Question

Yesterday the closing price of a stock was $95, and today’s volatility was estimated as 1.8% per day. If today’s closing price is 92, update the volatility estimate using:

(a) The EWMA model with l = 0.92.

(b) The GARCH (1,1) model with w = 0.000002, a = 0.08, and b = 0.91.

Answer 1

Return on asset = ln(Today's closing price / Yesterday's closing price)

Return on asset = ln($92 / $95)

Return on asset = -3.21%

a)

(Updated Volatility)² = l * (Today's Volatility)²+ (1 - l) * (Return on asset)²

(Updated Volatility)² = 0.92 * (1.8%)² + 0.08 * (-3.21%)²

(Updated Volatility)² = 0.0003805128

Updated Volatility = 0.0003805128

Updated Volatility = 1.95%

b)

(Updated Volatility)² = w + a * (Return on asset)² + b * (Today's Volatility)²

(Updated Volatility)² = 0.000002 + 0.08 * (-3.21%)² + 0.91 * (1.8%)²

(Updated Volatility)² = 0.0003792728

Updated Volatility = 0.0003792728

Updated Volatility = 1.9475% or 1.95%