August 28th, 2006, 8:19 pm
My reasoning behind using strike instead of spot: Imagine an asset manager that is long $10m of an index. He wishes to hedge the downside of this completely. If he wants to hedge this at the money, the number of options needed is $10m/spot, so the notional of the hedge is $10m. If however, he wants hedge this, let's say, at the 90-strike, the number of options he needs is $10m/(90_strike). In this case the notional would still be the same if we define notional as number of options * strike, i.e. the notional is $10m. If however, we use the definition notional = number of options * spot, his notional would be greater than $10m, i.e. $10m/(90_strike) * spot > $10m.So, to summarise, the notional to hedge $10m varies with strike if we use the spot definition.With the strike definition it is constant at $10m, so I would have thought the strike definition makes more sense, but that does not seem to be the standard in equity markets.