xt[i]<-c(Vt[i-1]-Pt[i-1])
}
Xt<-ts(Xt[(length(Xt)-n+1):length(Xt)])
plot(Xt)

## Eq. 14 (pice dynamics)
P_init_cond<-0
Pt<-Rt*0
Pt[1]<-P_init_cond+Rt[1]
for(i in 2:(n+100)) {
Pt[i]<-Pt[i-1]+Rt[i]
}
Pt<-ts(Pt[(length(Pt)-n+1):length(Pt)])
plot(Pt)
Rt_init_cond<-0
Rt<-Rt_init_cond*0
Rt[2]<- -a*Rt[1]+a*Et[1]+e[2]
for(i in 2:(n)){
Rt[i]<- -a*Rt[i-1]+a*Et[i-1]+e[i]
}
Rt<-ts(Rt[(length(Rt)-n+1):length(Rt)])
plot(Rt)

I don???t think the code above is correct, and I don???t even know if
this is the approach I have to take.
Any suggestion is warmly appreciated.

thanks,
Simone Gogna
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