Trying to find an error on the implementation of a simple BS formula


Blackscholes_formula <- function(spot,timetomat,strike,r,q=0,sigma,opt_type=1,greek_type=1)
  {
  
  d_1<-(log(spot/k) + (r+ (sigma^2)/2)(timetomat))/sigma*sqrt(T-t)
        
  d_2 <-d_1-((sigma^2)/2)*timetomat) 
  
  if(greek_type == 1) result <- spot*pnorm(d_1)- K exp(-r*timetomat)*pnorm(d_2)
  
  if(greek_type == 2) result <- pnorm(d_1)

  Blackscholes_formula <- result
}

I am starting to program, and due to my field I started with R. However I am struggling to write a piece of code that works. Upon programming the Black-Scholes valuation formula above I get the error message:

Error: unexpected '}' in "}" I have searched on the web for similar errors but despite the fact that the "symptom" is the same, the source of errors are different. I do not know if I am doing a major mistake on the code or what it is the problem.

Question:

I would be grateful if someone could give feed-back on how to improve the aforementioned code.

Thanks in advance!

Solution

A few things. First, I think you are missing an asterisk, but there are other issues.

Your function needs a prompt for K. This variable is also upper and lower case in your function. You also need variables t and t_cap. (We don't use T as a variable because it is reserved for TRUE)
You have a loose K in the first if() statement (how does K interact with exp()?)
I'm not 100% positive, but your asking your function to return itself. I'd just type result.

Here's a function that compiled for me, with all new variables set to 1

Blackscholes_formula <- function(spot,timetomat,strike,r, K = 1, t = 1, t_cap = 1, q=0,sigma = 1,opt_type=1,greek_type=1){
  
  d_1 <- (log(spot/K) + (r+ (sigma^2)/2) * (timetomat))/sigma*sqrt(t_cap-t)

  d_2 <- d_1-((sigma^2)/2)*timetomat
  
if(greek_type == 1) result <- spot*pnorm(d_1)- K*exp(-r*timetomat)*pnorm(d_2)

if(greek_type == 2) result <- pnorm(d_1)

 result
}

Blackscholes_formula(1,2,3,4)