NuclearPhynance Archive

Hi,



I'm trying to figure out whether there is a good way to optimize gamma hedging frequency in FX market.



Given that the future price action of the underlying spot is unknown, and the p&l of long (or short) gamma position is a function of the hedging frequency, i came up with three strategies to hedge the delta risk:

1. based on time (dt) - every t units of time

2. based on spot change (dS) - every % change of the underlying spot

3. based on delta accumulated -(dD) - offset the entire delta risk once accumulating D units of delta



Each strategy will be optimal in a certain market condition, however, as i cannot predict future spot behavior i'm trying to optimize the strategy and frequency.



Any thoughts?

First you should define what you mean by optimal.

If you mean reduce the noise so that if you had realized vol equal implied you have a flat PL, Dupire and Taleb wrote (among many others) about 2. being much better than 1.

Taleb has a nice discussion of this in in Dynamic hedging.



Unless you have a very weird gamma profile 2. and 3. are likely to give similar results for moderate underlying moves.



But clearly the question is: define optimal



If you mean making the most money, you end up looking if your asset is mean reverting (hedge your gamma very often) or trending (hedge much less often).

I generally think most options MMs think in terms of dD as that's the really what you "want to hedge"



This isn't really "just" a numerical optimization problem -- risk management is likely not going to let you set your dD to 1000000 deltas even if that's what your model tells you. (My model tells me the correct dD is infinity -- but my model maximizes my personal take home pnl)

Thanks for the feedback...



@Baltazar - by optimal i mean the best sharpe ratio, so i'm looking to have the best return/vol ratio. I agree that 2 and 3 are similar, but as the option gets closer to expiry they might produce different results (depends on the distance from strike)



@Radikal - I agree that this is a risk management issue, yet this is part of my optimization process (to maximize pnl with the lowest level of risk).

>> by optimal i mean the best sharpe ratio, so i'm looking to have the best return/vol ratio.



You can check this Optimization of Sharpe Ratio for Delta-Hedging Strategy under Discrete Hedging and Transaction Costs