Total rookie question....

There is no formula for implied volatility. You have to solve for it numerically.

 

what do you mean by that?

 

i mean, given the stock price, strike price, call price, interest rate... etc there should be a way to derive it using the black-scholes formula, correct?

Thanks,

The New Guy

 

Here is an intro / overview ...
http://www.crbtrader.com/support/options.asp

There is more to it .. basically pick up any good options book and it will be discussed .....

 

very cool, thanks.

I'll start on this, and if anyone else has any links they feel would help i'd greatly appreciate it.

Thanks,

The New Guy

 

Yes, you can reverse the Black-Scholes or any other option pricing model to solve for Implied Volatility. I wouldn't recommend doing that by hand though. Any decent option calculator should be able to do that for you.

 

Use code keyword so that it looks formatted, like this:

Code:

public class OptionMath
	{
		const double AnualTradingDays = 260.0;

		public static double[] HistoricalVolitilitySeries(double[] prices, int period)
		{
			Debug.Assert(prices.Length-1 >= period);

			double[] v = new double[prices.Length-period];

			for (int j=0,i=1; j < v.Length; j++,i++)
			{
				v[j] = HistoricalVolitility(prices, i, period);
			}

			return v;
		}

		public static double HistoricalVolitility(double[] prices, int index, int period)
		{
			double[] P = prices;
			double[] X = new double[period];

			double mean = 0;

			// get the logarithms of the daily price ratio
			for (int j = 0, i=index; j < period; j++,i++)
			{
				X[j] = Math.Log(P[i]/P[i-1]);

				mean += X[j];
			}

			// compute the mean of the logarithms of the price changes
			mean /= period;

			// compute the deviations from the mean
			double sum = 0;
			for (int k = 0; k < period; k++)
			{
				double d = (X[k] - mean);

				sum += d*d;
			}

            // standard deviation of the daily volatilities over the period
			double v = Math.Sqrt(sum/(period-1));

            // scale to an annualized value for use in the BS equation
			double annualVolatility = v*Math.Sqrt(AnualTradingDays);

			return annualVolatility;
		}
	}

nitro

 

You can take a look on this site : http://www.ivolatility.com

 

That's an interesting point. I have found EWMA to be useful and produce noticably better results than a simple moving average in some backtests, but I can't really justify it theoretically.

Yeah, more or less. I think the basic idea is that you can always get more information about volatility by looking at a shorter timescale. The more information you have the faster your estimate will converge, resulting in a more responsive estimator. However intraday data is difficult to work with, and less widely available than end of day data. Open-high-low-close bars provides some information about intra-period volatility and results in a slightly faster estimator than open-close bars.

You can find a lot of good stuff through scholar.google.com.

Martin

 

Thanks for all the replies!

In regards to the HV, I've noticed two different approaches, in excel.

ln(today's close/yesterday's close) equals something marginally different than (today's close/yesterday's close - 1) in excel.

Does anyone know which is more accurate?

Thanks,

The New Guy