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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Procedure for Pricing Bermudans and Callable Swaps
Asset swaps Credit spread options Documents. He mentions this approach in his paper on callable range accrual notes where he uses his LGM same as Llgm or Hull White model for pricing and observes that he does not calibrate to underlying Libor caplets or floorlets very well.
This is around the same magnitude of the underlying mismatch in the Gsr model. Of course there is a reason that we use a NonstandardSwap instead of a VanillaSwap. Namely evaluatin underlying swap is not atm, but has a fixed rate of.
The reversion speed is as well. The adjuster helper created here corresponds to the CMS coupons of our trade. Here i,c are the appropriate digitals.
First we set the heging evaluation date. The swapBase here encodes the conventions for standard market instruments. Skip to content This is going to be a guided tour through some example code I wrote to illustrate the usage of the Markov Functional and Gsr a.
I added these adjusters to the Gsr model. We can do more involved things and we will below: The underlying price, which can be retrieved as an additional result from the engine as follows.
In the Callable Range Note document we assumed the proxy deal only has 1fixing per period. 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?
Gaussian Models – Fooling around with QuantLib
What you can also see is that payer swaptions were generated. The following picture is from a different case it is taken from the paper I mentioned abovebut showing what is going on in principle. So for each swaption j, we have tofind the same quantities: This is expected however, since the market swaptions are discounted on OIS level, while for the bond we chose to use the 6m curve as a benchmark discounting curve.
A naively calibrated Gsr model yields.
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QuantExt: AnalyticLgmSwaptionEngine Class Reference
Actually there are some handy methods thanks to the fact that we chose an engine which implements the BasketGeneratingEngine interface, so we can just say. Then set re-define the weights by, 8. The NonStandardSwap allows for all this. For the moment it is just empty, so ignored.
Procedure breaks down the method into a specific procedure and set of algorithms. Markov Functional on the other hand evaluatihg any given smile termstructure exactly as long as it is arbitrage free. The inputs to the program are the eective funding leg coupons, 2. Here, the holiday centers, and end-of-month rule are the ones appropriate for fixed legs in the standard swap,and T0 is the first date with 4. You can set this up as a swap, too, with one zero leg and final notional exchange.
Ok, what does the Markov model spit out: In this procedure, we also need quatities which refer to the standard floating leg index such as 3mUS-DLibor and market default parameters for fixed legs opposite anr floating legs in single currency swaps. As you can see the calibrated rate for the market swaption is as expected.
Routine to create integration weights. What do we see here: