-0.015-1

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-Gamma1(1m) ---Gamma2(1m) --Gamma3(1m)

-0.015

Mar-98 May-98 Jul-98 Sep-98 Nov-98 Jan-99 Mar-99

-Gamma1(2m) ---Gamma2(2m) --Gamma3(2m)

-0.015

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-Gamma1(3m) - Gamma2(3m) --Gamma3(3m)

Figure 6.9 Gamma estimates for (a) 1-month, (b) 2-month and (c) 3-month volatilities.

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volatility (2 months).

The second principal component also plays a role in movements of the 3-month skew, but it is not as important as it is for the 1-month skew. In Figure 6.9c the estimate of y2 is negative during the springs of 1998 and 1999. Therefore, we may draw the same conclusions as for the 1-month volatilities, that the range in the skew of 3-month volatilities will generally narrow as the index increases and widen as the index falls, with most of the movement coming from the low volatilities. However, during the jumpy period in the summer of 1998 the estimates of y2 and were verv close to zero. Therefore, during the crash period the movements in 3-month volatilities will have been approximately parallel.

To see whether these observations are valid, look at the 3-month fixed strike volatilities shown in Figure 6.11. Some of the very low strikes have unrealistically high volatilities. In fact the 4025 and 4125 strikes have already been removed from the data set because their movements were quite out of line with the rest. The range narrowing and widening in the skew as the index moves up and down is very noticeable in the spring of 1999. And as predicted, most of the movement is coming from the low strikes. The 3-month fixed strike deviations graph in Figure 6.11b gives a somewhat clearer picture of what is happening during the crash period. The parallel shifts that the principal component model predicts are very evident in this picture.

The range narrowing and widening in the skew as the index moves up and down is very noticeable in the spring of 1999

The principal component model of fixed strike deviations has identified two different market regimes. When index moves are negatively correlated with the

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Figure 6.11 Three-month ATM volatility and the FTSE 100 index, (a) Fixed strike volatilities; (b) deviations of fixed strike volatilities from ATM volatility.

second principal component (y2 < 0) the range of the skew will narrow as the index moves up and widen as the index moves down, with most of the movement coming from low strike volatilities and little movement in the high strike volatilities. This regime has been apparent in the FTSE 100 index options during the springs of 1998 and 1999. However, during the 1998 crash the index moves appear to have zero, or even a positive, correlation with the second principal component. In this regime the skew will shift parallel as the index moves (y2 - 0). However, in the short-term volatilities where it seems that y2