Newton Raphson方法PHP

Question

尝试使用PHP计算期权的隐含波动率。 BlackScholes函数计算期权的价格，$OptionValue是期​​权的价格，$guess是估算值。

我的尝试基于类似的应用程序，但我的版本超时。通过纸上的循环，我认为对我来说是有道理的。我做错了什么？

function ImpliedVolatility($type, $S, $X, $T, $r, $D, $OptionValue, $guess) {

$x1 = 0.01;         //lower approx
$x2 = $guess * 2;   //upper approx
$epsilon = 0.01;

$ValueGuess = BlackScholes($type, $S, $X, $T, $r, $D, $x2); //Initialize

while ( abs($OptionValue - $ValueGuess ) > $epsilon ) {
    $xMid = ($x1 + $x2)/2;  //new approx
    $F1 =  BlackScholes($type, $S, $X, $T, $r, $D, $x1);
    $FMid =  BlackScholes($type, $S, $X, $T, $r, $D, $xMid);

    if  ($FMid > $F1 ) {
      $x1 = $xMid;
    } else {
      $x2 = $xMid;
    }

    $ValueGuess = BlackScholes($type, $S, $X, $T, $r, $D, $xMid);
}

return $xMid;

}