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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The effect is small however.

The inputs to the program are the eective funding leg coupons, 2. Anyhow, we can do it, so we do it. To make ane numbers a bit nicer I changed the original example code to include a basispoint margin on the Euribor leg. Now consider a callable bond. Published on Oct View Download exoic Markov Functional on the other hand mimics any given smile termstructure exactly as long as it is arbitrage free.

The theory an methodology for using the LGM model to evaluate Bermudans iscovered in: This site uses cookies.

QuantExt: AnalyticLgmSwaptionEngine Class Reference

Get the appropriate business day rule, holiday centers, and end of month rule for the k month ratebeing used as bedging index. The weight vector w0, w1, The pricing of callable preferred stock Documents. This can be used to introduce a flat credit termstructure into the pricing.


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The adjuster helper created here corresponds to the CMS coupons of our trade. Or read the paper.

The exercise has to be extended to carry a rebate payment reflecting the notional reimbursement in case of exercise. I am using the LinearTsrPricer here, with the same mean reversion as for the Gsr model above.

A pricing and performance study on auto-callable structured products Documents. I should note that the calibration method is not the default one defined in CalibratedModelwhich does a global optimization on all instruments, but a serialized version calibrating one step of the sigma function to one instrument at a time, which is much faster.

To preform the adjustment, we also need todays value C0i of each coupon making up the range note,V cpn1Vcpn2Here we make up for a completely wrong model smile.

Also, input are 4. In the appendix, we indicate2. Here we allow 2. First we set the global evaluation date.

London – Patrick Hagan on interest rate modelling for the new era

The calibration basket becomes: A perfect match is not expected from theory, because the dynamics of the linear TSR model is not the same as in the Markov model, of course. Naive ; to get a coterminal basket of at the money swaptions fitting the date schedules of our deal.


The exercise fees are 2. Not unrealistic from a qualitative standpoint, but you would have to be lucky to match the market skew decently of course. What is more interesting is to assume a positive credit spread.

Procedure for Pricing Bermudans and Callable Swaps

For the moment it is just empty, so ignored. This is around the same magnitude of evaluxting underlying mismatch in the Gsr model. He suggests to introduce an adjusting factor to be multiplied with the model volatility in case we are evaluating such a caplet or floorlet during the pricing of the exotic.

Note that the Add function just moves t to a good business day using theappropriate conventions for a k month caplet based on the rate indexStep 2c.