# Is a linear hedge sufficient for most purposes?

I was in a lecture of Bruno Dupire's when he said something along the lines of a linear hedge being sufficient for most purposes. He gave a counter example as well: a corporation producing something and multiple currencies, but it went over my head at the time. (I wish I had taken notes)

So my question is: is it true that a linear hedge is sufficient for most clients, ie. there is no inherent need for derivatives (except futures/swaps)? If so, where can I read more about this and see a possible counter example?

• could you provide a definition for linear hedge ? – MJ73550 Aug 8 '16 at 15:51

There are many times when a linear hedge is sufficient, and indeed the Black/Scholes option pricing theory shows that a linear hedge can even hedge a highly non-linear payoff.

However it's not hard to think of many situations where a linear hedge would not be sufficient eg:

• company has high sensitivity to one-off event, market might not be open or liquid for hedge rebalancing
• multinational company attempts to hedge currency positions but as rates of exchange change so do sales (2nd order effects)
• any correlation between the price of the hedging instrument and another material variable

If it's a linear risk or if the hedge can be rebalanced at any interval then probably linear hedges are sufficient, and to first approximation given the many uncertainties in the economy and business this might well be a good assumption.

• Thanks, it's good to know that my memory serves me well. Do you know a source where I could read through examples like this? – user357269 Aug 6 '16 at 11:41
• I'm sorry I don't really have a source for this - I'm just quoting from my own experiences and/or understanding. The Black/Scholes assumption will be in any derivation. – GodLovesATrier Aug 8 '16 at 10:01

When you talking about linear hedge you are talking about flattening the Delta on the Option. However, all greeks are local, as the underlying travels a long way away, your greeks will change too. Therefore, in a scenario where the underlying suddenly gaps up or down by a long way, your local linear hedge will have too little or too much effect. All optionalities of an Option are local phenomenons. A real world example would the EURCHF event in early 2015.