Pricing Bermudan Swaptions on the LIBOR Market Model using the Stochastic Grid Bundling Method. Stef Maree∗,. Jacques du Toit†. Abstract. We examine. Abstract. This paper presents a tree construction approach to pricing a Bermudan swaption with an efficient calibration method. The Bermudan swaption is an. The calibration adjusts the model parameters until the match satisfies a threshold of certain accuracy. This method, though, does not take into account the pricing.
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Pricing Bermudan Swaptions with Monte Carlo Simulation – MATLAB & Simulink Example
The automated translation of this page is provided by a general purpose third party translator tool. MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. In this example, the ZeroRates for a zero curve is hard-coded.
The hard-coded data for the zero curve is defined as:. Black’s model is often used to price and quote European exercise interest-rate options, that is, caps, floors and swaptions. In the case of swaptions, Black’s model is used to imply a volatility given the current observed market price.
The following matrix shows the Black implied volatility for a range of swaption exercise dates columns and underlying swap maturities rows. Selecting the instruments to calibrate the model to is one of the tasks in calibration. For Bermudan swaptions, it is typical to calibrate to European swaptions that are co-terminal with the Bermudan swaption swaphion be priced. In this case, all swaptions having an underlying tenor that matures before the maturity of the swaption to be priced are used in the calibration.
Swaption prices are computed using Black’s Model.
The swaption prices are then used to compare the model’s predicted values. To compute the swaption prices using Black’s model:. The Hull-White one-factor model describes the evolution of the short rate and is specified by the following:.
The Hull-White model is calibrated using the function swaptionbyhwwhich constructs a trinomial tree to price the swaptions. Calibration consists of minimizing the difference between the observed market prices computed above using the Black’s implied swaption volatility matrix and the model’s predicted prices.
However, other approaches for example, simulated annealing may be appropriate. Starting parameters and constraints for and are set in the variables x0lband ub ; these prjcing also be varied depending upon the particular calibration approach. The function swaptionbylg2f is used to compute analytic values of the swaption price for model parameters, and consequently can be used to calibrate the model.
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Calibration consists of minimizing the difference between the observed market prices and the model’s predicted prices.
Specifically, the lognormal LMM specifies the following diffusion equation for each forward rate. The choice with the LMM is how to model volatility and correlation and how to estimate the parameters of these models for volatility and correlation. In practice, you may use a combination of historical data for example, observed correlation between forward rates and current market data. For this example, only swaption data is used. Further, many different parameterizations of the volatility and correlation exist.
For this example, two relatively straightforward parameterizations are used. For this example, all of the Phi’s will be taken to be 1. Once the functional forms have been specified, these parameters need to be estimated using market data.
One useful bermuadn, initially developed by Rebonato, is the following, which computes the Black volatility for a European swaption, given an LMM with a set bermuan volatility functions and a correlation matrix. This calculation is done using blackvolbyrebonato to compute analytic values of the swaption price for model parameters, and consequently, is then used to calibrate the model.
Calibration consists of minimizing the difference between the observed implied swaption Black volatilities and the predicted Black volatilities. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend swzption you select: Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location.
All Examples Functions More. Trial Software Product Updates. This is machine translation Translated by. Zero Curve In this example, the ZeroRates priciny a zero curve is hard-coded. The hard-coded data for the zero curve is defined as: Norm of First-order Iteration Func-count f x step optimality 0 3 0.
Norm of First-order Iteration Func-count f x step optimality 0 6 Norm of First-order Iteration Func-count f x step optimality 0 6 0.
Monte Carlo Methods in Financial Engineering. Options, Futures, and Other Derivatives. Select a Web Site Choose a web site to get translated content where available and see local events and offers.