Historical volatility from close prices (Haug pg 166)

Question

I have implemented a function for calculating historical volatility using close the close method as described by Haug on page 166.

When I implemented the formula given by Haug, it resulted in some negative values for the variance. The data I am using is not suspect, so the fault must lie in either:

• my implementation or
• the formula itself.

Here is a rough sketch of my implementation function (in Python)

# close_prices is a time sorted list of pricedata objects
# returns a list of calculated volatilities
def calc_volatility(close_prices, period):
    startpos, stoppos, raw_vols = (0, period, [])
    while True:
        subset = close_prices[startpos:stoppos+1]
        period_returns      = [ subset[i].close_price/subset[i-1].close_price for i in range(1,len(subset)) ]
        log_returns         = [ math.log(x) for x in period_returns ]
        log_squared_returns = [ math.log(pow(x,2)) for x in period_returns ]

        sum_squares_1 = sum( log_squared_returns ) / (period-1)
        sum_squares_2 = pow( sum( log_returns ), 2) / (period * (period -1))

        variance = sum_squares_1 - sum_squares_2
        print "ss1: {0} - ss2: {1}. Variance: {2}".format(sum_squares_1, sum_squares_2, variance)

        volatility = math.sqrt(variance)

        raw_vols.append (volatility)

        startpos += period
        stoppos  += period

        if stoppos >= len(close_prices):
            break

    return raw_vols

Is there something wrong in my implementation, or is the formula I am using, incorrect?

Answer 1

I have a different solution, which calculates the vol for a list of prices.

import math

#workout volatility
def perc_change(price_list):
 return [(v / price_list[abs(i-1)])-1 for i, v in enumerate(price_list)]

def variance(price_list):
 perc = perc_change(price_list)
 avg = average(perc)
 return [(x - avg)**2 for x in perc]

def average(x):
 return sum(x)/len(x)


var = variance(list_of_prices)

volatility = math.sqrt(average(var))