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EVALUATING AND HEDGING EXOTIC SWAP INSTRUMENTS VIA LGM PDF

Bermudans, callable swaps. 1. Introduction. This is part of three related papers: Evaluating and hedging exotic swap instruments via LGM explains the theory. Analytic LGM swaption engine for european exercise. More #include Hagan, Evaluating and hedging exotic swap instruments via LGM. Lichters, Stamm. The evaluation of sensitivities in the Hull White model with respect to changes Evaluating and Hedging Exotic Swap Instruments via LGM.

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You are commenting using your Facebook account. Call characterization routineStep 4. Or read the paper. Namely our underlying swap is not atm, but has a fixed rate of.

I added these adjusters to the Gsr model. Routine for evaluating the European options.

Gaussian Models – Fooling around with QuantLib

Now we consider a bermudan swaption as above, with yearly exercises on this underlying. Anyhow, we can do it, so we do it. To complete the picture, the Markov model also has a volatility function that can be calibrated to a second instrument set like coterminal swaptions to approximate call rights.

Fill in the swaption schedules. Ok, what does the Markov model spit out: So we should use an apdapted basket. He mentions this approach in his paper on callable range accrual notes where he uses his LGM same as Gsr or Hull White model for pricing and observes that he does not calibrate to underlying Libor caplets or floorlets very well.

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Calculate discount factors for each coupon date 2. Call evaluatijg calibration routineStep 5.

Naive ; to get a coterminal basket of at the money swaptions fitting the date schedules of our deal. Since we want to match the market quotes for european calls later on we chose the grid points identical to the exercise dates, except that we do not need a step at the last exercise date obviously.

Procedure for Pricing Bermudans and Callable Swaps

Published on Oct View Download At least it is not flat but a skew. This is because always out of the money options are chosen to be calibration instruments for the usual reason. The todays value V eurj of the jth European option7. Pricing and hedging swaps Extoic.

This is handled by the RebatedExercise extension. We assume that the vi j before today have already been excluded. The rate curves will be flat, but we assume basis spreads to demonstrate that the models can handle them in a decent way.

The initial model volatility is set to std:: The Gsr model is not able to price the underlying swap correctly, the price is around basispoints higher than in the analytical pricer. MaturityStrikeByDeltaGamma ; with the parameter MaturityStrikeByDeltaGamma indicating that the market swaptions for calibration are chosen from the set of all possible market swaptions defined by the swapBaseremember?

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The npv hdeging the option is basispoints. To make the numbers a bit nicer I changed the original example code hedginf include a basispoint margin on the Euribor leg. Here is the result of the calibration.

The reversion speed is as well. In addition a global calibration to all coterminals simultaneously is necessary, the iterative approach will not work for the model. This can be a little thing like five instead of two notification dates for a call, different day count conventions on the legs, a non-yearly fixed leg payment frequency, or bigger things like a different Euribor index, an amortizing notional schedule and so on.

In the appendix, we indicate2. The model is set up like this boost::