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Pardon me for intruding on this exchange -
>Mike, as I understand it, derivatives such as options find their
precise equivalents (or can only be precisely hedged) by other
derivatives, and stock by stock...the derivatives and the stocks are
the different animals...correct me if I have this wrong.
--
The specific statement is wrong, because a derivative by definition derives
its lifetime behavior courtesy the existence of the underlying asset
(stocks, in this discussion) - and in addition to that influence from the
underlying asset, derivatives have a set of properties/behaviors of their
own that the underlying asset may or may not have (eg - "value",
"volatility", "shelf life" etc).
One can find precise equivalents of the derivative in
- another derivative of the same underlying asset. or in
- the underlying asset itself or in
- a combination of both -
as long as the person finding the equivalence understands that the
equivalence exists as a snapshot of that timeframe alone - hence the need
for dynamically taking snapshots and adjusting for the changed equivalents
should the desire be to remain neutral on some/all parameters (price,
capital exposure courtesy changes in "value", the evolving directional bias
etc).
Gitanshu
> Option equivalents, by definition, require total equality with the
original
> position regardless of time, price, or volatility of the
underlying. In
> contrast, dynamic hedges are, of necessity, fleeting approximations
to an
> ever-changing reality, thus needing constant readjustment. For the
latter
> only, delta/gamma calculus is the right tool.
> I would
> simply add that if one wishes to remain fully hedged after buying
> say, 10 ATM options and selling 500 shares of the underlying stock,
> dynamic asset replication is necessary. That would typically be
> conducted by buying or selling amounts of the underlying in reaction
> to changes in the variable relationship you have outlined (the
> results of which can never be perfect).
> > > Von: Robert Hodge [mailto:r-hodge@x...]
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