我有一個函式可以計算此處找到的看漲期權或看跌期權的二項式樹。我將它們全部設為一個函式，其中包含鏈接中描述的所有其他函式，例如：
Binomial_Call = function(S0, K, r, Ti, sigma,N) {
delta_t=Ti/N
q_prob = function(r, delta_t, sigma) {
u = exp(sigma*sqrt(delta_t))
d = exp(-sigma*sqrt(delta_t))
return((exp(r*delta_t) - d)/(u-d))
}
q = q_prob(r=r, delta_t=delta_t, sigma=sigma)
build_stock_tree = function(S0, sigma, delta_t, N) {
tree = matrix(0, nrow=N 1, ncol=N 1)
U = exp(sigma*sqrt(delta_t))
D = exp(-sigma*sqrt(delta_t))
for (i in 1:(N 1)) {
for (j in 1:i) {
tree[i, j] = S0 * U^(j-1) * D^((i-1)-(j-1))
} }
return(tree)
}
tree = build_stock_tree(S0=S0, sigma=sigma, delta_t=delta_t, N=N)
value_binomial_option = function(tree, sigma, delta_t, r, K) {
q_prob = function(r, delta_t, sigma) {
u = exp(sigma*sqrt(delta_t))
d = exp(-sigma*sqrt(delta_t))
return((exp(r*delta_t) - d)/(u-d))
}
q = q_prob(r, delta_t, sigma)
option_tree = matrix(0, nrow=nrow(tree), ncol=ncol(tree))
option_tree[nrow(option_tree),] = pmax(tree[nrow(tree),] - K, 0)
for (i in (nrow(tree)-1):1) {
for(j in 1:i) {
option_tree[i,j]=((1-q)*option_tree[i 1,j] q*option_tree[i 1,j 1])/exp(r*delta_t)
}
}
return(option_tree)
}
option = value_binomial_option(tree, sigma=sigma, delta_t=Ti/N, r=r, K=K)
#return(list(q=q, stock=tree, option=option, price=option[1,1]))
price=option[1,1]
print(price)
}
現在我有一個資料框：
stock = rep(42,4)
strike = rep(40,4)
risk = rep(0.1)
time = rep(0.25)
sigma = rep(0.2)
N = rep(60,4)
option = c(rep(c("C","P"),2))
Asset = c(rep("FTSE",2),"FACEBOOK","TWITTER")
data = tibble(stock,strike,risk,time,sigma,N,option,Asset);data
A tibble: 4 × 8
stock strike risk time sigma N option Asset
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr>
1 42 40 0.1 0.25 0.2 60 C FTSE
2 42 40 0.1 0.25 0.2 60 P FTSE
3 42 40 0.1 0.25 0.2 60 C FACEBOOK
4 42 40 0.1 0.25 0.2 60 P TWITTER
當我嘗試在 mutate 中實作該功能時：
data%>%
mutate(price = case_when(Asset != "FTSE" & option == "C" ~ Binomial_Call(stock,strike,risk,time,sigma,N)))
我收到以下錯誤：
錯誤mutate()：
! Problem while computing `price = case_when(...)`.
Caused by error in `tree[i, j] <- S0 * U^(j - 1) * D^((i - 1) - (j - 1))`:
! number of items to replace is not a multiple of replacement length
Run `rlang::last_error()` to see where the error occurred.
Warning message:
Problem while computing `price = case_when(...)`.
? numerical expression has 4 elements: only the first used
為什么 ？為什么會這樣？
uj5u.com熱心網友回復：
該函式似乎未矢量化。所以我們可以使用rowwise
library(dplyr)
data %>%
rowwise %>%
mutate(price = case_when(Asset != "FTSE" & option == "C" ~
Binomial_Call(stock,strike,risk,time,sigma,N))) %>%
ungroup
# A tibble: 4 × 9
stock strike risk time sigma N option Asset price
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr> <dbl>
1 42 40 0.1 0.25 0.2 60 C FTSE NA
2 42 40 0.1 0.25 0.2 60 P FTSE NA
3 42 40 0.1 0.25 0.2 60 C FACEBOOK 3.53
4 42 40 0.1 0.25 0.2 60 P TWITTER NA
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