We propose a general class of models for the simultaneous treatment of equity, corporate bonds, government bonds and derivatives. The noise is generated by a general affine Markov process. The framework allows for stochastic volatility, jumps, the possibility of default and correlations between different assets. We extend the notion of a discounted moment generation function of the log stock price to the case where the underlying can default and show how to calculate it in terms of a coupled system of generalized Riccati equations. This yields an efficient method to compute prices of power payoffs and Fourier transforms . European calls and puts as well as binaries and asset-or-nothing options can then be priced with the fast Fourier transform methods of Carr and Madan (1999) and Lee (2005). Other European payoffs can be approximated by a linear combination of  power payoffs and vanilla options. We show the results to be superior to using only  power payoffs or  vanilla options. We also give conditions for our models to be complete if enough financial instruments are liquidly tradable and study dynamic hedging strategies. As an example we discuss a Heston-type stochastic volatility model with possibility of default and stochastic interest rates.
We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the possibility of default and correlation between different assets. We show how to calculate discounted complex moments by solving a coupled system of generalized Riccati equations. This yields an efficient method to compute prices of power payoffs . European calls and puts as well as binaries and asset-or-nothing options can be priced with the fast Fourier transform methods of Carr and Madan (1999) and Lee (2005). Other European payoffs can be approximated with a linear combination of government bonds, power payoffs and vanilla options. We show the results to be superior to using only government bonds and power payoffs or government bonds and vanilla options. We also give conditions for European continent claims in our framework to be replicable if enough financial instruments are liquidly tradable and study dynamic hedging strategies. As an example we discuss a Heston-type stochastic volatility model with possibility of default and stochastic interest rates.
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class of models
framework
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treatment
modeling
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corporate bonds, government
government bonds, corporate
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The noise
Uncertainty
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framework
setting
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correlations
correlation
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extend the notion of a discounted moment generation function of the log stock price to the case where the underlying can default and
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it in terms of
discounted complex moments by solving
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and Fourier transforms
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then
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by
with
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government bonds,
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government bonds and
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government bonds and
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our models to be complete
European continent claims in our framework to be replicable