(), where Jamshidian decomposition is used for pricing credit default swap options under a CIR++ (extended Cox-Ingersoll-Ross) stochastic intensity model . Jamshidian Decomposition for Pricing Energy Commodity European Swaptions. Article (PDF Available) · January with Reads. Export this citation. Following Brigo 1 p, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian’s Trick). To do so, the.
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Calibrating time-dependent volatility to swaption prices
For simplicity, for the rest of this post we will assume all payments are annual, so year fractions are ignored. Pricing engines usually have one or more term structures tied to them for pricing. All float coupons with start date greater or equal to the respective option expiry are considered to be part of the exercise into right. Uses the term structure from the hull white model by default. Constructor for the TreeSwaptionEngine, using a time grid.
Pricing engines are the main pricing tools in QuantLib. We have seen in a previous post how to fit initial discount curves to swap rates in a model-independent way. Many alternatives are discussed in the literature to deal with this concern, but the general procedure is the same.
Practically, we should choose the most liquid swaptions and bootstrap to these, and only a few 5Y, 10Y etc will practically be tradable in any case.
With this construction, the necessary tree will not be generated until calculation. What if we want to control the volatility parameter to match vanilla rates derivatives as well?
When several are visible, the challenge becomes to choose a piecewise continuous function to match several of them.
A common choice is the interest rate swaption, which is the right to enter a swap at some future time with fixed payment dates and a strike.
Since these contracts have an exercise date when the swap starts and the swaps themselves will have another termination date jamshisian define a 2-dimensinal spaceit will not be possible to fit all market-observable swaptions with a one factor model.
Calculating these for time-varying parameters is algebra-intensive and I leave it for a later post, but for constant parameters the calculation is described in Brigo and Mercurio pg and gives a price of.
Constructor for the DiscountingSwapEngine that will generate a dummy null yield term structure. We can see how we could use the above to calibrate the volatility parameter to match a single market-observed swaption price. Shifted Lognormal Black-formula swaption engine.
Your email address will not be published. Swaption priced by means of the Black formula, using a Decokposition model. Every asset is associated with a pricing enginewhich is used to calculate NPV and other asset data. These are fairly liquid contracts so present a good choice for our calibration.
This will construct the volatility term structure.
This will generate the necessary lattice from the time grid. All fixed coupons decommposition start date greater or equal to the respective option expiry are considered to be part of the exercise into right. Cash settled swaptions are not supported. For redemption flows an associated start date is considered in the criterion, which is the start date of the regular xcoupon period with same payment date as the redemption flow.
Since rates are gaussian in HWeV this can be done analytically. So, the price of a swaption is an option on receiving a portfolio of coupon decoposition, each of which can be thought of as a dwcomposition bond paid at that time, and the value of the swaption is the positive part of the expected value of these:.
Constructor for the TreeSwaptionEngine, using a number of time steps. Looking at this expression, we see that each term is simply the present value of an option to buy a ZCB at time that expires at one of the payment dates with strike.
Calibrating time-dependent volatility to swaption prices – Quantopia
Callable fixed rate bond Black engine. Our next choice is which vanilla rates options we want to use for the calibration. Each asset type has a variety of different pricing engines, depending on the pricing method.
To see this, consider the price of a swap discussed before:. The engine assumes that the exercise date equals the start date of the passed swap. In HWeV this can be done analytically, but for more general models some sort of jamsbidian would be required. Read the Docs decompoition