[Case Study]Binomial Pricing Trees in R

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1. # Generate a binomial lattice
   
2. # for a given up, down, start value and number of steps
   
3. genlattice <- function(X0=100, u=1.1, d=.75, N=5) {
   
4. X <- c()
   
5. X[1] <- X0
   
6. count <- 2
   
7. 
   
8. for (i in 1:N) {
   
9. for (j in 0:i) {
   
10.   X[count] <- X0 * u^j * d^(i-j)
    
11.   count <- count + 1
    
12. }
    
13. }
    
14. return(X)
    
15. }

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1. genlattice(N=5, u=1.1, d=.9)

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1. function(S, labels=FALSE) {
   
2.     shape <- ifelse(labels == TRUE, "plaintext", "point")
   
3.      
   
4.     cat("digraph G {", "\n", sep="")
   
5.     cat("node[shape=",shape,", samehead, sametail];","\n", sep="")
   
6.     cat("rankdir=LR;","\n")
   
7.      
   
8.     cat("edge[arrowhead=none];","\n")
   
9.      
   
10.     # Create a dot node for each element in the lattice
    
11.     for (i in 1:length(S)) {
    
12.         cat("node", i, "[label=\"", S[i], "\"];", "\n", sep="")
    
13.     }
    
14.      
    
15.     # The number of levels in a binomial lattice of length N
    
16.     # is `$\frac{\sqrt{8N+1}-1}{2}[code]# Generate a binomial lattice
    
17. # for a given up, down, start value and number of steps
    
18. genlattice <- function(X0=100, u=1.1, d=.75, N=5) {
    
19. X <- c()
    
20. X[1] <- X0
    
21. count <- 2
    
22. 
    
23. for (i in 1:N) {
    
24. for (j in 0:i) {
    
25.   X[count] <- X0 * u^j * d^(i-j)
    
26.   count <- count + 1
    
27. }
    
28. }
    
29. return(X)
    
30. }

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1. genlattice(N=5, u=1.1, d=.9)

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1. L <- ((sqrt(8*length(S)+1)-1)/2 - 1)
   
2.      
   
3.     k<-1
   
4.     for (i in 1:L) {
   
5.         tabs <- rep("\t",i-1)
   
6.         j <- i
   
7.         while(j>0) {
   
8.             cat("node",k,"->","node",(k+i),";\n",sep="")
   
9.             cat("node",k,"->","node",(k+i+1),";\n",sep="")
   
10.             k <- k + 1
    
11.             j <- j - 1
    
12.         }
    
13.     }
    
14.      
    
15.     cat("}", sep="")
    
16. }

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Binomial Pricing Trees in R.pdf (608.23 KB)

2015-3-20 08:19:38 上传

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