Computting implied volatility massively.

implied.vol.R

implied.vol <- function(theo_price, eps=.Machine$double.eps, max.iter=1000) {
    .implied.vol <- function(S, K, Time, r, spot_price, sig=0.2, min.sig=1e-6, max.sig=1) {
        sig <- sig*rep(1, length(S))
        sig.up <- max.sig*rep(1, length(S))
        sig.down <- min.sig*rep(1, length(S))
        iter <- 0
        comp.err <- function(sig) theo_price(S, K, Time, r, sig) - spot_price
        err <- comp.err(sig)
        
        ## repeat until error is sufficiently small or `iter` hits max.iter
        while (all(abs(err) > eps) && iter < max.iter) {
            
            idx.err <- err < 0
            sig.down[idx.err] <- sig[idx.err]
            sig[idx.err] <- (sig.up[idx.err] + sig[idx.err])/2
            idx.err <- !idx.err
            sig.up[idx.err] <- sig[idx.err]
            sig[idx.err] <- (sig.down[idx.err] + sig[idx.err])/2
            
            err <- comp.err(sig)
            iter <- iter + 1
        }
        
        sig
    }
    
    .implied.vol
}

Massive Implied Volatility.md

This code uses R's vectorization features to execute a sort of parallel bisection for computing implied volatility. I used this code to compute implied volatility of a bunch of options (~ 200 thoudands). A loop with uniroot would take several minutes which I reduced to few seconds.

The example below uses GBSOption function from package fOptions.

bs.opt <- function(S, K, T, r, sig) GBSOption('c', S, K, T, r, r, sig)@price

impvol <- implied.vol(bs.opt)

impliedVol <- impvol(UnderlyingPrice, Strike, BusinessDays/252, RiskFreeRate, Premium)