VOLATILITY ESTIMATION METHODS

Volatility Estimation Methods

Volatility Estimation Methods

1. Introduction

Since the starting of the present high float, numerous theoretical papers have been published to interpret the consequences of advanced exchange-rate instability on trade, and even more have been released evaluating these concepts empirically. These investigations have applied different procedures and got different outcomes, but no agreement has been reached regarding how to form, or even how to properly assess, exchange-rate volatility (Arize, 2006).

2. Introduction to Volatility Estimation Methods

The procedures of measuring volatility have developed over time to contemplate new advances in econometric techniques.

Discrete Method

The discrete procedure calculates the come back worth. The formula for the come back worth is given by:

, (1)

where is the closing cost for the day and is yesterday's closing cost. There also exists a compound interest, which is calculated daily, a set number of times, which is not continuous.

For the numerical simulation the initial asset cost was set equal to 100. In terms of the model = 100, and is the closing cost for day i. It is assumed that a closing stock cost for 365 consecutive days can be obtained. To produce each of the next 365 asset prices, we use the equation

,(2)

where, is the new asset cost that is being generated from the previous closing stock cost, .,, and are the same as in equation (1). Equation (2) also has as the discrete change in time. In this simulation, there are 365 time augmentations corresponding to the 365 days that the closing cost is obtained from. The discrete change in time is computed by taking 1 year and dividing by the number of time increments.

Continuous Method

The continuous method corresponds to a continuous rate of return, which can be computed via

.(3)

In the study of finance, we see that continuously compounding money is a function of the exponential. Thus, equation (3) corresponds to the continuously compounding rate of return.

In both methods, the volatility was computed via dividing by (n-1) instead of just n. The motive for this comes from statistical analysis. If we divided by n instead of (n-1) we would have a biased approximation. The approximation would be biased to the time of day that the prices are taken from. If the approximation is biased to a certain part of the day, say the closing cost as in our simulation, then the approximation is not a good representative of the true volatility.

Benchmark Method

The popular GARCH(1,1) ...