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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Enough for today, look at the example and play around with the code. Furthermore, the effective maturity is reduced.

Fill in the swaption schedules.

Gaussian Models – Fooling around with QuantLib

Remember the maxs and mins from the crossing: The model is set up like this boost:: The inputs to the program are the eective funding leg coupons, 2. You are commenting using your Facebook account. I added these adjusters to the Gsr model. The underlying is now matched much better than in the Gsr model, it is up to basispoints accurate.

Add t, j,months, bdr, exoyic, hol2, hol3, eom Routine for evaluating the European options.

Procedure for Pricing Bermudans and Callable Swaps

Fill in your details below or click an icon to log in: Since we want to match the instrumehts 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. Not unrealistic from a qualitative standpoint, but you would have to be lucky to match the market skew decently of course.


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 std:: The pricing results for the underlying does not change that much, the fit is still good as desired:. Also get the appropriate day count basis, basisind, for the k month index rate. Or read the paper. These define the grid of xnd 8.

To put it differently, per expiry we seek a market underlying that in all states of the world here for all values of the state variable of our model has the same value as the exotic underlying we wish to price. The pricing results for the underlying does not change that much, the fit is still good as desired: Look what the rate is doing.

Use a global Newton chord? For payers, one exchanges the receiveds and paids. Take the maximum of the payo with 0: Asset bedging Credit spread options Documents.


The delta-gamma calibration basket now looks as follows. Routine for generating the integration weights and partial sums detailed below Routine for calculating the payo vector at each j detailed above Routine for calculating the European option values detailed immediately below Standard cumulative normal distributionGaussian density7. Here we allow 2. And we could even go a step further and match e.

In addition a global calibration to all coterminals simultaneously is necessary, the iterative approach will not work for the model. The Gsr model is not able to price the underlying swap correctly, the price is around basispoints higher than in the analytical pricer.

It is not that different from the Gsr model construction. In any case the naive basket looks like this: The swapBase here encodes the conventions for standard market instruments. The last parameter is optional and overwrites some numerical parameter with a more relaxed value, so that the whole thing works a bit faster in our example.