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Risk Neutral Densities for Financial Models

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Risk Neutral Densities for Financial Models

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Risk neutral densities for advanced financial models used for option pricing

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Description

We present methods for calculating the risk neutral density for several financial models. We consider:
Black, Displaced Diffusion, CEV, SABR, Heston, Bates, Hull-White, Heston-Hull-White, VG, NIG, CGMY, VGGOU, VGCIR, NIGCIR, NIGGOU.

For models where no analytic representation of the density is available we either use approximation formulae or methods based on fourier transform.
We study the effects of changing the model parameters. This illustrates the topics from chapters 2 and 3 of the book Financial Modelling - Theory, Implementation and Practice.
We provide scripts for testin each model and plot the densities.

Acknowledgements

Financial Modelling Ch2 Implied Volatility and Cms Spread Caps Stochastic Local Volatility Libor Market Model inspired this file.

This file inspired Cos Method (Multiple Strikes, Bermudan, Greeks) and Modern Pricing Method Using Transforms.

Required Products MATLAB
MATLAB release MATLAB 7.14 (R2012a)
Other requirements We tested the code with Matlab R2008b to R2012a
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