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An Introduction to Options Trading by Frans de Weert

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Appendix B
VARIANCE OF A COMPOSITE OPTION
It is very easy to prove that the variance of a composite option is equal to:
(B.2)
127
One just has to compare the movement of the underlying in the composite currency with the movement of a geometric basket option composed of the underlying in the local currency and the FX rate. The formula for this basket option is as follows:
128
where
129
and41
130
Since
(B.4)
131
and
(B.5)
133
(B.6)
134
(B.7)
135
the movement of the stock in the composite currency can be modelled according to equation (12.4).

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