I’d like to calculate the implied volatility (IV) of a table t containing an option chain.

The function to calculate the IV is:

// Newton-Raphson method to find implied volatility
impliedVol:{[S;K;T;r;isCall;marketPrice]
 sigma:0.5;  // Initial guess
 tolerance:1e-6;
 i:0;
 diff:1;
 while[abs[diff]>tolerance and i<100;
       result:.deriv.bsm[S;K;r;T;isCall;sigma];
       diff:result[`price]-marketPrice;
       sigma:sigma-diff%result[`vega];
       i+:1;
      ];
 sigma:$[i=100; 0N; sigma]
 };

The above function works OK for scalar inputs, however for using it inside a select statement it fails since it makes the variable diff a list (instead of scalar) presumed by the function. As a workaround I could do:

ivFunc:{[rate;row] impliedVol[row`S; row`K; row[`daysLeft]%365; rate; row`isCall; row`close]};
       t:update IV:100*ivFunc[rate] peach t from t

which despite peach is excrutiatingly slow.

How can i modify impliedVol so that I can write the following and thus expect vectorization to speed things through?

r:0.04;
t:update IV:100 * impliedVol[S;K;daysLeft%365;(count)#r;isCall;close];