[R] simulation

[Simone Gogna]

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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