# [R] repeat a function

Eric.Pueyo at avivainvestors.com Eric.Pueyo at avivainvestors.com
Thu Nov 2 17:54:29 CET 2017

```Hi Petr,

Many thanks for your response.

Basically I want to create a probability matrix to be used in a trinomial tree going forward. This is the reason why I thought to build the matrix around 0 would be much more efficient. I need to loop through because the probabilities will depend on my node and is not always the same per row (e.g. if N> jmax, jmax being defined in another function)
I found a workaround. Please see below.
Thereafter I want to optimize this function. Hopefully it works.

Many thanks,
Eric

HWMProb <- function(N) {
ProbUP<- function( a, j, dt) 1 / 6 + ((j ^ 2 * Mfactor(a, dt) ^ 2 + j * Mfactor(a, dt)) / 2)          ######### Probability X going up
ProbMID<- function(a, j, dt) 2 / 3 - (j ^ 2 * Mfactor(a, dt) ^ 2)                                     ######## Probability X going middle
ProbDWN<-function( a, j, dt) 1 / 6 + ((j ^ 2 * Mfactor(a, dt) ^ 2 - j * Mfactor(a, dt)) / 2)          #######  Probability X going down
TOPProbUP<- function( a, j, dt) 7 / 6 + (j ^ 2 * Mfactor(a, dt) ^ 2 + 3 * j * Mfactor(a, dt)) / 2     ####### Top branch probability going up
TOPProbMID<- function(a, j, dt) -1 / 3 - j ^ 2 * Mfactor(a, dt) ^ 2 - 2 * j * Mfactor(a, dt)          ####### Top branch probability going MID
TOPProbDWN<- function( a, j, dt) 1 / 6 + (j ^ 2 * Mfactor(a, dt) ^ 2 + j * Mfactor(a, dt)) / 2        ####### Top branch probability going DOWN
BTTMProbUP<- function( a, j, dt) 1 / 6 + (j ^ 2 * Mfactor(a, dt) ^ 2 - j * Mfactor(a, dt)) / 2        ####### Bottom branch probability going u
BTTMProbMID<- function( a, j, dt) -1 / 3 - j ^ 2 * Mfactor(a, dt) ^ 2 + 2 * j * Mfactor(a, dt)        ####### Bottom branch probability going MID
BTTMProbDWN<- function( a, j, dt) 7 / 6 + (j ^ 2 * Mfactor(a, dt) ^ 2 - 3 * j * Mfactor(a, dt)) / 2   ####### Bottom branch probability going DOWN

if (N>jmax) N=jmax

for (j in 0:N) {
if (j==0) {
prb["0","1"] <<- ProbUP(a,j,dt)
prb["0","0"] <<- ProbMID(a,j,dt)
prb["0","-1"] <<- ProbDWN(a,j,dt)
}
else {
if (j==jmax) {
prb[paste(j,sep = ""),"1"] <<- TOPProbUP(a,j,dt)
prb[paste(j,sep = ""),"0"] <<- TOPProbMID(a,j,dt)
prb[paste(j,sep = ""),"-1"] <<- TOPProbDWN(a,j,dt)
prb[paste(-j,sep = ""),"1"] <<- BTTMProbUP(a,-j,dt)
prb[paste(-j,sep = ""),"0"] <<- BTTMProbMID(a,-j,dt)
prb[paste(-j,sep = ""),"-1"] <<- BTTMProbDWN(a,-j,dt)
}
else {
prb[paste(j,sep = ""),"1"] <<- ProbUP(a,j,dt)
prb[paste(j,sep = ""),"0"] <<- ProbMID(a,j,dt)
prb[paste(j,sep = ""),"-1"] <<- ProbDWN(a,j,dt)
prb[paste(-j,sep = ""),"1"] <<- ProbUP(a,-j,dt)
prb[paste(-j,sep = ""),"0"] <<- ProbMID(a,-j,dt)
prb[paste(-j,sep = ""),"-1"] <<- ProbDWN(a,-j,dt)
} # Close 2nd IF
} # Close 1st IF
} #end for
}

-----Original Message-----
From: PIKAL Petr [mailto:petr.pikal at precheza.cz]
Sent: 02 November 2017 15:56
To: Eric Pueyo; r-help at r-project.org
Subject: RE: [R] repeat a function

Hi Eric

I did not see any answer and frankly speaking I cannot provide you with canned help.

AFAIK if a function is defined within another function (which is your case) it cannot be called directly so it is necessary to define it in global environment.

>  fff <- function(x) {
+  myf <- function(a) a+2
+  myf(x)^2}
>
> fff(5)
[1] 49
> myf(5)
Error in myf(5) : could not find function "myf"
>

Your function set is quite complicated but I wonder why would it be necessary to use for cycle for what seems to be simple table. Everything seems quite deterministic.

Basically you have combination of rows (-2,-1,0,1,2) and columns -1,-,1.
expand.grid(u=-2:2, v=-1:1)
for each row you can than use one function with parameters u, v and a and dt.
After you calculate vector of results, you can easily transform it to matrix by setting dim argument to it.

Cheers
Petr

> -----Original Message-----
> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of
> Eric.Pueyo at avivainvestors.com
> Sent: Wednesday, November 1, 2017 1:31 PM
> To: r-help at r-project.org
> Subject: [R] repeat a function
>
> I want to populate the matrix prb through the function HWMProb <-
> function
> (a,j,dt) that encapsulates different functions (please see code
> below), using j=
> 0:2 for each j.
>
> It only populates prb if I specify each function independently in the
> global environment and then run the loop with the iF statement, as per below.
> for (j in 0:2) {
>   if (j==0) {
>     prb["0","1"] <- ProbUP(a,j,dt)
>     prb["0","0"] <- ProbMID(a,j,dt)
>     prb["0","-1"] <- ProbDWN(a,j,dt)
>   }
>   else {
>     if (j==jmax) {
>       prb[paste(j,sep = ""),"1"] <- TOPProbUP(a,j,dt)
>       prb[paste(j,sep = ""),"0"] <- TOPProbMID(a,j,dt)
>       prb[paste(j,sep = ""),"-1"] <- TOPProbDWN(a,j,dt)
>       prb[paste(-j,sep = ""),"1"] <- BTTMProbUP(a,-j,dt)
>       prb[paste(-j,sep = ""),"0"] <- BTTMProbMID(a,-j,dt)
>       prb[paste(-j,sep = ""),"-1"] <- BTTMProbDWN(a,-j,dt)
>     }
>     else {
>       prb[paste(j,sep = ""),"1"] <- ProbUP(a,j,dt)
>       prb[paste(j,sep = ""),"0"] <- ProbMID(a,j,dt)
>       prb[paste(j,sep = ""),"-1"] <- ProbDWN(a,j,dt)
>       prb[paste(-j,sep = ""),"1"] <- ProbUP(a,-j,dt)
>       prb[paste(-j,sep = ""),"0"] <- ProbMID(a,-j,dt)
>       prb[paste(-j,sep = ""),"-1"] <- ProbDWN(a,-j,dt)
>     } # Close 2nd IF
>   } # Close 1st IF
> }
>
> Many thanks in advance.
> Kind regards,
>
> Eric Pueyo
> Investment Risk Analyst
> Email:
> Eric.Pueyo at avivainvestors.com<mailto:Eric.Pueyo at avivainvestors.com>
> D: +44 (0)20 7809 8070
> No. 1 Undershaft, London EC3P 3DQ
> Web:
> www.avivainvestors.com<https://urldefense.proofpoint.com/v2/url?u=http
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> 34SVFvqwmZvbxD0ShuYglbuijP84lygitjFgiP1fxI&m=kRg3I7ESFxV-
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> BCpgebe5AL9A_GC8&e=>
>
> jmax<-2
> prb <-matrix(0L,nrow=5, ncol=3)
> rownames(prb) <- c(seq(-2,2, by = 1))
> colnames(prb) <- c(-1,0,1)
> a<- 0.1
> dt<-1
>
> ExpX <-function(x,a,dt) {                              ######Defines the Expectation of X
> on t+1 | t
> ExpX <- x*exp(-a*dt)
> ExpX
> }
> Mfactor<-function(a,dt)  {                           #######Factor multiplicative
>   Mfactor<- exp(-a*dt)-1
>   Mfactor
> }
> VarX <-function(sigma,a,dt) {                         #######Defubes the Variance of X
> on t+1 | t
>   VarX <- (sigma^2/(2*a))*(1-exp(-2*a*dt))
>   VarX
> }
> DeltaX <-function(sigma,a,dt) {                       ######Defines the change of X
>   DeltaX<- sqrt(3*VarX(sigma,a,dt))
>   DeltaX<-value(DeltaX)
> }
>
> Mfactor<-function(a,dt)  {                           #######Factor multiplicative
>   Mfactor<- exp(-a*dt)-1
>   Mfactor
> }
>
> KNode<-function(sigma,x,a,j,dt) {                    ######Central Node
>   KNode<- round(ExpX(x,a,dt)/DeltaX(sigma,a,dt))
>   KNode
> }
>
> ####### Probability Calculations taking into account different
> branches HWMProb <- function (a,j,dt) {
>   ######################### DESCRIPTION
> #####################################
>   ProbUP<- function( a, j, dt) 1 / 6 + ((j ^ 2 * Mfactor(a, dt) ^ 2 + j * Mfactor(a,
> dt)) / 2)                     ######### Probability X going up
>   ProbMID<- function(a, j, dt) 2 / 3 - (j ^ 2 * Mfactor(a, dt) ^ 2)
> ######## Probability X going middle
>   ProbDWN<-function( a, j, dt) 1 / 6 + ((j ^ 2 * Mfactor(a, dt) ^ 2 - j * Mfactor(a,
> dt)) / 2)                  #######  Probability X going down
>   TOPProbUP<- function( a, j, dt) 7 / 6 + (j ^ 2 * Mfactor(a, dt) ^ 2 + 3 * j *
> Mfactor(a, dt)) / 2                 ####### Top branch probability going up
>   TOPProbMID<- function(a, j, dt) -1 / 3 - j ^ 2 * Mfactor(a, dt) ^ 2 - 2 * j *
> Mfactor(a, dt)              ####### Top branch probability going MID
>   TOPProbDWN<- function( a, j, dt) 1 / 6 + (j ^ 2 * Mfactor(a, dt) ^ 2 + j *
> Mfactor(a, dt)) / 2               ####### Top branch probability going DOWN
>   BTTMProbUP<- function( a, j, dt) 1 / 6 + (j ^ 2 * Mfactor(a, dt) ^ 2 - j *
> Mfactor(a, dt)) / 2           ####### Bottom branch probability going u
>   BTTMProbMID<- function( a, j, dt) -1 / 3 - j ^ 2 * Mfactor(a, dt) ^ 2 + 2 * j *
> Mfactor(a, dt)               ####### Bottom branch probability going MID
>   BTTMProbDWN<- function( a, j, dt) 7 / 6 + (j ^ 2 * Mfactor(a, dt) ^ 2 - 3 * j *
> Mfactor(a, dt)) / 2              ####### Bottom branch probability going DOWN
>
>   if (j==0) {
>     prb["0","1"] <- ProbUP(a,j,dt)
>     prb["0","0"] <- ProbMID(a,j,dt)
>     prb["0","-1"] <- ProbDWN(a,j,dt)
>   }
>   else {
>     if (j==jmax) {
>       prb[paste(j,sep = ""),"1"] <- TOPProbUP(a,j,dt)
>       prb[paste(j,sep = ""),"0"] <- TOPProbMID(a,j,dt)
>       prb[paste(j,sep = ""),"-1"] <- TOPProbDWN(a,j,dt)
>       prb[paste(-j,sep = ""),"1"] <- BTTMProbUP(a,-j,dt)
>       prb[paste(-j,sep = ""),"0"] <- BTTMProbMID(a,-j,dt)
>       prb[paste(-j,sep = ""),"-1"] <- BTTMProbDWN(a,-j,dt)
>     }
>     else {
>       prb[paste(j,sep = ""),"1"] <- ProbUP(a,j,dt)
>       prb[paste(j,sep = ""),"0"] <- ProbMID(a,j,dt)
>       prb[paste(j,sep = ""),"-1"] <- ProbDWN(a,j,dt)
>       prb[paste(-j,sep = ""),"1"] <- ProbUP(a,-j,dt)
>      prb[paste(-j,sep = ""),"0"] <- ProbMID(a,-j,dt)
>       prb[paste(-j,sep = ""),"-1"] <- ProbDWN(a,-j,dt)
>     } # Close 2nd IF
>   } # Close 1st IF
> } #Close Formula
>
> for (j in 0:2) {
>   HWMProb(a,j,dt)
>
> }
>
>
>       [[alternative HTML version deleted]]
>
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