Question

Suppose that the price of an asset at the close of trading yesterday was $450, and its volatility was estimated as 1. 3% per day. The price at the close of trading today is $446. The proportional change in the price of the asset is Answer

-0. 00088889

Round your calculations to 8 decimal places (e. G. , 0. 00987654)

The volatility estimate using the EWMA model with λ = 0. 94 is

Answer 1

The proportional change in the price of the asset is calculated as follows:

Proportional change = (Price today - Price yesterday) / Price yesterday

Proportional change = ($446 - $450) / $450

Proportional change = -0.00888889

Therefore, the proportional change in the price of the asset is -0.00888889.

The volatility estimate using the EWMA model with λ = 0.94 is calculated as follows:

Volatility estimate = Square root of [λ * (Price today - Price yesterday)^2 + (1 - λ) * (Previous volatility estimate)^2]

Volatility estimate = Square root of [0.94 * ($446 - $450)^2 + (1 - 0.94) * (0.013^2)]

Volatility estimate = Square root of [0.94 * (-4)^2 + 0.06 * 0.013^2]

Volatility estimate = Square root of [0.94 * 16 + 0.06 * 0.000169]

Volatility estimate = Square root of [0.01504]

Volatility estimate = 0.1226 or approximately 0.123

Therefore, the volatility estimate using the EWMA model with λ = 0.94 is approximately 0.123 or 12.3%.