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SG

Market risk management - Gamma limits

January 29th, 2002, 3:07 pm

We use to have gamma limits to control our FX options desk but these have since been removed. In it's place, we have introduced what our market risk guys called "event risk" test which essentially involving shifting the spot by say + and - 5% (depending on currency). We dealt in both plain vanilla options as well as barriers. Can anyone tell me whether the "event risk" thingie at least achieve the same control objective as that of the gamma limits? if not, why?
 
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Paul
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Market risk management - Gamma limits

January 29th, 2002, 3:12 pm

In one sense it will be better because gamma may not be a good measure for moves as large as 5%.

On the other hand, gamma measures other things, such as size of hedging errors and transaction costs, which have nothing to do with your new event methodology.

Ideally you'd look at both measures.

P
 
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Collector
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Market risk management - Gamma limits

January 29th, 2002, 3:37 pm

Most systems only spits out a single gamma number (for each underlying). However gamma itself is moving around quite a bit itself, based on moves in implied vol, and moves in underlying, as times move on,..... So in general, as Paul indicates, gamma is only a good risk measure for smaller moves.
If you on the other hand generate a gamma surface (in 3 or more dimensions) or something like that, and then put limits on the whole surface (I guess on negative walleyes) it makes more sense, this is basically combining gamma (micro move risk) and stress testing (major move risk).

The size of limit should be dependent on market liquidity etc. If easy to go our of your options possibly bigger limits etc?
 
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gammashark
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Market risk management - Gamma limits

January 29th, 2002, 4:25 pm

My recollection of Nassim Taleb's Dynamic Hedging is that it has a lot do with promulgating very hardy methods for dealing with such issues. Perhaps a (re?)read would answer your question, and allow you to query your "market risk guys" about why they have dropped gamma measurement/control.
 
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Aaron
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Joined: July 23rd, 2001, 3:46 pm

Market risk management - Gamma limits

January 31st, 2002, 12:22 am

We use to have gamma limits to control our FX options desk but these have since been removed. In it's place, we have introduced what our market risk guys called "event risk" test which essentially involving shifting the spot by say + and - 5% (depending on currency). We dealt in both plain vanilla options as well as barriers. Can anyone tell me whether the "event risk" thingie at least achieve the same control objective as that of the gamma limits? if not, why? >>

To a second order, the two limits are identical, if properly calibrated. You can set a delta limit either by calculating an analytic delta or by a DV01, setting a limit on the price movement for a 0.01% price or rate movement. Given a delta limit, you can set a gamma limit either by computing an analytical gamma, or setting a limit on price movement for a larger interval than you use for delta.

One difference, as Paul said, is that your 5% test might capture some higher order risk. It's easy to put together a position that is analytically delta and gamma neutral, that generates a lot of P&L at a 5% spot movement.

Another difference is aggregation. Gamma risk is usually aggregated by assuming some correlation among spot prices. Event risk is usually aggregated by looking at specific past events. Thus event risk gives a better picture of the possibility of catastrophic losses, while gamma gives a more accurate estimate of the day-to-day P&L volatility.

I agree you need both greeks and shifts to get an adequate picture of risk.
 
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doublebarrier1971

Market risk management - Gamma limits

February 1st, 2002, 12:07 am

Hi

surely this 'event' risk (shifting spot by as much as 5%) won't take into account the delta hedging you would be doing while spot is moving to this level.

Generally (having created risk methods) this 'event' risk is someimes called 'disaster' risk. ie. assuming an immediate jump in spot. Usually these types of calculations are used for Capital Adequacy measures.

I would suggest one should measure Gamma (and Theta come to think of it---noone seems to set limits for this)as, FX barriers have both +ve and -ve gamma depending on spot.
 
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Aaron
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Market risk management - Gamma limits

February 1st, 2002, 2:38 pm

You're right that it's hard to get desks to accept theta limits. There is a bias in risk management. The first order bias is that you worry more about sudden price declines than sudden price increases. The second order bias is you worry more about losses from movements that are larger than you expect, than losses from movements that are smaller than you expect. It is the second-order bias than leads people to neglect theta risk. Even the dimmest manager understands when you say "if the spot rate moves 1%, the bank could fail!" But you get blank looks if you say "if the spot rate stays exactly the same, and one day passes, the bank could fail!"
The first order bias has some justification. Liquidity crises are always associated with market declines and, of course, you worry most about large losses or large required rebalancings in illiquid markets. Moreover, correlations go up when prices go down. Even with FX, where there is no natural market "down," there is a difference between crises caused by the weakening of a currency (sudden, severe and contagious) and those caused by the strenghening (slow, milder and noncontagious). The key is whether the news causing the movement is about the weakening or the strengthening currency.
I don't know any reason for the second bias. Financial institutions are as vulnerable to sluggish markets as volatile ones.