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ClosetChartist
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Joined: July 17th, 2003, 4:41 pm

Hedging with Factor Models

January 18th, 2011, 6:55 pm

I have a multi-factor interest rate model with factors that may be interpretted as Shift-Tilt-Flex. For the sake of argument, we can assume this is the LIBOR Market Model, although it could be anything.Theoretically, I can hedge ANY exposure by dynamically trading a 3mo, 5yr and 30yr bond. But this approach is naive in the extreme. For example, to manage a 7yr cashflow it would make far more sense to trade a {5yr, 10yr} bond pair than it would a {5yr, 30yr}. Can anyone suggest a good reference for selecting dynamic hedge assets in a factor framework?
 
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Gmike2000
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Joined: September 25th, 2003, 9:49 pm

Hedging with Factor Models

January 18th, 2011, 9:41 pm

3m, 5y, and 30yr are not optimal. choose 2y,10y,30y for a portfolio that spans the whole mkt and/or add 5yr if you like.3m only moves when the FED changes interest rates. 2y however, moves with market expectations regarding FED changes.
 
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ClosetChartist
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Joined: July 17th, 2003, 4:41 pm

Hedging with Factor Models

January 19th, 2011, 2:56 pm

Let me phrase my question differently.If I am using a three-factor LMM to value my book, there are two ways I can hedge:(i) I can use a model-independent hedge, such as matching key-rate durations.(ii) I can use a model-based hedge, such as trading 2-10-30 points on the curve.In general, the model-independent approach will be more robust. Even if something odd occurs in the rate structure the hedge will generally perform well. On the other hand, the model-independent approach can result in over-hedging - more trading than you really need. The model-based approach imposes additional structure and limits over-hedging. But if reality contradicts your assumed structure, your hedge breaks downs.Can you provide a practical reference for how one balances and/or integrates these approaches?
 
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spv205
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Hedging with Factor Models

January 20th, 2011, 1:09 pm

Can you explain your application better?I can't see why you wouldn't use the model independent hedge. You presumably have a portfolio of options of different maturities?
 
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ClosetChartist
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Joined: July 17th, 2003, 4:41 pm

Hedging with Factor Models

January 21st, 2011, 1:01 pm

For the sake of discussion, assume I am dynamically replicating a cap/floor contract with a maturity of fifteen years. So I am trying to replicate a series of rate contingent cash flows occurring over fifteen years. (My real situation has considerably more rate-gamma than this example, however.)If I only rely on my factor model, I can theoretically trade any three securities to dynamically hedge: 2-10-30, 5-15-20, 1-2-3, etc. This highly-compact trading is a bad idea because I am completely dependent upon my model assumptions.If I only rely model-independent key rate durations, I might wind up trading all the cannonical tenors 1-2-3-4-5-7-10-15-20-30. This is more trading than I really need and creates expense and "maintenance issues".Where is the middle way?
 
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spv205
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Joined: July 14th, 2002, 3:00 am

Hedging with Factor Models

January 21st, 2011, 11:03 pm

I am still not clear why this is a major expense (within an interest rate options book), but how about getting the risks out in the model -independent way and then finding a hedging portfolio for that. I am not sure how you do it exactly, but seems like a standard portfolio optimisation problem. Ie How do I choose n instruments that minimise the (empirical ) variance.
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