产生虚拟的股票期权价格变动 [英] Generate a fictitious stock option price variation

问题描述

我做什么

我正在制作虚拟股票期权图. 使用此功能

I am making graph of fictitious stock options. The price is updated each second, with this function

function stockVariation($price,$max_up,$max_down)
{
    // Price > 1
    if($price > 1)
    {
        // Calculate
        $ratio=(mt_rand(0,$max_up/2)-mt_rand(0,$max_down/2))/1000;
        $price+=$ratio;
    }
    // Price <=1 (we don't want 0 or negative price...)
    else
    $price+=mt_rand(1,$max_up)/1000;

    return round($price,3);
}

我使用max_up和max_down值(从10到100)使价格逐渐变化并模拟一些波动性.

I use a max_up and max_down values (from 10 to 100) to make the price change progressively and simulate some volatility.

例如，对于max_up:40和max_down:45，价格将逐渐下降.

For example, with max_up : 40 and max_down : 45, the price will progressively go down.

我的问题

但是问题是，即使max_up = max_down，产生的价格也会波动太大. 结果是非自然的". (例如，以15,000的基本价格在一天中获得+10积分).

But the problem, is that prices generated are too much volatile, even if max_up = max_down. The result is "non-natural". (for example +10 points in one day for a base price of 15,000).

24小时内每小时价格演变的结果

Result of price evolution per hour in 24 hour

也许进行舍入($ price，4)并除以10000而不是1000会更好吗?

Perhaps making round($price,4) and divisions by 10 000 instead of 1 000, will be better ?

如果有人对产生自然的"价格变化有想法或建议，请先感谢.

If anyone have an idea or an advice to generate "natural" prices evolution, thanks in advance.

推荐答案

一天中有86400秒，因此您需要除以更大的数字.而且，您可能希望将当前价格乘以一个略大于或小于1的因子，而不是相加或相减.这将模拟一个百分比的增加或减少，而不是绝对的收益或损失.

There are 86400 seconds in a day, so you'll need to divide by a much larger number. And rather than adding and subtracting, you may want to multiply the current price by a factor that's slightly larger or smaller than 1. That would simulate a percentage increase or decrease, rather than an absolute gain or loss.

function stockVariation($price, $max_up, $max_down)
{
  // Convert up/down to fractions of the current price.
  // These will be very small positive numbers.
  $random_up = mt_rand(0, $max_up) / $price;
  $random_down = mt_rand(0, $max_down) / $price;

  // Increase the price based on $max_up and decrease based on $max_down.
  // This calculates the daily change that would result, which is slightly
  // larger or smaller than 1.
  $daily_change = (1 + $random_up) / (1 + $random_down);

  // Since we're calling this function every second, we need to convert
  // from change-per-day to change-per-second.  This will make only a
  // tiny change to $price.
  $price = $price * $daily_change / 86400;

  return round($price, 3);
}

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