[R-SIG-Finance] Option valuation for arbitrary distribution using monte carlo simulation

[msalese]

Hi Joachim , I'm not a prof but I recommend you the following book: 
Option Pricing and Estimation of Financial Models with R
Stafano M. Iacus
http://www.amazon.com/Option-Pricing-Estimation-Financial-Models/dp/0470745843/ref=sr_1_48?ie=UTF8&qid=1321974343&sr=8-48

it'll explain a lot of thinks with code samples.
Some very base simple code, I started with this one and while was reading
the book I started to improve it 

#define functions
require(package='fBasics',quietly=FALSE)

#This function to create innovation
#We keep innovation function autside of process because 
#once computed leave it stored for next usage
innovation.norm<-function(pTrials=5000){
  # remember to add the seed
  #generate standard normal innovation
  z <- rnorm(n=pTrials,mean=0,sd=1)
  #genereta anthitetic innovation
  ant.z <--z
  #combine in the new one:
  z <- c(z,ant.z)
  #return innovation vector
  return(z)
}

#this function to create the price distribution
st.proc.norm<-function(pInnVect=z,mu=0,pSnow=15,pVol=0.15,pTradDaysToExp=20){
  #set the number of trading days in one year
  yearTradDays<-252
  #compute the interval time 
  dt<-pTradDaysToExp/yearTradDays
  s.final <- rep(0,length(pInnVect))
  s.final<-pSnow*exp(pVol*sqrt(dt)*pInnVect)
  out<-c(s.final,pSnow)
  return(s.final)
}

#this function to build the option chain
price.chain<-function(pSFinal,pIntRate=0.02,pStrikeMin=10,pStrikeMax=15,pDStrike=0.5,pCalDaysToExp=30){
  #build strike chain
  K<-seq(from=pStrikeMin,to=pStrikeMax,by=pDStrike)
  #compute dicount factor
  calDays<-365
  dt<-pCalDaysToExp/calDays
  #prepare storage for chain
  prCall<-rep(x=0,length(K))
  prPut<-rep(x=0,length(K))
  se.call<-rep(x=0,length(K))
  se.put<-rep(x=0,length(K))
  
  for (i in (1:length(K))){
    #print(i)
    #print(K[i])
    #formula for pricing
    c<- ifelse(pSFinal>K[i],exp(-pIntRate*dt)*(pSFinal-K[i]), 0)
    p<- ifelse(pSFinal<K[i],exp(-pIntRate*dt)*(K[i]-pSFinal), 0)
    #price as average
    prCall[i]<-mean(c)
    prPut[i]<-mean(p)
    #standard error
    se.call[i]<-sd(c)/sqrt(length(pSFinal))
    se.put[i]<-sd(p)/sqrt(length(pSFinal))
    
    ## make a confidence interval estimate
    alpha<-0.05
    t.star<-qt(p=(1-alpha/2),df=length(pSFinal)-1,lower.tail=TRUE)
    prCall[i]+c(-1,1)*t.star*se.call[i]
    prPut[i]+c(-1,1)*t.star*se.put[i]
  }
  
  #build the data frame for option's chain
 
pr.chain<-data.frame(CALL=round(prCall,digits=3),Strike=K,PUT=round(prPut,digits=3))
  
  return(pr.chain)
}


##################################################################################
##  PRICING WITH NORMAL
inn.n<-innovation.norm(pTrials=500)
hist(inn.n)
#you must estimate volatility from past data
s.final.n<-st.proc.norm(pInnVect=inn.n,pSnow=13.40,pVol=0.25,pTradDaysToExp=20)
hist(s.final.n)
#you must estimate interest rate
price.chain(pSFinal=s.final.n,pIntRate=0.02,pStrikeMin=10,pStrikeMax=15,pDStrike=0.5,pCalDaysToExp=20)




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