An Introduction to Options Trading

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)

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:

where

and⁴¹

(B.3)

Since

(B.4)

and

(B.5)

(B.6)

(B.7)

the movement of the stock in the composite currency can be modelled according to equation (12.4).