  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.
