Therefore, we construct an implied volatility index for the New Zealand market by first computing implied volatility indices for each stock individually and then combining the implied volatilities of the four stock option prices.
Each individual stock's implied volatility index is computed as a weighted-average of the implied volatilities of eight near-the-money options consisting of four first-nearby (shorter than three months time to maturity) and four second-nearby options (longer than three months time to maturity).
The eight component implied volatilities are shown in the following matrix:
To compute the implied volatility index for a single stock, we first average the call and put options' implied volatilities for each pair of options.
1994), we compute the implied volatility for an at-the-money option by linearly interpolating between the implied volatilities of the in-the-money and out-of-money options.
The last step is to create an implied volatility index with a constant time to maturity by combining the first-nearby and second-nearby at-the-money implied volatilities.
From 1990 to 1995, the average correlation between daily returns on the S&P 500 and the daily changes in implied volatilities was -0.
Another feature of implied volatilities that could adversely impact the seller of the straddle if the price of the underlying asset goes up is the so-called skew or smirk in implied volatilities.
As a first exercise, the trader sells the straddles every day (1990-95) without comparing their implied and historical volatilities.
The returns from short positions in the straddles could result from a change in the level of the market or changes in the implied volatilities of the options constituting the straddles.
Short positions in straddles stand to gain mainly from the decrease in implied volatilities over the holding period.
10) Table 4 shows some of the returns generated by selling short-maturity straddles using this decision rule, based on comparisons between implied and historical volatilities.